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data.values

Value Parameter Processing Module for AFCCP

This module manages the construction, manipulation, transformation, and comparison of value parameters for the CadetCareerProblem object. Value parameters define the objectives, weights, and nonlinear utility functions used to evaluate cadet-to-AFSC assignments under Value-Focused Thinking (VFT) and Goal Programming (GP) frameworks.

The functions in this module enable dynamic adjustment of value preferences, conversion between modeling formats, and consistent export or validation of weight/value configurations for modeling, diagnostics, or user inspection.

Main Functionalities

  • Build and scale value functions based on cadet and AFSC preferences
  • Generate AFOCD-based weights and objectives using tiered education alignment
  • Update and regenerate weights and utility functions after changes
  • Condense redundant value function breakpoints for speed and clarity
  • Translate between VFT and Goal Programming formats (e.g., for GP solver compatibility)
  • Export value parameters to Excel for audit and transparency
  • Compare multiple value parameter sets for consistency diagnostics

Key Concepts

  • Value Parameters: Contain objective weights, utility functions, and constraints used in the optimization.
  • Breakpoints: Discrete x/y points used to approximate nonlinear value functions.
  • Objective Types: Tier-based education goals, demographic balancing, quota constraints, cadet merit, etc.
  • Constraint Types: Enforce structural bounds (e.g., minimum quotas, tier alignment).
  • AFOCD Alignment: Relates cadet degrees (via CIP codes) to tiered AFSC requirements.
  • Merit-Based Assignment: Rewards cadet-AFSC matches according to percentile rank.

Available Functions

  • update_value_and_weight_functions — Rebuilds weight/value functions after updates
  • value_function_builder — Generates piecewise exponential approximations of utility functions
  • generate_afocd_value_parameters — Applies AFOCD rules to populate objective targets and constraints
  • model_value_parameters_to_defaults — Exports value parameter set to Excel for auditing
  • compare_value_parameters — Compares two value parameter dictionaries for equivalency
  • condense_value_functions — Removes redundant zeros in piecewise value functions
  • translate_vft_to_gp_parameters — Converts VFT model structure to Goal Programming inputs

value_parameters_sets_additions(parameters, value_parameters, printing=False)

Enhances the value_parameters dictionary by adding derived sets and metadata required for optimization and constraint evaluation in the cadet-AFSC matching problem.

This function precomputes various subset structures (e.g., AFSCs relevant to specific objectives, cadets with utility constraints, constrained objectives, etc.) to avoid unnecessary computation during model solving and value function evaluations.

Parameters

parameters : dict Dictionary of fixed model parameters (cadets, AFSCs, quotas, preferences, etc.). value_parameters : dict Dictionary of value model parameters including objectives, weights, constraints, and utility functions. printing : bool, optional Whether to print diagnostic output during execution. Default is False.

Returns

dict Updated value_parameters dictionary with added sets and utility matrices, including:

  • K : np.ndarray Indices for all objectives

  • K^A[j] : dict[int → np.ndarray] Objectives with non-zero weights for AFSC j

  • K^C[j] : dict[int → np.ndarray] Constrained objectives (non-zero constraint types) for AFSC j

  • J^A[k] : dict[int → np.ndarray] AFSCs that include objective k

  • I^C : np.ndarray Cadets with value constraints (non-zero minimum value)

  • J^Top_Choice[i] : dict[int → np.ndarray] Preferred AFSCs for cadet i that satisfy the cadet's value constraint

  • J^C : np.ndarray AFSCs with value constraints

  • r[j, k] : np.ndarray Number of breakpoints in the value function for AFSC j and objective k

  • L[j][k] : np.ndarray Indices for breakpoints in the value function

  • objective_min, objective_max : np.ndarray Lower and upper bounds on constrained objectives by AFSC

  • global_utility : np.ndarray Combined cadet and AFSC utility used for global utility optimization (if available)

Notes

  • The function corrects legacy constraint types (3 and 4 → 1 and 2 respectively).
  • It supports objectives tied to cadet demographics such as USAFA Proportion, and Tier objectives.
  • The function also scales and rounds weights for numerical stability.
Source code in afccp/data/values.py 
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def value_parameters_sets_additions(parameters, value_parameters, printing=False):
    """
    Enhances the `value_parameters` dictionary by adding derived sets and metadata required
    for optimization and constraint evaluation in the cadet-AFSC matching problem.

    This function precomputes various subset structures (e.g., AFSCs relevant to specific objectives,
    cadets with utility constraints, constrained objectives, etc.) to avoid unnecessary computation
    during model solving and value function evaluations.

    Parameters
    ----------
    parameters : dict
        Dictionary of fixed model parameters (cadets, AFSCs, quotas, preferences, etc.).
    value_parameters : dict
        Dictionary of value model parameters including objectives, weights, constraints, and utility functions.
    printing : bool, optional
        Whether to print diagnostic output during execution. Default is False.

    Returns
    -------
    dict
        Updated `value_parameters` dictionary with added sets and utility matrices, including:

    - `K` : np.ndarray
      Indices for all objectives

    - `K^A[j]` : dict[int → np.ndarray]
      Objectives with non-zero weights for AFSC `j`

    - `K^C[j]` : dict[int → np.ndarray]
      Constrained objectives (non-zero constraint types) for AFSC `j`

    - `J^A[k]` : dict[int → np.ndarray]
      AFSCs that include objective `k`

    - `I^C` : np.ndarray
      Cadets with value constraints (non-zero minimum value)

    - `J^Top_Choice[i]` : dict[int → np.ndarray]
      Preferred AFSCs for cadet `i` that satisfy the cadet's value constraint

    - `J^C` : np.ndarray
      AFSCs with value constraints

    - `r[j, k]` : np.ndarray
      Number of breakpoints in the value function for AFSC `j` and objective `k`

    - `L[j][k]` : np.ndarray
      Indices for breakpoints in the value function

    - `objective_min`, `objective_max` : np.ndarray
      Lower and upper bounds on constrained objectives by AFSC

    - `global_utility` : np.ndarray
      Combined cadet and AFSC utility used for global utility optimization (if available)

    Notes
    -----
    - The function corrects legacy constraint types (3 and 4 → 1 and 2 respectively).
    - It supports objectives tied to cadet demographics such as `USAFA Proportion`, and `Tier` objectives.
    - The function also scales and rounds weights for numerical stability.
    """
    if printing:
        print('Adding AFSC and objective subsets to value parameters...')

    # Shorthand
    p, vp = parameters, value_parameters

    # Temporary manual adjustment of constraint_type matrix
    indices_3 = np.where(vp['constraint_type'] == 3)
    indices_4 = np.where(vp['constraint_type'] == 4)
    vp['constraint_type'][indices_3] = 1
    vp['constraint_type'][indices_4] = 2

    # Set of Objectives
    vp['K'] = np.arange(vp["O"])

    # Set of objectives for each AFSC
    vp['K^A'] = {}  # objectives
    vp['K^C'] = {}  # constrained objectives
    for j in p["J"]:
        vp['K^A'][j] = np.where(vp['objective_weight'][j, :] > 0)[0].astype(int)
        vp['K^C'][j] = np.where(vp['constraint_type'][j, :] > 0)[0].astype(int)

    # 5% of total USAFA graduating class set
    vp["J^USAFA"] = None

    # Add the AFSC indices to the set
    if "USAFA-Constrained AFSCs" in vp:
        if "," in vp["USAFA-Constrained AFSCs"]:
            vp["J^USAFA"] = np.array([])
            usafa_afscs = vp["USAFA-Constrained AFSCs"].split(",")
            for afsc in usafa_afscs:
                afsc = afsc.strip()
                j = np.where(p["afscs"] == afsc)[0]
                if len(j) == 0:
                    print("WARNING: Something is wrong with the USAFA-Constrained AFSCs! "
                          "'" + afsc + "' is not in the list of AFSCs.")
                else:
                    vp["J^USAFA"] = np.hstack((vp["J^USAFA"], j))
            vp["J^USAFA"] = vp["J^USAFA"].astype(int)

    # Set of objectives that seek to balance some cadet demographic
    vp['K^D'] = ['USAFA Proportion', 'Mandatory', 'Desired', 'Permitted', 'Tier 1', 'Tier 2', 'Tier 3', 'Tier 4']

    # Set of AFSCs for each objective:
    vp['J^A'] = {}
    for k in range(vp["O"]):
        vp['J^A'][k] = np.where(vp['objective_weight'][:, k] > 0)[0].astype(int)

    # Cadet Value Constraint Set
    vp['I^C'] = np.where(vp['cadet_value_min'] > 0)[0]

    # Create a set of preferred AFSCs that are constrained for cadets with utility constraints
    vp['J^Top_Choice'] = {}
    for i in vp['I^C']:
        vp['J^Top_Choice'][i] = np.intersect1d(np.where(p['cadet_utility'][i, :] >= vp['cadet_value_min'][i])[0],
                                               p['J^E'][i])

    # AFSC Value Constraint Set
    vp['J^C'] = np.where(vp['afsc_value_min'] > 0)[0]

    # number of breakpoints
    vp['r'] = np.array([[len(vp['a'][j][k]) for k in vp["K"]] for j in p["J"]])

    # set of breakpoints
    vp['L'] = np.array([[np.arange(vp['r'][j, k]) for k in range(vp["O"])] for j in range(p["M"])], dtype=object)

    # Round weights
    vp['objective_weight'] = np.around(vp['objective_weight'], 8)
    vp['afsc_weight'] = np.around(vp['afsc_weight'], 8)
    vp['cadet_weight'] = np.around(vp['cadet_weight'], 8)

    # Extract AFSC objective min/max measures
    vp["objective_min"], vp["objective_max"] = np.zeros([p['M'], vp['O']]), np.zeros([p["M"], vp["O"]])
    for j in p['J']:
        for k in vp['K^C'][j]:
            value_list = vp['objective_value_min'][j, k].split(",")
            vp["objective_min"][j, k] = float(value_list[0].strip())
            vp["objective_max"][j, k] = float(value_list[1].strip())

    # "Global Utility" matrix
    if "afsc_utility" in p and "cadet_utility" in p:
        vp['global_utility'] = np.zeros([p['N'], p['M'] + 1])
        for j in p['J']:
            vp['global_utility'][:, j] = vp['cadets_overall_weight'] * p['cadet_utility'][:, j] + \
                                         vp['afscs_overall_weight'] * p['afsc_utility'][:, j]

    return vp

model_value_parameters_to_defaults(instance, filepath, printing=False)

Export Instance Value Parameters to Excel Defaults File.

This function extracts the current value parameters from the provided AFCCP model instance and saves them into a structured Excel file. This allows users to export and preserve a particular configuration of value weights, objectives, and constraints for cadets and AFSCs.

Parameters:

  • instance (CadetCareerProblem): The current problem instance containing value parameters in instance.value_parameters.
  • filepath (str): Full path (including .xlsx extension) where the Excel file will be saved.
  • printing (bool, optional): If True, prints progress message during export. Default is False.

Returns:

None: Saves structured Excel file to disk with sheets for overall weights, AFSC weights, and objective components.

Examples:

model_value_parameters_to_defaults(instance, filepath='outputs/vp_defaults.xlsx', printing=True)
Source code in afccp/data/values.py 
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def model_value_parameters_to_defaults(instance, filepath, printing=False):
    """
    Export Instance Value Parameters to Excel Defaults File.

    This function extracts the current value parameters from the provided AFCCP model `instance`
    and saves them into a structured Excel file. This allows users to export and preserve
    a particular configuration of value weights, objectives, and constraints for cadets and AFSCs.

    Parameters:
    --------
    - instance (`CadetCareerProblem`): The current problem instance containing value parameters in `instance.value_parameters`.
    - filepath (str): Full path (including `.xlsx` extension) where the Excel file will be saved.
    - printing (bool, optional): If True, prints progress message during export. Default is False.

    Returns:
    --------
    None: Saves structured Excel file to disk with sheets for overall weights, AFSC weights, and objective components.

    Examples:
    --------
    ```python
    model_value_parameters_to_defaults(instance, filepath='outputs/vp_defaults.xlsx', printing=True)
    ```
    """
    if printing:
        print('Exporting value parameters as defaults to excel...')

    # Shorthand
    p, vp = instance.parameters, instance.value_parameters

    # Create "Overall Weights" dataframe
    overall_weights_df = pd.DataFrame({'Cadets Weight': [vp['cadets_overall_weight']],
                                       'AFSCs Weight': [vp['afscs_overall_weight']],
                                       'Cadets Min Value': [vp['cadets_overall_value_min']],
                                       'AFSCs Min Value': [vp['afscs_overall_value_min']],
                                       'Cadet Weight Function': [vp['cadet_weight_function']],
                                       'AFSC Weight Function': [vp['afsc_weight_function']]})

    # Construct other dataframes
    afsc_weights_df = pd.DataFrame({'AFSC': p['afscs'][:p["M"]],
                                    'AFSC Swing Weight': np.around((vp['afsc_weight'] / max(vp['afsc_weight'])) * 100, 2),
                                    'AFSC Min Value': vp['afsc_value_min']})

    # AFSC Objective Components Translations Dictionary
    ao_trans_dict = {'AFSC Objective Weights': 'objective_weight', 'AFSC Objective Targets': 'objective_target',
                     'AFSC Objective Min Value': 'objective_value_min', 'Constraint Type': 'constraint_type',
                     'Value Functions': 'value_functions'}

    # Create the AFSC Objective Components DataFrames
    ao_dfs = {component: pd.DataFrame({'AFSC': p['afscs'][:p["M"]]}) for component in ao_trans_dict}
    for component in ao_dfs:

        # Scale AFSC Objective Weights so that the largest is set to 100 rather than forcing them all to sum to 1
        if component == "AFSC Objective Weights":
            comp_arr = np.array([(vp["objective_weight"][j] / max(vp["objective_weight"][j])) * 100 for j in p["J"]])
        else:
            comp_arr = vp[ao_trans_dict[component]]  # "Component Array", vp["objective_target"] for example

        # Load columns of the dataframe
        for k, objective in enumerate(vp['objectives']):
            ao_dfs[component][objective] = comp_arr[:, k]

    # Export to excel
    with pd.ExcelWriter(filepath) as writer:
        overall_weights_df.to_excel(writer, sheet_name="Overall Weights", index=False)
        afsc_weights_df.to_excel(writer, sheet_name="AFSC Weights", index=False)
        for component in ao_dfs:
            ao_dfs[component].to_excel(writer, sheet_name=component, index=False)

generate_afocd_value_parameters(parameters, default_value_parameters)

Generate AFOCD-Based Value Parameters for AFSC Assignment.

This function builds out the objective weights, targets, and constraints for each AFSC based on their tiered degree requirements as specified in the AFOCD (Air Force Officer Classification Directory). Each tier (1–4) contributes differently based on whether the degree requirement is Mandatory, Desired, or Permitted.

The function modifies the provided value parameters dictionary in-place by populating:

  • objective_weight
  • objective_target
  • objective_value_min
  • constraint_type
  • value_functions

It uses multipliers for tier importance and maps the degree tier qualifications to model-ready value and constraint settings.

Parameters:

  • parameters (dict): Problem instance parameters dictionary (contains tier structure, tier types, and tier proportions).
  • default_value_parameters (dict): Template or pre-initialized dictionary of value parameters to be modified and returned.

Returns:

  • dict: Updated default_value_parameters dictionary with AFOCD-based settings applied.

Examples:

```python updated_value_parameters = generate_afocd_value_parameters(instance.parameters, default_vp)

Source code in afccp/data/values.py 
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def generate_afocd_value_parameters(parameters, default_value_parameters):
    """
    Generate AFOCD-Based Value Parameters for AFSC Assignment.

    This function builds out the objective weights, targets, and constraints for each AFSC
    based on their tiered degree requirements as specified in the AFOCD (Air Force Officer
    Classification Directory). Each tier (1–4) contributes differently based on whether the degree
    requirement is Mandatory, Desired, or Permitted.

    The function modifies the provided value parameters dictionary in-place by populating:

    - `objective_weight`
    - `objective_target`
    - `objective_value_min`
    - `constraint_type`
    - `value_functions`

    It uses multipliers for tier importance and maps the degree tier qualifications to model-ready
    value and constraint settings.

    Parameters:
    --------
    - parameters (dict): Problem instance parameters dictionary (contains tier structure, tier types, and tier proportions).
    - default_value_parameters (dict): Template or pre-initialized dictionary of value parameters to be modified and returned.

    Returns:
    --------
    - dict: Updated `default_value_parameters` dictionary with AFOCD-based settings applied.

    Examples:
    --------
    ```python
    updated_value_parameters = generate_afocd_value_parameters(instance.parameters, default_vp)
    """
    p, vp = parameters, default_value_parameters

    # AFOCD Objective Indices
    tier_objectives = np.array([np.where(vp["objectives"] == "Tier " + t)[0][0] for t in ["1", "2", "3", "4"]])

    # Tier multipliers
    tm = {1: 1, 2: 0.8, 3: 0.6, 4: 0.4}

    # Loop through each AFSC
    for j in p["J"]:

        # Loop through each AFOCD tier
        for t, k in enumerate(tier_objectives):
            tier = t + 1

            # We only do this for valid AFOCD tiers
            if tier <= p["t_count"][j]:

                # Objective Weight
                if p["t_mandatory"][j, t] == 1:
                    vp["objective_weight"][j, k] = round(90 * tm[tier], 2)
                elif p["t_desired"][j, t] == 1:
                    vp["objective_weight"][j, k] = round(70 * tm[tier], 2)
                elif p["t_permitted"][j, t] == 1:
                    vp["objective_weight"][j, k] = round(50 * tm[tier], 2)
                else:
                    vp["objective_weight"][j, k] = 0  # Tier doesn't exist or is an ineligible tier

                # Objective Target
                vp["objective_target"][j, k] = p["t_proportion"][j, t]

                # Objective Min Value
                if p["t_leq"][j, t] == 1:
                    vp["objective_value_min"][j, k] = "0, " + str(p["t_proportion"][j, t])
                else:  # <= OR ==
                    vp["objective_value_min"][j, k] = str(p["t_proportion"][j, t]) + ", 5"

                # Constraint Type (Default to turning all constraints on. It's easier to make them zeros later...)
                if p["t_mandatory"][j, t] == 1:
                    vp["constraint_type"][j, k] = 1  # Easier to meet "at least" constraint (M >/= x) based on PGL
                elif p["t_desired"][j, t] == 1:
                    if p["t_leq"][j, t] == 1:
                        vp["constraint_type"][j, k] = 2  # Easier to meet "at most" constraint (D < x) based on proportion
                    elif p["t_geq"][j, t] == 1:
                        vp["constraint_type"][j, k] = 1  # Easier to meet "at least" constraint (D > x) based on PGL
                elif p["t_permitted"][j, t] == 1:
                    vp["constraint_type"][j, k] = 2  # Easier to meet "at most" constraint (P < x) based on proportion

                # Value Functions
                if p['t_leq'][j, t] == 1:
                    vp['value_functions'][j, k] = "Min Decreasing|0.3"
                else:  # <= OR ==
                    vp['value_functions'][j, k] = "Min Increasing|0.3"

    return vp

update_value_and_weight_functions(instance, num_breakpoints=None)

Update Value and Weight Functions for the Current Value Parameter Set.

This function recalculates the cadet weights, AFSC weights, and value function breakpoints (a and f^hat) for the currently loaded set of value parameters in the instance. It is useful for refreshing value structures after manual edits to the value parameters, such as changes in weight functions or objective targets.

It does not add or remove objectives from the current set — only updates the internal structure based on the existing configuration. For structural changes (adding/removing objectives), you must reinitialize the value parameter set entirely.

Parameters:

  • instance (CadetCareerProblem): The active problem instance containing parameters and value_parameters.
  • num_breakpoints (int, optional): Number of breakpoints used to approximate the nonlinear value functions. If not specified, defaults to internal value function settings.

Returns:

  • dict: The updated value_parameters dictionary with recalculated weights and piecewise linear segments.

Examples:

instance.value_parameters = update_value_and_weight_functions(instance, num_breakpoints=10)

See Also:

Source code in afccp/data/values.py 
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def update_value_and_weight_functions(instance, num_breakpoints=None):
    """
    Update Value and Weight Functions for the Current Value Parameter Set.

    This function recalculates the cadet weights, AFSC weights, and value function breakpoints
    (`a` and `f^hat`) for the currently loaded set of value parameters in the instance. It is useful
    for refreshing value structures after manual edits to the value parameters, such as changes
    in weight functions or objective targets.

    It does not add or remove objectives from the current set — only updates the internal structure
    based on the existing configuration. For structural changes (adding/removing objectives), you must
    reinitialize the value parameter set entirely.

    Parameters:
    --------
    - instance (CadetCareerProblem): The active problem instance containing `parameters` and `value_parameters`.
    - num_breakpoints (int, optional): Number of breakpoints used to approximate the nonlinear value functions.
      If not specified, defaults to internal value function settings.

    Returns:
    --------
    - dict: The updated `value_parameters` dictionary with recalculated weights and piecewise linear segments.

    Examples:
    --------
    ```python
    instance.value_parameters = update_value_and_weight_functions(instance, num_breakpoints=10)
    ```

    See Also:
    --------
    - [`cadet_weight_function`](../../../../afccp/reference/data/values/#data.values.cadet_weight_function):
      Generates cadet weights from merit scores using a user-defined weighting function.
    - [`afsc_weight_function`](../../../../afccp/reference/data/values/#data.values.afsc_weight_function):
      Generates AFSC weights based on PGL using either 'Linear', 'Square', or 'Custom' mappings.
    - [`value_function_builder`](../../../../afccp/reference/data/values/#data.values.value_function_builder):
      Builds piecewise linear approximations (`a`, `f^hat`) of nonlinear value functions.
    - [`create_segment_dict_from_string`](../../../../afccp/reference/data/values/#data.values.create_segment_dict_from_string):
      Parses the string representation of a value function and returns a segment definition.
    """

    # Shorthand
    p, vp = instance.parameters, instance.value_parameters

    # Determine weights on cadets
    if 'merit_all' in p:
        vp['cadet_weight'] = cadet_weight_function(p['merit_all'], func=vp['cadet_weight_function'])
    else:
        vp['cadet_weight'] = cadet_weight_function(p['merit'], func=vp['cadet_weight_function'])

    # Determine weights on AFSCs
    if vp['afsc_weight_function'] != 'Custom':  # If the AFSC weight function is not "custom", we regenerate the weights
        vp['afsc_weight'] = afsc_weight_function(p["pgl"], vp['afsc_weight_function'])

    # Initialize breakpoints
    vp['a'] = [[[] for _ in range(vp['O'])] for _ in p["J"]]
    vp['f^hat'] = [[[] for _ in range(vp['O'])] for _ in p["J"]]

    # Loop through each AFSC
    for j, afsc in enumerate(p['afscs'][:p['M']]):  # Skip the "unmatched AFSC": '*'

        # Loop through each objective
        for k, objective in enumerate(vp['objectives']):

            # Value Function specific parameters
            actual, minimum, maximum = None, None, None
            if objective == 'Merit':
                actual = np.mean(p['merit'][p['I^E'][j]])
            if objective in ['USAFA Proportion', 'Male', 'Minority']:
                actual = len(p['I^D'][objective][j]) / len(p['I^E'][j])
            if objective in ['Combined Quota', 'ROTC Quota', 'USAFA Quota', 'OTS Quota']:

                # Dictionaries for getting the right value for the specific quota objective
                min_dict = {"Combined Quota": 'quota_min', 'ROTC Quota': 'rotc_quota',
                            'USAFA Quota': 'usafa_quota', 'OTS Quota': 'ots_quota'}
                target_dict = {"Combined Quota": 'quota_d', 'ROTC Quota': 'rotc_quota',
                               'USAFA Quota': 'usafa_quota', 'OTS Quota': 'ots_quota'}
                minimum, maximum = int(p[min_dict[objective]][j]), int(p['quota_max'][j])

                # Update minimum values for combined quota objective
                vp['objective_value_min'][j, k] = str(minimum) + ', ' + str(maximum)
                vp['objective_min'][j, k], vp['objective_max'][j, k] = minimum, maximum
                vp['objective_target'][j, k] = p[target_dict[objective]][j]

            # If we care about this objective, we load in its value function breakpoints
            if vp['objective_weight'][j, k] != 0:

                # Create the non-linear piecewise exponential segment dictionary
                segment_dict = create_segment_dict_from_string(vp['value_functions'][j, k],
                                                               vp['objective_target'][j, k],
                                                               minimum=minimum, maximum=maximum, actual=actual)

                # Linearize the non-linear function using the specified number of breakpoints
                vp['a'][j][k], vp['f^hat'][j][k] = value_function_builder(
                    segment_dict, num_breakpoints=num_breakpoints)

        # Scale the objective weights for this AFSC, so they sum to 1
        vp['objective_weight'][j] = vp['objective_weight'][j] / sum(vp['objective_weight'][j])

    # Scale the weights across all AFSCs, so they sum to 1
    vp['afsc_weight'] = vp['afsc_weight'] / sum(vp['afsc_weight'])

    return vp  # Return set of value parameters

generate_value_parameters_from_defaults(parameters, default_value_parameters, generate_afsc_weights=True, num_breakpoints=None, printing=False)

Generates structured value parameters for the assignment problem based on the factory defaults.

This function constructs a complete vp dictionary used by value-focused optimization models. It loads and modifies default parameters to match the structure and constraints of the current problem instance, accounting for objective targets, weights, breakpoints, and constraint types.

Note

  • If Qual Type is "Tiers", the function replaces legacy AFOCD objectives with Tiered ones.
  • If Qual Type is "Relaxed", Tier objectives are removed.

Note

Use this function when you have:

  • Loaded default value parameters from Excel
  • A structured cadet-AFSC assignment problem (parameters)
  • Need to prepare a consistent set of inputs for a value-based matching model (e.g., VFT)

Parameters

parameters : dict Dictionary of instance parameters (cadets, AFSCs, quotas, preferences, etc.).

default_value_parameters : dict Dictionary of default value parameters imported via default_value_parameters_from_excel.

generate_afsc_weights : bool, optional If True (default), compute AFSC weights using the specified function in defaults. If False, use static AFSC weights from the defaults (used for "Custom").

num_breakpoints : int, optional Number of breakpoints used to discretize value functions. Defaults to what's in defaults.

printing : bool, optional Whether to print status updates during generation (default is False).

Returns

dict A structured dictionary vp containing:

  • objectives: List of active objective names
  • objective_weight: Array of objective weights by AFSC
  • objective_target: Array of target values for each AFSC-objective pair
  • objective_value_min: Text bounds for constrained objectives
  • constraint_type: Type of constraint (e.g., inequality, convex) for each objective
  • afsc_weight, afsc_value_min, cadet_weight, cadets_overall_weight, ...
  • a, f^hat: Piecewise value function breakpoints
  • K^A: Dictionary mapping AFSC index to active objective indices
Source code in afccp/data/values.py 
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def generate_value_parameters_from_defaults(parameters, default_value_parameters, generate_afsc_weights=True,
                                            num_breakpoints=None, printing=False):
    """
    Generates structured value parameters for the assignment problem based on the factory defaults.

    This function constructs a complete `vp` dictionary used by value-focused optimization models.
    It loads and modifies default parameters to match the structure and constraints of the current
    problem instance, accounting for objective targets, weights, breakpoints, and constraint types.

    !!! note
        - If `Qual Type` is `"Tiers"`, the function replaces legacy AFOCD objectives with Tiered ones.
        - If `Qual Type` is `"Relaxed"`, Tier objectives are removed.

    !!! note
        Use this function when you have:

        - Loaded default value parameters from Excel
        - A structured cadet-AFSC assignment problem (`parameters`)
        - Need to prepare a consistent set of inputs for a value-based matching model (e.g., VFT)

    Parameters
    ----------
    parameters : dict
        Dictionary of instance parameters (cadets, AFSCs, quotas, preferences, etc.).

    default_value_parameters : dict
        Dictionary of default value parameters imported via `default_value_parameters_from_excel`.

    generate_afsc_weights : bool, optional
        If True (default), compute AFSC weights using the specified function in defaults.
        If False, use static AFSC weights from the defaults (used for "Custom").

    num_breakpoints : int, optional
        Number of breakpoints used to discretize value functions. Defaults to what's in defaults.

    printing : bool, optional
        Whether to print status updates during generation (default is False).

    Returns
    -------
    dict
    A structured dictionary `vp` containing:

    - `objectives`: List of active objective names
    - `objective_weight`: Array of objective weights by AFSC
    - `objective_target`: Array of target values for each AFSC-objective pair
    - `objective_value_min`: Text bounds for constrained objectives
    - `constraint_type`: Type of constraint (e.g., inequality, convex) for each objective
    - `afsc_weight`, `afsc_value_min`, `cadet_weight`, `cadets_overall_weight`, ...
    - `a`, `f^hat`: Piecewise value function breakpoints
    - `K^A`: Dictionary mapping AFSC index to active objective indices
    """
    if printing:
        print('Generating value parameters from defaults...')

    # Shorthand
    p, dvp = parameters, default_value_parameters

    # Variable to control if we load in AFOCD value parameters from the default excel workbook or create them here
    init_afocd = False

    # Manipulate AFOCD objectives based on what "system" we're using (Tiers or "Old")
    if p["Qual Type"] == "Tiers":

        # Weight "Old" AFOCD Objectives at zero (but keep them in because we can select them if needed)
        for objective in ["Mandatory", "Desired", "Permitted"]:
            if objective in dvp["objectives"]:
                k = np.where(dvp["objectives"] == objective)[0][0]
                dvp["objective_weight"][:, k] = np.zeros(len(dvp["objective_weight"]))

        # Add in "Tier" AFOCD Objectives
        for t in ["1", "2", "3", "4"]:
            objective = "Tier " + t
            if objective not in dvp["objectives"]:
                init_afocd = True  # We're going to initialize the value parameters for AFOCD objectives
                dvp["objectives"] = np.hstack([dvp["objectives"], objective])

                # Add these columns in the other arrays as well
                for vp_key in ["objective_weight", "objective_value_min", "constraint_type", "objective_target",
                               "value_functions"]:
                    if vp_key in ["objective_weight", "constraint_type", "objective_target"]:
                        new_column = np.array([[0] for _ in p["J"]])
                    else:
                        new_column = np.array([["0"] for _ in p["J"]])
                    dvp[vp_key] = np.hstack((dvp[vp_key], new_column))

    elif p["Qual Type"] == "Relaxed":

        # Remove "Tier" AFOCD Objectives
        for t in ["1", "2", "3", "4"]:
            objective = "Tier " + t
            if objective in dvp["objectives"]:
                k = np.where(dvp["objectives"] == objective)[0][0]
                dvp["objectives"] = np.delete(dvp["objectives"], k)

    # Generate AFOCD value parameters if necessary
    if init_afocd:
        dvp = generate_afocd_value_parameters(p, dvp)

    # Objective to parameters lookup dictionary (if the parameter is in "p", we include the objective)
    objective_lookups = {'Norm Score': 'a_pref_matrix', 'Merit': 'merit', 'USAFA Proportion': 'usafa',
                         'Combined Quota': 'quota_d', 'USAFA Quota': 'usafa_quota', 'ROTC Quota': 'rotc_quota',
                         'OTS Quota': 'ots_quota',
                         'Mandatory': 'mandatory', 'Desired': 'desired', 'Permitted': 'permitted',
                         'Utility': 'utility', 'Male': 'male', 'Minority': 'minority'}
    for t in ["1", "2", "3", "4"]:  # Add in AFOCD Degree tiers
        objective_lookups["Tier " + t] = "tier " + t

    # Add the AFSC objectives that are included in this instance (check corresponding parameters using dict above)
    objectives = []
    objective_indices = []
    for k, objective in enumerate(dvp["objectives"]):
        if objective_lookups[objective] in p:
            objectives.append(objective)
            objective_indices.append(k)

    # Convert to numpy arrays
    objectives = np.array(objectives)
    objective_indices = np.array(objective_indices)

    # Additional information
    afsc_indices = np.array([np.where(dvp['complete_afscs'] == p['afscs'][j])[0][0] for j in p["J"]])
    O = len(objectives)
    if num_breakpoints is None:
        num_breakpoints = dvp['num_breakpoints']

    # Initialize set of value p
    vp = {'cadets_overall_weight': dvp['cadets_overall_weight'],
          'afscs_overall_weight': dvp['afscs_overall_weight'],
          'cadet_weight_function': dvp['cadet_weight_function'],
          'afsc_weight_function': dvp['afsc_weight_function'],
          'cadets_overall_value_min': dvp['cadets_overall_value_min'],
          'afscs_overall_value_min': dvp['afscs_overall_value_min'],
          'afsc_value_min': np.zeros(p["M"]), 'cadet_value_min': np.zeros(p["N"]),
          'objective_weight': np.zeros([p["M"], O]), 'afsc_weight': np.zeros(p["M"]), "M": p["M"],
          'objective_target': np.zeros([p["M"], O]), 'objectives': objectives, 'O': O,
          'objective_value_min': np.array([[" " * 20 for _ in range(O)] for _ in p["J"]]),
          'constraint_type': np.zeros([p["M"], O]).astype(int),
          'num_breakpoints': num_breakpoints}

    # Determine weights on cadets
    if 'merit_all' in p:
        vp['cadet_weight'] = cadet_weight_function(p['merit_all'], func=vp['cadet_weight_function'])
    else:
        vp['cadet_weight'] = cadet_weight_function(p['merit'], func=vp['cadet_weight_function'])

    # Determine weights on AFSCs
    if generate_afsc_weights:
        func = vp['afsc_weight_function']
        if func == 'Custom':  # We take the AFSC weights directly from the defaults
            generate_afsc_weights = False
        else:
            vp['afsc_weight'] = afsc_weight_function(p["pgl"], func)

    # Initialize breakpoints
    vp['a'] = [[[] for _ in range(O)] for _ in p["J"]]
    vp['f^hat'] = [[[] for _ in range(O)] for _ in p["J"]]

    # Load value function strings
    value_functions = dvp['value_functions'][:, objective_indices]
    value_functions = value_functions[afsc_indices, :]
    vp['value_functions'] = value_functions

    # Initialize objective set
    vp['K^A'] = {}

    # Loop through each AFSC to load in their value parameters
    for j, afsc in enumerate(p['afscs']):

        if afsc != "*":

            # Get location of afsc in the default value parameters (matters if this set of afscs does not match)
            loc = np.where(dvp['complete_afscs'] == afsc)[0][0]

            # Initially assign all default weights, targets, etc.
            vp['objective_weight'][j, :] = dvp['objective_weight'][loc, objective_indices]
            vp['objective_target'][j] = dvp['objective_target'][loc, objective_indices]
            vp['objective_value_min'][j] = dvp['objective_value_min'][loc, objective_indices]
            vp['afsc_value_min'][j] = dvp['afsc_value_min'][loc]
            vp['constraint_type'][j] = dvp['constraint_type'][loc, objective_indices]
            vp['K^A'][j] = np.where(vp['objective_weight'][j, :] > 0)[0].astype(int)

            # If we're not generating afsc weights using the specified weight function...
            if not generate_afsc_weights:  # Also, if the weight function is "Custom"
                vp['afsc_weight'][j] = dvp['afsc_weight'][loc]

            # Loop through each objective to load their targets
            for k, objective in enumerate(vp['objectives']):

                maximum, minimum, actual = None, None, None
                if objective == 'Merit':
                    vp['objective_target'][j, k] = p['sum_merit'] / p['N']
                    actual = np.mean(p['merit'][p['I^E'][j]])

                elif objective == 'USAFA Proportion':
                    vp['objective_target'][j, k] = p['usafa_proportion']
                    if len(p['I^E'][j]) == 0:  # In case there are no eligible USAFA cadets
                        actual = 0
                    else:
                        actual = len(p['I^D'][objective][j]) / len(p['I^E'][j])

                elif objective == 'Combined Quota':
                    vp['objective_target'][j, k] = p['quota_d'][j]

                    # Get bounds
                    minimum, maximum = p['quota_min'][j], p['quota_max'][j]
                    vp['objective_value_min'][j, k] = str(int(minimum)) + ", " + str(int(maximum))

                elif objective == 'USAFA Quota':
                    vp['objective_target'][j, k] = p['usafa_quota'][j]
                    vp['objective_value_min'][j, k] = str(int(p['usafa_quota'][j])) + ", " + \
                                                                    str(int(p['quota_max'][j]))

                elif objective == 'ROTC Quota':
                    vp['objective_target'][j, k] = p['rotc_quota'][j]
                    vp['objective_value_min'][j, k] = str(int(p['rotc_quota'][j])) + ", " + \
                                                                    str(int(p['quota_max'][j]))
                elif objective == 'OTS Quota':
                    vp['objective_target'][j, k] = p['ots_quota'][j]
                    vp['objective_value_min'][j, k] = str(int(p['ots_quota'][j])) + ", " + \
                                                                    str(int(p['quota_max'][j]))

                elif objective == 'Male':
                    vp['objective_target'][j, k] = p['male_proportion']
                    if len(p['I^E'][j]) == 0:  # In case there are no eligible male cadets
                        actual = 0
                    else:
                        actual = len(p['I^D'][objective][j]) / len(p['I^E'][j])

                elif objective == 'Minority':
                    vp['objective_target'][j, k] = p['minority_proportion']
                    if len(p['I^E'][j]) == 0:  # In case there are no eligible minority cadets
                        actual = 0
                    else:
                        actual = len(p['I^D'][objective][j]) / len(p['I^E'][j])

                # If we care about this objective, we load in its value function breakpoints
                if vp['objective_weight'][j, k] != 0:

                    # Create the non-linear piecewise exponential segment dictionary
                    segment_dict = create_segment_dict_from_string(value_functions[j, k],
                                                                   vp['objective_target'][j, k],
                                                                   minimum=minimum, maximum=maximum, actual=actual)

                    # Linearize the non-linear function using the specified number of breakpoints
                    vp['a'][j][k], vp['f^hat'][j][k] = value_function_builder(
                        segment_dict, num_breakpoints=num_breakpoints)

            # Scale the objective weights for this AFSC, so they sum to 1
            vp['objective_weight'][j] = vp['objective_weight'][j] / sum(vp['objective_weight'][j])

    # Scale the weights across all AFSCs, so they sum to 1
    vp['afsc_weight'] = vp['afsc_weight'] / sum(vp['afsc_weight'])

    return vp

default_value_parameters_from_excel(filepath, num_breakpoints=24, printing=False)

Loads the factory default value parameters from an Excel file into a structured dictionary.

This function is typically used to initialize a consistent baseline for value-focused models (such as VFT and GP), including AFSC weights, objective weights/targets, constraint types, and breakpoint-based value functions.

It pulls multiple sheets from a specified Excel file and organizes them into a structured dictionary suitable for assignment model optimization.

Note

The filepath must point to a valid Excel file containing the following sheets:

  • "Overall Weights"
  • "AFSC Weights"
  • "AFSC Objective Weights"
  • "AFSC Objective Targets"
  • "AFSC Objective Min Value"
  • "Constraint Type"
  • "Value Functions"

Parameters

filepath : str Path to the Excel file containing all value parameter sheets. num_breakpoints : int, optional Number of breakpoints to use for piecewise value functions (default is 24). printing : bool, optional Whether to print status messages during execution (default is False).

Returns

dict A dictionary containing all default value parameter arrays and scalars:

  • cadet_weight_function: str
  • afsc_weight_function: str
  • cadets_overall_weight: float
  • afscs_overall_weight: float
  • afsc_weight: np.ndarray
  • objective_weight: np.ndarray
  • objective_target: np.ndarray
  • objective_value_min: np.ndarray
  • constraint_type: np.ndarray
  • value_functions: np.ndarray
  • cadets_overall_value_min: float
  • afscs_overall_value_min: float
  • afsc_value_min: np.ndarray
  • objectives: np.ndarray of objective names
  • complete_afscs: np.ndarray of AFSC names
  • num_breakpoints: int (copied from input)
  • M: int (number of AFSCs)
Source code in afccp/data/values.py 
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def default_value_parameters_from_excel(filepath, num_breakpoints=24, printing=False):
    """
    Loads the factory default value parameters from an Excel file into a structured dictionary.

    This function is typically used to initialize a consistent baseline for value-focused models
    (such as VFT and GP), including AFSC weights, objective weights/targets, constraint types,
    and breakpoint-based value functions.

    It pulls multiple sheets from a specified Excel file and organizes them into a structured dictionary
    suitable for assignment model optimization.

    !!! note
        The `filepath` must point to a valid Excel file containing the following sheets:

        - "Overall Weights"
        - "AFSC Weights"
        - "AFSC Objective Weights"
        - "AFSC Objective Targets"
        - "AFSC Objective Min Value"
        - "Constraint Type"
        - "Value Functions"

    Parameters
    ----------
    filepath : str
        Path to the Excel file containing all value parameter sheets.
    num_breakpoints : int, optional
        Number of breakpoints to use for piecewise value functions (default is 24).
    printing : bool, optional
        Whether to print status messages during execution (default is False).

    Returns
    -------
    dict
    A dictionary containing all default value parameter arrays and scalars:

    - `cadet_weight_function`: str
    - `afsc_weight_function`: str
    - `cadets_overall_weight`: float
    - `afscs_overall_weight`: float
    - `afsc_weight`: np.ndarray
    - `objective_weight`: np.ndarray
    - `objective_target`: np.ndarray
    - `objective_value_min`: np.ndarray
    - `constraint_type`: np.ndarray
    - `value_functions`: np.ndarray
    - `cadets_overall_value_min`: float
    - `afscs_overall_value_min`: float
    - `afsc_value_min`: np.ndarray
    - `objectives`: np.ndarray of objective names
    - `complete_afscs`: np.ndarray of AFSC names
    - `num_breakpoints`: int (copied from input)
    - `M`: int (number of AFSCs)
    """
    if printing:
        print('Importing default value parameters...')

    # Get dataframes
    overall_weights_df = afccp.globals.import_data(filepath, sheet_name="Overall Weights")
    afsc_weights_df = afccp.globals.import_data(filepath, sheet_name="AFSC Weights")
    afsc_objective_weights_df = afccp.globals.import_data(filepath, sheet_name="AFSC Objective Weights")
    afsc_objective_targets_df = afccp.globals.import_data(filepath, sheet_name="AFSC Objective Targets")
    afsc_objective_value_min_df = afccp.globals.import_data(filepath, sheet_name="AFSC Objective Min Value")
    afsc_objective_convex_constraints_df = afccp.globals.import_data(filepath, sheet_name="Constraint Type")
    afsc_value_functions_df = afccp.globals.import_data(filepath, sheet_name="Value Functions")
    objectives = np.array(afsc_objective_weights_df.keys()[1:])
    default_value_parameters = {'cadet_weight_function': overall_weights_df['Cadet Weight Function'][0],
                                'afsc_weight_function': overall_weights_df['AFSC Weight Function'][0],
                                'cadets_overall_weight': overall_weights_df['Cadets Weight'][0],
                                'afscs_overall_weight': overall_weights_df['AFSCs Weight'][0],
                                'afsc_weight': np.array(afsc_weights_df['AFSC Swing Weight']),
                                'objective_weight': np.array(afsc_objective_weights_df.iloc[:,
                                                             1:(len(objectives) + 1)]),
                                'objective_target': np.array(
                                    afsc_objective_targets_df.iloc[:, 1:(len(objectives) + 1)]),
                                'objective_value_min': np.array(
                                    afsc_objective_value_min_df.iloc[:, 1:(len(objectives) + 1)]),
                                'constraint_type': np.array(
                                    afsc_objective_convex_constraints_df.iloc[:, 1:(len(objectives) + 1)]),
                                'value_functions': np.array(afsc_value_functions_df.iloc[:, 1:(len(objectives) + 1)]),
                                'cadets_overall_value_min': overall_weights_df['Cadets Min Value'][0],
                                'afscs_overall_value_min': overall_weights_df['AFSCs Min Value'][0],
                                'afsc_value_min': np.array(afsc_weights_df['AFSC Min Value']),
                                'objectives': objectives,
                                'complete_afscs': np.array(afsc_weights_df['AFSC']),
                                'num_breakpoints': num_breakpoints, "M": len(afsc_weights_df)}

    return default_value_parameters

cadet_weight_function(merit, func='Curve_1')

Take in a merit array and generate cadet weights depending on function specified

Source code in afccp/data/values.py 
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def cadet_weight_function(merit, func="Curve_1"):
    """
    Take in a merit array and generate cadet weights depending on function specified
    """

    # Number of Cadets
    N = len(merit)

    # Generate Swing Weights based on function
    if func == 'Linear':
        swing_weights = np.array([1 + (2 * x) for x in merit])
    elif func == "Direct":
        swing_weights = merit
    elif func == 'Curve_1':
        swing_weights = np.array([1 + 2 / (1 + exp(-10 * (x - 0.5))) for x in merit])
    elif func == 'Curve_2':
        swing_weights = np.array([1 + 2 / (1 + exp(-12 * (x - 0.7))) for x in merit])
    elif func == 'Equal':
        swing_weights = np.ones(N)
    else:  # Exponential Function
        rho = -0.3
        swing_weights = np.array([(1 - exp(-x / rho)) / (1 - exp(-1 / rho)) for x in merit])

    # Normalize weights and return them
    weights = swing_weights / sum(swing_weights)
    return weights

afsc_weight_function(quota, func='Curve')

Take in an AFSC quota array and generate AFSC weights depending on function specified

Source code in afccp/data/values.py 
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def afsc_weight_function(quota, func="Curve"):
    """
    Take in an AFSC quota array and generate AFSC weights depending on function specified
    """

    # Number of AFSCs
    M = len(quota)

    # Scale quota to be 0-1 (referencing biggest AFSC)
    quota_scale = quota / np.max(quota)

    # Generate Swing Weights based on function
    if func == 'Linear':
        swing_weights = np.array([1 + (10 * x) for x in quota_scale])
    elif func in ["Direct", "Size"]:  # Direct relationship between size and importance
        swing_weights = quota
    elif func == "Piece":
        swing_weights = np.zeros(M)
        for j, x in enumerate(quota):
            if x >= 200:
                swing_weights[j] = 1
            elif 150 <= x < 200:
                swing_weights[j] = 0.9
            elif 100 <= x < 150:
                swing_weights[j] = 0.8
            elif 50 <= x < 100:
                swing_weights[j] = 0.7
            elif 25 <= x < 50:
                swing_weights[j] = 0.6
            else:
                swing_weights[j] = 0.5
    elif func == 'Curve_1':  # Sigmoid Function
        swing_weights = np.array([1 + 10 / (1 + exp(-5 * (x - 0.5))) for x in quota_scale])
    elif func == 'Curve_2':  # Sigmoid Function
        swing_weights = np.array([1 + 12 / (1 + exp(-20 * (x - 0.5))) for x in quota_scale])
    elif func == 'Equal':  # They're all the same
        swing_weights = np.ones(M)
    else:  # Exponential Function
        rho = -0.3
        swing_weights = np.array([(1 - exp(-x / rho)) / (1 - exp(-1 / rho)) for x in quota_scale])

    # Scale weights and return them
    weights = swing_weights / sum(swing_weights)
    return weights

create_segment_dict_from_string(vf_string, target=None, maximum=None, actual=None, multiplier=False, minimum=None)

Converts a value function string into a segment dictionary.

Args:

  • vf_string (str): Value function string.
  • target (float, optional): Target objective measure.
  • maximum (float, optional): Maximum objective measure.
  • actual (float, optional): Proportion of eligible cadets.
  • multiplier (bool, optional): Specifies whether the target values are multiplied by a scalar for quota objectives.
  • minimum (float, optional): Minimum objective measure.

Returns: segment_dict (dict): A dictionary representing the segments of the value function.

Notes:

  • The function assumes that the value function string follows a specific format.
  • The segment dictionary contains keys representing the segment number and values representing the segment details.

  • Each segment is represented by a dictionary with the following keys:

    • 'x1': The starting point on the x-axis.
    • 'y1': The starting point on the y-axis.
    • 'x2': The ending point on the x-axis.
    • 'y2': The ending point on the y-axis.
    • 'rho': The value of the rho parameter for the segment.
Source code in afccp/data/values.py 
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def create_segment_dict_from_string(vf_string, target=None, maximum=None, actual=None, multiplier=False, minimum=None):
    """
    Converts a value function string into a segment dictionary.

    Args:

    - vf_string (str): Value function string.
    - target (float, optional): Target objective measure.
    - maximum (float, optional): Maximum objective measure.
    - actual (float, optional): Proportion of eligible cadets.
    - multiplier (bool, optional): Specifies whether the target values are multiplied by a scalar for quota objectives.
    - minimum (float, optional): Minimum objective measure.

    Returns:
        segment_dict (dict): A dictionary representing the segments of the value function.

    Notes:

    - The function assumes that the value function string follows a specific format.
    - The segment dictionary contains keys representing the segment number and values representing the segment details.
    - Each segment is represented by a dictionary with the following keys:

        - 'x1': The starting point on the x-axis.
        - 'y1': The starting point on the y-axis.
        - 'x2': The ending point on the x-axis.
        - 'y2': The ending point on the y-axis.
        - 'rho': The value of the rho parameter for the segment.
    """

    # Collect the kind of function we're creating
    split_list = vf_string.split('|')
    f_type = split_list[0]

    if f_type == 'Balance':

        # Receive values from string
        f_param_list = split_list[1]
        split_list = f_param_list.split(',')
        left_bm = float(split_list[0].strip())
        right_bm = float(split_list[1].strip())
        rho1 = float(split_list[2].strip())
        rho2 = float(split_list[3].strip())
        rho3 = float(split_list[4].strip())
        rho4 = float(split_list[5].strip())
        buffer_y = float(split_list[6].strip())

        if actual < target:
            left_margin = (target - actual) / 4 + left_bm
            right_margin = right_bm
        elif actual > target:
            left_margin = left_bm
            right_margin = (actual - target) / 4 + right_bm
        else:
            left_margin = left_bm
            right_margin = right_bm

        # Build segments
        segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': round(target - left_margin, 3), 'y2': buffer_y, 'rho': -rho1},
                        2: {'x1': round(target - left_margin, 3), 'y1': buffer_y, 'x2': target, 'y2': 1, 'rho': rho2},
                        3: {'x1': target, 'y1': 1, 'x2': round(target + right_margin, 3), 'y2': buffer_y, 'rho': rho3},
                        4: {'x1': round(target + right_margin, 3), 'y1': buffer_y, 'x2': 1, 'y2': 0, 'rho': -rho4}}

    elif f_type == 'Quota_Normal':  # "Method 1" as described in thesis

        # Receive values from string
        f_param_list = split_list[1]
        split_list = f_param_list.split(',')
        domain_max = float(split_list[0].strip())
        rho1 = float(split_list[1].strip()) * target
        rho2 = float(split_list[2].strip()) * target
        if multiplier:
            maximum = int(target * maximum)
        real_max = max(int(target + (maximum - target) + target * domain_max), maximum + 1)

        # Build segments
        segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': target, 'y2': 1, 'rho': -rho1},
                        2: {'x1': maximum, 'y1': 1, 'x2': real_max, 'y2': 0, 'rho': -rho2}}

    elif f_type == 'Quota_Over':  # "Method 2" as described in thesis

        # Receive values from string
        f_param_list = split_list[1]
        split_list = f_param_list.split(',')
        domain_max = float(split_list[0].strip())
        rho1 = float(split_list[1].strip()) * target
        rho2 = float(split_list[2].strip()) * target
        rho3 = float(split_list[3].strip()) * target
        buffer_y = float(split_list[4].strip())
        if multiplier:
            maximum = int(target * maximum)
            actual = int(target * actual)
        real_max = max(int(target + (actual - target) + target * domain_max), actual + 1)

        # Build segments
        segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': target, 'y2': 1, 'rho': -rho1},
                        2: {'x1': maximum, 'y1': 1, 'x2': actual, 'y2': buffer_y, 'rho': rho2},
                        3: {'x1': actual, 'y1': buffer_y, 'x2': real_max, 'y2': 0, 'rho': -rho3}}

    elif f_type == 'Quota_Direct':  # The benefit of value functions is here! Captures ambiguity of PGL/constraints

        # Receive values from string
        f_param_list = split_list[1]
        split_list = f_param_list.split(',')
        domain_max = 1.05  # Arbitrary max (this doesn't really matter since we constrain quota anyway)
        rho1 = float(split_list[0].strip())
        rho2 = float(split_list[1].strip())
        rho3 = float(split_list[2].strip())
        rho4 = float(split_list[3].strip())
        y1 = float(split_list[4].strip())
        y2 = float(split_list[5].strip())

        assert rho1 > 0, f"rho1 must be greater than 0 for a Quota_Direct value function, got: {rho1}"
        assert rho2 > 0, f"rho2 must be greater than 0 for a Quota_Direct value function, got: {rho2}"
        assert rho3 > 0, f"rho3 must be greater than 0 for a Quota_Direct value function, got: {rho3}"
        assert rho4 > 0, f"rho4 must be greater than 0 for a Quota_Direct value function, got: {rho4}"
        assert 0 < y1 < 1, f"y1 must be between 0 and 1 for a Quota_Direct value function, got: {y1}"
        assert 0 < y2 < 1, f"y2 must be between 0 and 1 for a Quota_Direct value function, got: {y2}"

        # Build segments
        if target == minimum:
            if target == maximum:
                segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': target, 'y2': 1, 'rho': -(rho1 * target)},
                                2: {'x1': maximum, 'y1': 1, 'x2': domain_max * maximum, 'y2': 0,
                                    'rho': -(rho4 * (maximum - target))}}
            else:
                segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': target, 'y2': 1, 'rho': -(rho1 * target)},
                                2: {'x1': target, 'y1': 1, 'x2': maximum, 'y2': y2,
                                    'rho': (rho3 * (maximum - target))},
                                3: {'x1': maximum, 'y1': y2, 'x2': domain_max * maximum, 'y2': 0,
                                    'rho': -(rho4 * (domain_max * maximum - maximum))}}

        else:
            if target == maximum:
                segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': minimum, 'y2': y1, 'rho': -(rho1 * (minimum - 0))},
                                2: {'x1': minimum, 'y1': y1, 'x2': target, 'y2': 1,
                                    'rho': (rho2 * (target - minimum))},
                                3: {'x1': target, 'y1': 1, 'x2': domain_max * maximum, 'y2': 0,
                                    'rho': -(rho4 * (domain_max * maximum - maximum))}}
            else:
                segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': minimum, 'y2': y1, 'rho': -(rho1 * (minimum - 0))},
                                2: {'x1': minimum, 'y1': y1, 'x2': target, 'y2': 1,
                                    'rho': (rho2 * (target - minimum))},
                                3: {'x1': target, 'y1': 1, 'x2': maximum, 'y2': y2,
                                    'rho': (rho3 * (maximum - target))},
                                4: {'x1': maximum, 'y1': y2, 'x2': domain_max * maximum, 'y2': 0,
                                    'rho': -(rho4 * (domain_max * maximum - maximum))}}

    else:  # Must be a "Min Increasing/Decreasing" function

        # Receive values from string
        f_param_list = split_list[1]
        split_list = f_param_list.split(',')
        rho = float(split_list[0].strip()) * target  # Multiplying by the target normalizes the domain space

        # Build segments
        if f_type == 'Min Increasing':
            segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': target, 'y2': 1, 'rho': -rho}}
        else:
            segment_dict = {1: {'x1': target, 'y1': 1, 'x2': 1, 'y2': 0, 'rho': -rho}}

    return segment_dict

value_function_builder(segment_dict=None, num_breakpoints=None, derivative_locations=False)

Build Piecewise Linear Value Function from Exponential Segments.

This function takes a dictionary of exponential segment definitions and returns a pair of arrays representing the piecewise linear approximation of the nonlinear value function: one for the x-axis breakpoints (a) and one for the corresponding values (f^hat).

The segment dictionary defines the start and end points, curvature (via rho), and optionally the number of breakpoints to use for each segment. The function supports both fixed-interval spacing along the x-axis and derivative-based breakpoint spacing.

Parameters:

  • segment_dict (dict, optional): A dictionary specifying exponential segments. Each key maps to a sub-dictionary with:

    • 'x1', 'y1': Starting point of the segment
    • 'x2', 'y2': Ending point of the segment
    • 'rho': Curvature parameter controlling steepness of the segment
    • 'r' (optional): Number of breakpoints for this segment
    • num_breakpoints (int, optional): Overrides the per-segment breakpoint count. Distributes breakpoints equally if specified.
    • derivative_locations (bool, optional): If True, breakpoints are spaced using derivative intervals instead of uniform spacing on the x-axis.

Returns:

  • a (np.ndarray): Array of breakpoint locations (measures) on the x-axis.
  • fhat (np.ndarray): Array of function values at those breakpoint locations.

Examples:

segment_def = {
    1: {'x1': 0, 'y1': 0, 'x2': 0.5, 'y2': 1, 'rho': 0.1, 'r': 10},
    2: {'x1': 0.5, 'y1': 1, 'x2': 1, 'y2': 0, 'rho': -0.1, 'r': 10}
}
a, fhat = value_function_builder(segment_def, num_breakpoints=20, derivative_locations=False)

See Also:

Source code in afccp/data/values.py 
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def value_function_builder(segment_dict=None, num_breakpoints=None, derivative_locations=False):
    """
    Build Piecewise Linear Value Function from Exponential Segments.

    This function takes a dictionary of exponential segment definitions and returns a pair of
    arrays representing the piecewise linear approximation of the nonlinear value function:
    one for the x-axis breakpoints (`a`) and one for the corresponding values (`f^hat`).

    The segment dictionary defines the start and end points, curvature (via `rho`), and optionally
    the number of breakpoints to use for each segment. The function supports both fixed-interval
    spacing along the x-axis and derivative-based breakpoint spacing.

    Parameters:
    --------
    - segment_dict (dict, optional): A dictionary specifying exponential segments. Each key maps to a sub-dictionary with:

        - `'x1'`, `'y1'`: Starting point of the segment
        - `'x2'`, `'y2'`: Ending point of the segment
        - `'rho'`: Curvature parameter controlling steepness of the segment
        - `'r'` (optional): Number of breakpoints for this segment
    - num_breakpoints (int, optional): Overrides the per-segment breakpoint count. Distributes breakpoints equally if specified.
    - derivative_locations (bool, optional): If True, breakpoints are spaced using derivative intervals
      instead of uniform spacing on the x-axis.

    Returns:
    --------
    - a (np.ndarray): Array of breakpoint locations (measures) on the x-axis.
    - fhat (np.ndarray): Array of function values at those breakpoint locations.

    Examples:
    --------
    ```python
    segment_def = {
        1: {'x1': 0, 'y1': 0, 'x2': 0.5, 'y2': 1, 'rho': 0.1, 'r': 10},
        2: {'x1': 0.5, 'y1': 1, 'x2': 1, 'y2': 0, 'rho': -0.1, 'r': 10}
    }
    a, fhat = value_function_builder(segment_def, num_breakpoints=20, derivative_locations=False)
    ```

    See Also:
    --------
    - [`exponential_function`](../../../../afccp/reference/data/values/#data.values.exponential_function):
      Computes the value for an exponential segment at a given x.
    - [`derivative_function`](../../../../afccp/reference/data/values/#data.values.derivative_function):
      Returns the derivative of the exponential function at a given x.
    - [`inverse_derivative_function`](../../../../afccp/reference/data/values/#data.values.inverse_derivative_function):
      Finds the x-value corresponding to a specific derivative magnitude for exponential functions.
    """

    if segment_dict is None:
        segment_dict = {1: {'x1': 0, 'y1': 0, 'x2': 0.2, 'y2': 0.8, 'rho': -0.2, 'r': 10},
                        2: {'x1': 0.2, 'y1': 0.8, 'x2': 0.3, 'y2': 1, 'rho': 0.2, 'r': 10},
                        3: {'x1': 0.5, 'y1': 1, 'x2': 0.7, 'y2': 0.8, 'rho': 0.2, 'r': 10},
                        4: {'x1': 0.7, 'y1': 0.8, 'x2': 1, 'y2': 0, 'rho': -0.2, 'r': 10}}

    # Collect segments
    segments = list(segment_dict.keys())
    num_segments = len(segments)

    # We need number of breakpoints for each exponential segment
    if num_breakpoints is None:
        num_breakpoints = 0
        for segment in segments:
            if 'r' in segment_dict[segment].keys():
                segment_dict[segment]['r'] = segment_dict[segment]['r']
            else:
                segment_dict[segment]['r'] = 10

            num_breakpoints += segment_dict[segment]['r']

    else:
        new_num_breakpoints = 0
        for segment in segments:
            if 'r' in segment_dict[segment].keys():
                segment_dict[segment]['r'] = max(int(num_breakpoints / num_segments), segment_dict[segment]['r'])
            else:
                segment_dict[segment]['r'] = int(num_breakpoints / num_segments)
            new_num_breakpoints += segment_dict[segment]['r']
        num_breakpoints = new_num_breakpoints

    # Number of breakpoints are determined based on which kinds of exponential segments we're using
    add_bp = False
    extra = False
    insert = False
    if (num_segments == 4 and segment_dict[2]['x2'] != segment_dict[3]['x1']) or num_segments == 2:
        a = np.zeros(num_breakpoints + 2)
        fhat = np.zeros(num_breakpoints + 2)
        extra = True
    elif num_segments == 1 and segment_dict[1]['x2'] < 1:
        a = np.zeros(num_breakpoints + 2)
        fhat = np.zeros(num_breakpoints + 2)
        add_bp = True
    elif num_segments == 1 and segment_dict[1]['x1'] != 0:
        a = np.zeros(num_breakpoints + 2)
        fhat = np.zeros(num_breakpoints + 2)
        fhat[0] = 1
        insert = True
    else:
        a = np.zeros(num_breakpoints + 1)
        fhat = np.zeros(num_breakpoints + 1)

    # Loop through each exponential segment
    i = 1
    for segment in segments:

        # Load variables
        x1 = segment_dict[segment]['x1']
        y1 = segment_dict[segment]['y1']
        x2 = segment_dict[segment]['x2']
        y2 = segment_dict[segment]['y2']
        rho = segment_dict[segment]['rho']
        r = segment_dict[segment]['r']

        # Necessary operations
        x_diff = x2 - x1
        y_diff = y2 - y1
        x_over_y = abs(x_diff / y_diff)
        if y_diff < 0:
            positive = False
        else:
            positive = True

        if derivative_locations:  # We place x breakpoints at fixed intervals based on derivative
            y_prime_i = round(derivative_function(0, x_over_y, rho, positive), 2)
            y_prime_f = round(derivative_function(x_over_y, x_over_y, rho, positive), 2)
            y_prime_step = (y_prime_f - y_prime_i) / r
            y_prime_arr = np.array([y_prime_i + y_prime_step * i for i in range(1, r + 1)])
            x_arr = np.array([
                inverse_derivative_function(y_prime, x_over_y, rho, positive) for y_prime in y_prime_arr])

        else:  # We place them at fixed intervals based on x
            x_arr = (np.arange(1, r + 1) / r) * x_over_y

        vals = np.array([exponential_function(x, 0, x_over_y, rho, positive) for x in x_arr])

        # If we need to add extra breakpoints
        if y1 == 1 and extra:
            a[i] = x1
            fhat[i] = 1
            i += 1

        if insert:
            a[1] = x1
            fhat[1] = 1
            a[2:2 + r] = x1 + x_arr * abs(y_diff)
            fhat[2:2 + r] = y2 + vals * abs(y_diff)
        else:
            a[i:i + r] = x1 + x_arr * abs(y_diff)
            if positive:
                fhat[i:i + r] = y1 + vals * y_diff
            else:
                fhat[i:i + r] = y2 + vals * abs(y_diff)
            i += r

            if add_bp:
                a[r + 1] = 1
                fhat[r + 1] = 1

    # Return breakpoint measures and values used in value function
    a = np.around(a, 5)
    fhat = np.around(fhat, 5)
    return a, fhat

exponential_function(x, x_i, x_f, rho, positive)

This function returns the value obtained from the specified exponential value function

Parameters:

Name Type Description Default
x

current x

 required
x_i

initial x from segment

 required
x_f

final x from segment

 required
rho

rho parameter

 required
positive

if we have an increasing function or not

 required

Returns:

Type Description

current y
Source code in afccp/data/values.py 
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def exponential_function(x, x_i, x_f, rho, positive):
    """
    This function returns the value obtained from the specified exponential value function
    :param x: current x
    :param x_i: initial x from segment
    :param x_f: final x from segment
    :param rho: rho parameter
    :param positive: if we have an increasing function or not
    :return: current y
    """
    if positive:
        y = (1 - exp(-(x - x_i) / rho)) / \
            (1 - exp(-(x_f - x_i) / rho))
    else:

        y = (1 - exp(-(x_f - x) / rho)) / \
            (1 - exp(-(x_f - x_i) / rho))

    return y

derivative_function(x, x_f, rho, positive)

This function calculates the derivative of x for some point along a line segment

Parameters:

Name Type Description Default
x

some x

 required
x_f

final x from segment

 required
rho

rho parameter

 required
positive

if we have an increasing function or not

 required

Returns:

Type Description

y_prime
Source code in afccp/data/values.py 
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def derivative_function(x, x_f, rho, positive):
    """
    This function calculates the derivative of x for some point
    along a line segment
    :param x: some x
    :param x_f: final x from segment
    :param rho: rho parameter
    :param positive: if we have an increasing function or not
    :return: y_prime
    """
    if positive:
        y_prime = exp(-x / rho) / (rho * (1 - exp(-x_f / rho)))
    else:
        y_prime = -exp(-(x_f - x) / rho) / (rho * (1 - exp(-x_f / rho)))
    return y_prime

inverse_derivative_function(y_prime, x_f, rho, positive)

This function calculates the position of x based on its derivative

Parameters:

Name Type Description Default
y_prime

first derivative of x

 required
x_f

final x from segment

 required
rho

rho parameter

 required
positive

if we have an increasing function or not

 required

Returns:

Type Description

x
Source code in afccp/data/values.py 
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def inverse_derivative_function(y_prime, x_f, rho, positive):
    """
    This function calculates the position of x based on its derivative
    :param y_prime: first derivative of x
    :param x_f: final x from segment
    :param rho: rho parameter
    :param positive: if we have an increasing function or not
    :return: x
    """
    if positive:
        x = -rho * log(rho * (1 - exp(-x_f / rho)) * y_prime)
    else:
        x = x_f + rho * log(-rho * (1 - exp(-x_f / rho)) * y_prime)

    return x

condense_value_functions(parameters, value_parameters)

Remove Redundant Zero Segments in Value Functions.

This procedure cleans up the value function breakpoints (a, f^hat) by removing unnecessary internal segments where the value remains zero, which do not affect the overall utility calculation but may clutter the optimization model.

Parameters:

  • parameters (dict): Dictionary of cadet/AFSC parameters (e.g., J, K^A, etc.).

  • value_parameters (dict): Dictionary of value and weight parameter arrays, including:

    • a: Breakpoint measures (list of lists by AFSC and objective index)
    • f^hat: Breakpoint values (list of lists by AFSC and objective index)

Returns:

  • value_parameters (dict): Updated dictionary with condensed a and f^hat arrays, where redundant zero-valued breakpoints have been removed.

Examples:

new_value_parameters = condense_value_functions(parameters, value_parameters)
Source code in afccp/data/values.py 
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def condense_value_functions(parameters, value_parameters):
    """
    Remove Redundant Zero Segments in Value Functions.

    This procedure cleans up the value function breakpoints (`a`, `f^hat`) by removing
    unnecessary internal segments where the value remains zero, which do not affect
    the overall utility calculation but may clutter the optimization model.

    Parameters:
    --------
    - parameters (dict): Dictionary of cadet/AFSC parameters (e.g., `J`, `K^A`, etc.).
    - value_parameters (dict): Dictionary of value and weight parameter arrays, including:

        - `a`: Breakpoint measures (list of lists by AFSC and objective index)
        - `f^hat`: Breakpoint values (list of lists by AFSC and objective index)

    Returns:
    --------
    - value_parameters (dict): Updated dictionary with condensed `a` and `f^hat` arrays,
      where redundant zero-valued breakpoints have been removed.

    Examples:
    --------
    ```python
    new_value_parameters = condense_value_functions(parameters, value_parameters)
    ```
    """

    # Shorthand
    p, vp = parameters, value_parameters
    for j in p['J']:
        for k in vp['K^A'][j]:
            a = np.array(vp['a'][j][k])
            fhat = np.array(vp['f^hat'][j][k])

            # Find unnecessary zeros
            zero_indices = np.where(fhat == 0)[0]
            last_i = len(a) - 1
            removals = []
            for i in zero_indices:
                if i + 1 in zero_indices and i + 1 != last_i and i != 0:
                    removals.append(i)

            # Remove unnecessary zeros
            vp['a'][j][k] = np.delete(a, removals)
            vp['f^hat'][j][k] = np.delete(fhat, removals)

    return vp

compare_value_parameters(parameters, vp1, vp2, vp1name, vp2name, printing=False)

Compare Two Sets of Value Parameters for Equality.

This function compares two dictionaries of value parameters used in cadet-AFSC utility modeling. It checks structural consistency (array shapes) and content equality across keys that define objective weights, constraints, value functions, and other relevant configurations.

Parameters:

  • parameters (dict): The shared cadet-AFSC parameter dictionary used for indexing and labels.
  • vp1 (dict): The first value parameter dictionary to compare.
  • vp2 (dict): The second value parameter dictionary to compare.
  • vp1name (str): Name label for the first value parameter set (used in print statements).
  • vp2name (str): Name label for the second value parameter set (used in print statements).
  • printing (bool, optional): If True, prints the first detected mismatch with context. Default is False.

Returns:

  • identical (bool): True if all structure and content matches exactly between the two value parameter sets; False otherwise.

Examples:

result = compare_value_parameters(p, vp_baseline, vp_candidate, 'Baseline', 'Candidate', printing=True)
if not result:
    print("Differences found between value parameter sets.")
Source code in afccp/data/values.py 
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def compare_value_parameters(parameters, vp1, vp2, vp1name, vp2name, printing=False):
    """
    Compare Two Sets of Value Parameters for Equality.

    This function compares two dictionaries of value parameters used in cadet-AFSC utility modeling.
    It checks structural consistency (array shapes) and content equality across keys that define
    objective weights, constraints, value functions, and other relevant configurations.

    Parameters:
    --------
    - parameters (dict): The shared cadet-AFSC parameter dictionary used for indexing and labels.
    - vp1 (dict): The first value parameter dictionary to compare.
    - vp2 (dict): The second value parameter dictionary to compare.
    - vp1name (str): Name label for the first value parameter set (used in print statements).
    - vp2name (str): Name label for the second value parameter set (used in print statements).
    - printing (bool, optional): If True, prints the first detected mismatch with context. Default is False.

    Returns:
    --------
    - identical (bool): True if all structure and content matches exactly between the two value parameter sets;
      False otherwise.

    Examples:
    --------
    ```python
    result = compare_value_parameters(p, vp_baseline, vp_candidate, 'Baseline', 'Candidate', printing=True)
    if not result:
        print("Differences found between value parameter sets.")
    ```
    """
    # Shorthand
    p = parameters

    # Assume identical until proven otherwise
    identical = True

    # Loop through each value parameter key
    for key in vp1:

        if np.shape(vp1[key]) != np.shape(vp2[key]):
            if printing:
                print(vp1name + ' and ' + vp2name + ' not the same. ' + key + ' is a different size.')
            identical = False
            break

        if key in ['afscs_overall_weight', 'cadets_overall_weight', 'cadet_weight_function', 'afsc_weight_function',
                   'cadets_overall_value_min', 'afscs_overall_value_min']:
            if vp1[key] != vp2[key]:
                if printing:
                    print(vp1name + ' and ' + vp2name + ' not the same. ' + key + ' is different.')
                identical = False
                break

        elif key in ['afsc_value_min', 'cadet_value_min', 'objective_value_min', 'value_functions', 'objective_target',
                     'objective_weight', 'afsc_weight', 'cadet_weight', 'I^C', 'J^C', 'value_functions',
                     'constraint_type']:
            if key not in ['objective_value_min', 'value_functions']:
                vp_1_arr, vp_2_arr = np.ravel(np.around(vp1[key], 4)), np.ravel(np.around(vp2[key], 4))
            else:
                vp_1_arr, vp_2_arr = np.ravel(vp1[key]), np.ravel(vp2[key])

            diff_arr = np.array([vp_1_arr[i] != vp_2_arr[i] for i in range(len(vp_1_arr))])
            if sum(diff_arr) != 0 and (vp1[key] != [] or vp2[key] != []):
                if printing:
                    print(vp1name + ' and ' + vp2name + ' not the same. ' + key + ' is different.')
                identical = False
                break

        elif key == 'a':  # Check the breakpoints

            for j in p['J']:
                afsc = p["afscs"][j]
                for k in vp1['K^A'][j]:
                    objective = vp1["objectives"][k]
                    for l in vp1['L'][j][k]:
                        try:
                            if vp1[key][j][k][l] != vp2[key][j][k][l]:
                                identical = False
                                if printing:
                                    print(vp1name + ' and ' + vp2name + ' not the same. '
                                                                        'Breakpoints are different for AFSC ' + afsc +
                                          ' Objective ' + objective + '.')
                                    print(vp1name + ":", vp1[key][j][k])
                                    print(vp2name + ":", vp2[key][j][k])
                                break
                        except:  # If there was a range error, then the breakpoints are not the same
                            identical = False
                            if printing:
                                print(vp1name + ' and ' + vp2name + ' not the same. '
                                                                    'Breakpoints are different for AFSC ' + afsc +
                                      ' Objective ' + objective + '.')
                                print(vp1name + ":", vp1[key][j][k])
                                print(vp2name + ":", vp2[key][j][k])
                            break
                    if not identical:
                        break
                if not identical:
                    break
            if not identical:
                break

    if identical and printing:
        print(vp1name + ' and ' + vp2name + ' are the same.')

    return identical

translate_vft_to_gp_parameters(instance)

Translates VFT (Value-Focused Thinking) Parameters to Goal Programming (GP) Model Parameters.

This function maps the VFT-based cadet-AFSC assignment model parameters stored in a CadetCareerProblem instance into a format suitable for a separate goal programming model structure (e.g., Rebecca's model). It builds constraint sets, cadet eligibility mappings, parameter values, and associated reward/penalty weights.

Parameters

  • instance : CadetCareerProblem An instance containing:

    • parameters (dict): Core cadet and AFSC parameter structures.
    • value_parameters (dict): Weighting schemes, objective values, and constraints.
    • gp_df (DataFrame): Reward and penalty configurations used in GP model.

Returns

  • gp : dict A dictionary of goal programming model parameters with the following structure:

  • Sets: A, C, A^, C^ for AFSCs and Cadets by constraint type.

  • Parameters: param for bounds and targets, utility, merit, Big_M, u_limit.
  • Reward/Penalty: lam^, mu^ representing incentive structures.
  • Constraint Types: con defines the list of all modeled constraints.

Notes

  • The model assumes AFSCs are indexed by A (0 to M-1), cadets by C (0 to N-1).

  • Constraint types include:

    • T: Target quotas (min)
    • F: Over-classification limits (max)
    • M, D_under, D_over, P: Education tier constraints
    • U_under, U_over: Bounds on USAFA proportions
    • R_under, R_over: Percentile constraints (e.g., merit)
    • W: Minimum preference coverage
    • Cadets’ eligible and expressed-preference AFSCs are stored in A^['E'] and A^['W^E'].
    • lam^['S'] rewards assignments that match cadet preferences in order of merit.
    • Constraint-specific cadet sets are available via C^[con], e.g., C^['D_under'].

Examples

gp_parameters = translate_vft_to_gp_parameters(instance)
Source code in afccp/data/values.py 
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def translate_vft_to_gp_parameters(instance):
    """
    Translates VFT (Value-Focused Thinking) Parameters to Goal Programming (GP) Model Parameters.

    This function maps the VFT-based cadet-AFSC assignment model parameters stored in a `CadetCareerProblem`
    instance into a format suitable for a separate goal programming model structure (e.g., Rebecca's model).
    It builds constraint sets, cadet eligibility mappings, parameter values, and associated reward/penalty weights.

    Parameters
    --------
    - instance : CadetCareerProblem
        An instance containing:

        - `parameters` (dict): Core cadet and AFSC parameter structures.
        - `value_parameters` (dict): Weighting schemes, objective values, and constraints.
        - `gp_df` (DataFrame): Reward and penalty configurations used in GP model.

    Returns
    --------
    - gp : dict
    A dictionary of goal programming model parameters with the following structure:

    - Sets: `A`, `C`, `A^`, `C^` for AFSCs and Cadets by constraint type.
    - Parameters: `param` for bounds and targets, `utility`, `merit`, `Big_M`, `u_limit`.
    - Reward/Penalty: `lam^`, `mu^` representing incentive structures.
    - Constraint Types: `con` defines the list of all modeled constraints.

    Notes
    --------
    - The model assumes AFSCs are indexed by `A` (0 to M-1), cadets by `C` (0 to N-1).
    - Constraint types include:

        - `T`: Target quotas (min)
        - `F`: Over-classification limits (max)
        - `M`, `D_under`, `D_over`, `P`: Education tier constraints
        - `U_under`, `U_over`: Bounds on USAFA proportions
        - `R_under`, `R_over`: Percentile constraints (e.g., merit)
        - `W`: Minimum preference coverage
    - Cadets’ eligible and expressed-preference AFSCs are stored in `A^['E']` and `A^['W^E']`.
    - `lam^['S']` rewards assignments that match cadet preferences in order of merit.
    - Constraint-specific cadet sets are available via `C^[con]`, e.g., `C^['D_under']`.

    Examples
    --------
    ```python
    gp_parameters = translate_vft_to_gp_parameters(instance)
    ```
    """

    # Shorthand
    p = instance.parameters
    vp = instance.value_parameters
    objectives = vp['objectives']

    # Other parameters
    large_afscs = np.where(p['pgl'] >= 40)[0]  # set of large AFSCs
    mand_k = np.where(objectives == 'Mandatory')[0][0]  # mandatory objective index
    des_k = np.where(objectives == 'Desired')[0][0]  # desired objective index
    perm_k = np.where(objectives == 'Permitted')[0][0]  # permitted objective index
    usafa_k = np.where(objectives == 'USAFA Proportion')[0][0]  # USAFA proportion objective index

    # Initialize "gp" dictionary (Goal Programming Model Parameters)
    gp = {}

    # Main sets
    A = np.arange(p['M'])
    C = np.arange(p['N'])
    gp['A'], gp['M'] = A, len(A)  # AFSCs, number of AFSCs
    gp['C'], gp['N'] = C, len(C)  # Cadets, number of Cadets

    # List of constraints
    gp['con'] = ['T',  # Target constraint
                 'F',  # Over-classification constraint
                 'M',  # Mandatory education constraint
                 'D_under',  # Desired education constraint (lower bound)
                 'D_over',  # Desired education constraint (upper bound)
                 'P',  # Permitted education constraint
                 'U_under',  # USAFA proportion constraint (lower bound)
                 'U_over',  # USAFA proportion constraint (upper bound)
                 'R_under',  # Percentile constraint (lower bound)
                 'R_over',  # Percentile constraint (upper bound)
                 'W']  # Cadet preference constraint

    # Subsets of AFSCs that pertain to each constraint (1 dimensional arrays)
    gp['A^'] = {'T': A,  # Subset of AFSCs with a minimum target quota: assumed all AFSCs
                'F': A,  # Subset of AFSCs with over-classification limits: assumed all AFSCs
                'M': np.array([a for a in A if 'Mandatory' in objectives[vp['K^A'][a]]]),  # Mandatory AFSCs
                'D_under': np.array([a for a in A if 'Increasing' in vp['value_functions'][a, des_k]]),  # Desired AFSCs
                'D_over': np.array([a for a in A if 'Decreasing' in vp['value_functions'][a, des_k]]),  # Desired AFSCs
                'P': np.array([a for a in A if 'Permitted' in objectives[vp['K^A'][a]]]),  # Permitted AFSCs
                'U_under': large_afscs,  # USAFA Proportion constrained AFSCs
                'U_over': large_afscs,  # USAFA Proportion constrained AFSCs
                'R_under': large_afscs,  # Percentile constrained AFSCs
                'R_over': large_afscs,  # Percentile constrained AFSCs
                'W': A}  # Subset of AFSCs with a cadet preference constraint: assumed all AFSCs

    # Subset of AFSCs for which each cadet is eligible (Replaced A | A^I)
    gp['A^']['E'] = p['J^E']

    # Subset of AFSCs that each cadet has placed a preference for
    A_Utility = [np.where(p['utility'][c, :] > 0)[0] for c in C]

    # Subset of AFSCs that each cadet has placed a preference for and is also eligible for
    gp['A^']['W^E'] = [np.intersect1d(A_Utility[c], gp['A^']['E'][c]) for c in C]

    # Subset of AFSCs which have an upper bound on the number of USAFA cadets
    gp['A^']['U_lim'] = np.array([a for a in A if ',' in vp['objective_value_min'][a, usafa_k]])

    # Set of cadets that have placed preferences on each of the AFSCs
    C_Utility = [np.where(p['utility'][:, a] > 0)[0] for a in A]

    # Subsets of Cadets that pertain to each constraint  (2 dimensional arrays)
    gp['C^'] = {'T': p['I^E'],  # Eligible Cadets for each AFSC
                'F': p['I^E'],  # Eligible Cadets for each AFSC
                'M': p['I^D']['Mandatory'],  # Cadets that have mandatory degrees for each AFSC
                'D_under': p['I^D']['Desired'],  # Cadets that have desired degrees for each AFSC
                'D_over': p['I^D']['Desired'],  # Cadets that have desired degrees for each AFSC
                'P': p['I^D']['Permitted'],  # Cadets that have permitted degrees for each AFSC
                'U_under': p['I^D']['USAFA Proportion'],  # Eligible USAFA Cadets for each AFSC
                'U_over': p['I^D']['USAFA Proportion'],  # Eligible USAFA Cadets for each AFSC
                'R_under': p['I^E'],  # Eligible Cadets for each AFSC
                'R_over': p['I^E'],  # Eligible Cadets for each AFSC

                # Eligible Cadets that have placed preferences for each AFSC
                'W': [np.intersect1d(C_Utility[a], p['I^E'][a]) for a in A]}

    # Subset of eligible cadets for each AFSC
    gp['C^']['E'] = p['I^E']

    # Subset of eligible usafa cadets for each AFSC
    gp['C^']['U'] = p['I^D']['USAFA Proportion']

    # Parameters for each of the constraints (1 dimensional arrays)
    gp['param'] = {'T': p['quota_min'],  # Target quotas
                   'F': p['quota_max'],  # Over-classification amounts
                   'M': vp['objective_target'][:, mand_k],  # Mandatory targets
                   'D_under': vp['objective_target'][:, des_k],  # Desired targets
                   'D_over': vp['objective_target'][:, des_k],  # Desired targets
                   'P': vp['objective_target'][:, perm_k],  # Permitted targets
                   'U_under': np.repeat(0.2, p['M']),  # USAFA Proportion lower bound
                   'U_over': np.repeat(0.4, p['M']),  # USAFA Proportion upper bound
                   'R_under': np.repeat(0.35, p['M']),  # Percentile lower bound
                   'R_over': np.repeat(0.65, p['M']),  # Percentile upper bound
                   'W': np.repeat(0.5, p['M'])}  # Cadet preference lower bound

    # Other parameters
    gp['utility'] = p['utility']  # utility matrix (replaced "w" since "w" was already a parameter in her model)
    gp['Big_M'] = 2000  # sufficiently large number
    gp['u_limit'] = 0.05  # limit on number of USAFA cadets for certain AFSCs
    gp['merit'] = p['merit']  # cadet percentiles

    # Penalty and Reward parameters
    columns = ['Normalized Penalty', 'Normalized Reward', 'Run Penalty', 'Run Reward']
    column_dict = {column: np.array(instance.gp_df[column]) for column in columns}

    # actual reward parameters
    reward = column_dict['Normalized Reward'] * column_dict['Run Reward']

    # actual penalty parameters
    penalty = column_dict['Normalized Penalty'] * column_dict['Run Penalty']

    # mu parameters (Penalties)
    gp['mu^'] = {con: penalty[index] for index, con in enumerate(gp['con'])}

    # lambda parameters (Rewards)
    gp['lam^'] = {con: reward[index] for index, con in enumerate(gp['con'])}
    gp['lam^']['S'] = reward[len(gp['con'])]  # extra reward for preference in order of merit

    return gp