simopt.models.chessmm

Simulate matching of chess players on an online platform.

Module Contents

simopt.models.chessmm.MEAN_ELO: Final[int] = 1200

simopt.models.chessmm.MAX_ALLOWABLE_DIFF: Final[int] = 150

class simopt.models.chessmm.ChessMatchmakingConfig

Bases: pydantic.BaseModel

Configuration model for Chess Matchmaking simulation.

A model that simulates a matchmaking problem with a Elo (truncated normal) distribution of players and Poisson arrivals and returns the average difference between matched players.

elo_mean: Annotated[float, Field(default=MEAN_ELO, description='mean of normal distribution for Elo rating', gt=0)]

elo_sd: Annotated[float, Field(default=round(MEAN_ELO / (np.sqrt(2) * special.erfcinv(1 / 50)), 1), description='standard deviation of normal distribution for Elo rating', gt=0)]

poisson_rate: Annotated[float, Field(default=1.0, description='rate of Poisson process for player arrivals', gt=0)]

num_players: Annotated[int, Field(default=1000, description='number of players', gt=0)]

allowable_diff: Annotated[float, Field(default=MAX_ALLOWABLE_DIFF, description='maximum allowable difference between Elo ratings', gt=0)]

class simopt.models.chessmm.ChessAvgDifferenceConfig

Bases: pydantic.BaseModel

Configuration model for Chess Average Difference Problem.

A problem configuration that minimizes the average difference in Elo ratings between matched chess players while maintaining wait time constraints.

initial_solution: Annotated[tuple[float, Ellipsis], Field(default=MAX_ALLOWABLE_DIFF, description='initial solution')]

budget: Annotated[int, Field(default=1000, description='max # of replications for a solver to take', gt=0, json_schema_extra={'isDatafarmable': False})]

upper_time: Annotated[float, Field(default=5.0, description='upper bound on wait time', gt=0)]

class simopt.models.chessmm.EloInputModel

Bases: simopt.input_models.InputModel

Input model for player Elo ratings.

rng: random.Random | None = None

random(mean: float, std: float, min_rating: float, max_rating: float) → float

Draw a truncated normal rating within [min_rating, max_rating].

class simopt.models.chessmm.ChessMatchmaking(fixed_factors: dict | None = None)

Bases: simopt.base.Model

Matchmaking model following an Elo distribution.

A model that simulates a matchmaking problem with a Elo (truncated normal) distribution of players and Poisson arrivals and returns the average difference between matched players.

Initialize the ChessMatchmaking model.

Parameters:

fixed_factors (dict, optional) – Fixed factors for the model. Defaults to None.

class_name_abbr: ClassVar[str] = 'CHESS'

Short name of the model class.

class_name: ClassVar[str] = 'Chess Matchmaking'

Long name of the model class.

config_class: ClassVar[type[pydantic.BaseModel]]

Configuration class for the model.

n_rngs: ClassVar[int] = 2

Number of RNGs used to run a simulation replication.

n_responses: ClassVar[int] = 2

Number of responses (performance measures).

elo_model

arrival_model

before_replicate(rng_list: list[mrg32k3a.mrg32k3a.MRG32k3a]) → None

Prepare the model just before generating a replication.

Parameters:

rng_list (list[MRG32k3a]) – RNGs used to drive the simulation.

Raises:

NotImplementedError – If the subclass does not implement this hook.

replicate() → tuple[dict, dict]

Simulate a single replication for the current model factors.

Parameters:

rng_list (list[MRG32k3a]) – List of random number generators used to simulate the replication.

Returns:

A tuple containing:

• dict: Performance measures of interest, including:

  • ”avg_diff”: Average Elo difference between all pairs.

  • ”avg_wait_time”: Average waiting time.

• dict[str, dict]: Gradient estimates for each response.

Return type:

tuple[dict, dict[str, dict]]

class simopt.models.chessmm.ChessAvgDifference(name: str = '', fixed_factors: dict | None = None, model_fixed_factors: dict | None = None)

Bases: simopt.base.Problem

Base class to implement simulation-optimization problems.

Initialize a problem object.

Parameters:

• name (str) – Name of the problem.

• fixed_factors (dict | None) – Dictionary of user-specified problem factors.

• model_fixed_factors (dict | None) – Subset of user-specified non-decision factors passed to the model.

class_name_abbr: ClassVar[str] = 'CHESS-1'

Short name of the problem class.

class_name: ClassVar[str] = 'Min Avg Difference for Chess Matchmaking'

Long name of the problem class.

config_class: ClassVar[type[pydantic.BaseModel]]

Configuration class for problem.

model_class: ClassVar[type[simopt.base.Model]]

Simulation model class for problem.

n_objectives: ClassVar[int] = 1

Number of objectives.

n_stochastic_constraints: ClassVar[int] = 1

Number of stochastic constraints.

minmax: ClassVar[tuple[int, Ellipsis]]

Indicators of maximization (+1) or minimization (-1) for each objective.

constraint_type: ClassVar[simopt.base.ConstraintType]

Description of constraints types.

variable_type: ClassVar[simopt.base.VariableType]

Description of variable types.

gradient_available: ClassVar[bool] = False

Indicates whether the solver provides direct gradient information.

optimal_value: ClassVar[float | None] = None

Optimal objective function value (if known).

optimal_solution: tuple | None = None

Optimal solution if known; defaults to None.

model_default_factors: ClassVar[dict]

Default values for overriding model-level default factors.

model_decision_factors: ClassVar[set[str]]

Set of keys for factors that are decision variables.

property dim: int

Number of decision variables.

property lower_bounds: tuple

Lower bound for each decision variable.

property upper_bounds: tuple

Upper bound for each decision variable.

vector_to_factor_dict(vector: tuple) → dict

Convert a vector of variables to a dictionary with factor keys.

Parameters:

vector (tuple) – A vector of values associated with decision variables.

Returns:

Dictionary with factor keys and associated values.

Return type:

dict

factor_dict_to_vector(factor_dict: dict) → tuple

Convert a dictionary with factor keys to a vector of variables.

Parameters:

factor_dict (dict) – Dictionary with factor keys and associated values.

Returns:

Vector of values associated with decision variables.

Return type:

tuple

replicate(_x: tuple) → simopt.base.RepResult

Replicate the problem for a given solution.

Parameters:

x (tuple) – The solution to evaluate.

check_deterministic_constraints(x: tuple) → bool

Check if a solution x satisfies the problem’s deterministic constraints.

Parameters:

x (tuple) – A vector of decision variables.

Returns:

True if the solution satisfies all deterministic constraints;

False otherwise.

Return type:

bool

get_random_solution(rand_sol_rng: mrg32k3a.mrg32k3a.MRG32k3a) → tuple

Generate a random solution for starting or restarting solvers.

Parameters:

rand_sol_rng (MRG32k3a) – Random number generator used to sample the solution.

Returns:

A tuple representing a randomly generated vector of decision

variables.

Return type:

tuple