solve_constraint_model

Solve a general constraint or optimization model.

This tool solves discrete optimization and constraint satisfaction problems. It supports integer and boolean variables, linear constraints, global constraints (all_different, element, table), implications, and linear objectives.

Use cases include:

• Project scheduling and resource allocation

• Sudoku and logic puzzles

• Configuration optimization

• Tool/model selection under constraints

• Routing and assignment problems

• Budget allocation

Args: mode: Solver mode - 'satisfy' to find any feasible solution, 'optimize' to find the best solution according to the objective. variables: List of decision variables, each with: - id (str): Unique identifier - domain (dict): Domain specification with: - type (str): 'bool' or 'integer' - lower (int): Lower bound for integers (default 0) - upper (int): Upper bound for integers (default 1) - metadata (dict, optional): Context for explanations constraints: List of constraints, each with: - id (str): Unique identifier - kind (str): Constraint type - 'linear', 'all_different', 'element', 'table', or 'implication' - params (dict): Constraint-specific parameters: For 'linear': terms (list of {var, coef}), sense ('<=', '>=', '=='), rhs (number) For 'all_different': vars (list of variable ids) For 'element': index_var (str), array (list of int), target_var (str) For 'table': vars (list of str), allowed_tuples (list of lists) For 'implication': if_var (str), then (nested constraint dict) - metadata (dict, optional): Description and context objective: Optional objective function (required if mode='optimize'): - sense (str): 'min' or 'max' - terms (list): Linear terms as {var, coef} - metadata (dict, optional): Description search: Optional search configuration: - max_time_ms (int): Maximum solver time in milliseconds - max_solutions (int): Maximum solutions to return (default 1)

Returns: SolveConstraintModelResponse containing: - status: 'optimal', 'feasible', 'satisfied', 'infeasible', 'unbounded', 'timeout', or 'error' - objective_value: Objective value if applicable - solutions: List of solutions with variable assignments - explanation: Human-readable summary and binding constraints

Tips for LLMs: - Start with a small model to test; gradually add complexity. - For Sudoku: use 'all_different' constraints for rows, columns, and blocks. - For scheduling: use linear constraints for precedence and capacity. - Variable metadata is useful for building readable explanations. - Constraint metadata helps identify which constraints are tight. - If infeasible, check constraint metadata to diagnose conflicts. - Use 'satisfy' mode for puzzles; 'optimize' mode for cost/time minimization.

Example (simple knapsack): python response = await solve_constraint_model( mode="optimize", variables=[ {"id": "take_item_1", "domain": {"type": "bool"}}, {"id": "take_item_2", "domain": {"type": "bool"}}, ], constraints=[ { "id": "capacity", "kind": "linear", "params": { "terms": [ {"var": "take_item_1", "coef": 3}, {"var": "take_item_2", "coef": 5}, ], "sense": "<=", "rhs": 7, }, } ], objective={ "sense": "max", "terms": [ {"var": "take_item_1", "coef": 10}, {"var": "take_item_2", "coef": 15}, ], }, )