Constrained Optimization MCP Server

from returns.result import Success from usolver_mcp.models.ortools_models import ( Constraint, Objective, ObjectiveType, Problem, Variable, VariableType, ) from usolver_mcp.solvers.ortools_solver import solve_problem pytest_plugins: list[str] = [] def test_simple_boolean_satisfiability() -> None: """Test solving a simple boolean satisfiability problem. Problem: Find boolean values for x, y, z such that: - x OR y = True - y OR z = True - NOT x OR NOT z = True One valid solution: x=True, y=False, z=True """ problem = Problem( variables=[ Variable(name="x", type=VariableType.BOOLEAN), Variable(name="y", type=VariableType.BOOLEAN), Variable(name="z", type=VariableType.BOOLEAN), ], constraints=[ Constraint( expression="model.add_bool_or([x, y])", description="x OR y must be true", ), Constraint( expression="model.add_bool_or([y, z])", description="y OR z must be true", ), Constraint( expression="model.add_bool_or([x.Not(), z.Not()])", description="NOT x OR NOT z must be true", ), ], description="Simple boolean satisfiability problem", ) result = solve_problem(problem) assert isinstance(result, Success) solution = result.unwrap() # Check that the problem is feasible assert solution.is_feasible assert solution.status in ["FEASIBLE", "OPTIMAL"] # Check that we have values for all variables assert len(solution.values) == 3 assert all(var in solution.values for var in ["x", "y", "z"]) # Verify constraints are satisfied x, y, z = solution.values["x"], solution.values["y"], solution.values["z"] assert x or y # x OR y assert y or z # y OR z assert not x or not z # NOT x OR NOT z def test_integer_programming() -> None: """Test OR-Tools with integer variables. Problem: Find integers x, y such that: - 2x + 3y <= 14 - x + y >= 2 - x >= 0, y >= 0 - maximize x + 2y Expected solution: x=1, y=4 with objective value 9 """ problem = Problem( variables=[ Variable(name="x", type=VariableType.INTEGER, domain=(0, 10)), Variable(name="y", type=VariableType.INTEGER, domain=(0, 10)), ], constraints=[ Constraint( expression="model.add(2*x + 3*y <= 14)", description="Resource constraint", ), Constraint( expression="model.add(x + y >= 2)", description="Minimum production" ), ], objective=Objective(type=ObjectiveType.MAXIMIZE, expression="x + 2*y"), description="Integer programming problem", ) result = solve_problem(problem) assert isinstance(result, Success) solution = result.unwrap() assert solution.is_feasible assert solution.status in ["FEASIBLE", "OPTIMAL"] # Check constraint satisfaction x, y = solution.values["x"], solution.values["y"] assert 2 * x + 3 * y <= 14 assert x + y >= 2 assert x >= 0 and y >= 0 # Check that we found a good solution assert solution.objective_value is not None assert solution.objective_value >= 8 # Should be close to optimal def test_simple_scheduling() -> None: """Test a simple scheduling problem with OR-Tools. Problem: Schedule 2 tasks on 2 time slots - Each task must be scheduled exactly once - No two tasks can be scheduled at the same time """ problem = Problem( variables=[ Variable( name="schedule", type=VariableType.BOOLEAN, shape=[2, 2], # [tasks, time_slots] description="schedule[i][j] = task i is scheduled at time j", ), ], constraints=[ # Each task scheduled exactly once Constraint( expression="model.add(sum([schedule[0][t] for t in range(2)]) == 1)", description="Task 0 scheduled exactly once", ), Constraint( expression="model.add(sum([schedule[1][t] for t in range(2)]) == 1)", description="Task 1 scheduled exactly once", ), # No two tasks at same time Constraint( expression="model.add(sum([schedule[i][0] for i in range(2)]) <= 1)", description="At most one task at time 0", ), Constraint( expression="model.add(sum([schedule[i][1] for i in range(2)]) <= 1)", description="At most one task at time 1", ), ], description="Simple task scheduling problem", ) result = solve_problem(problem) assert isinstance(result, Success) solution = result.unwrap() assert solution.is_feasible assert solution.status in ["FEASIBLE", "OPTIMAL"] # Check solution structure schedule = solution.values["schedule"] assert len(schedule) == 2 # 2 tasks assert len(schedule[0]) == 2 # 2 time slots assert len(schedule[1]) == 2 # 2 time slots # Verify constraints # Each task scheduled exactly once assert sum(schedule[0]) == 1 assert sum(schedule[1]) == 1 # No conflicts at each time slot assert schedule[0][0] + schedule[1][0] <= 1 # time 0 assert schedule[0][1] + schedule[1][1] <= 1 # time 1 def test_infeasible_problem() -> None: """Test OR-Tools with an infeasible problem. Problem: Find boolean x such that: - x = True - x = False This should be infeasible. """ problem = Problem( variables=[ Variable(name="x", type=VariableType.BOOLEAN), ], constraints=[ Constraint(expression="model.add(x == True)", description="x must be true"), Constraint( expression="model.add(x == False)", description="x must be false" ), ], description="Infeasible boolean problem", ) result = solve_problem(problem) assert isinstance(result, Success) solution = result.unwrap() # Should be infeasible assert not solution.is_feasible assert solution.status in ["INFEASIBLE", "INVALID"] assert len(solution.values) == 0 # No solution values def test_optimization_with_arrays() -> None: """Test OR-Tools optimization with array variables. Problem: Binary knapsack with 3 items - Items have weights [2, 3, 4] and values [3, 4, 5] - Knapsack capacity is 5 - Maximize total value Expected: select items 0 and 1 for total value 7 """ problem = Problem( variables=[ Variable( name="selected", type=VariableType.BOOLEAN, shape=[3], # 3 items description="selected[i] = item i is selected", ), ], constraints=[ Constraint( expression="model.add(2*selected[0] + 3*selected[1] + 4*selected[2] <= 5)", description="Weight capacity constraint", ), ], objective=Objective( type=ObjectiveType.MAXIMIZE, expression="3*selected[0] + 4*selected[1] + 5*selected[2]", ), description="Binary knapsack problem", ) result = solve_problem(problem) assert isinstance(result, Success) solution = result.unwrap() assert solution.is_feasible assert solution.status in ["FEASIBLE", "OPTIMAL"] # Check solution selected = solution.values["selected"] assert len(selected) == 3 # Check constraint satisfaction total_weight = 2 * selected[0] + 3 * selected[1] + 4 * selected[2] assert total_weight <= 5 # Check that we found a good solution assert solution.objective_value is not None assert solution.objective_value >= 6 # Should find a decent solution