optimize

Given a set of constraints and an objective function, find the optimal value. Z3 supports both hard constraints (must hold) and soft constraints (weighted preferences), as well as lexicographic multi-objective optimization. # Step 1: Formulate the problem Action: Write constraints and an objective using `(minimize ...)` or `(maximize ...)` directives, followed by `(check-sat)` and `(get-model)`. Expectation: A valid SMT-LIB2 formula with at least one optimization directive and all variables declared. Result: If the formula is well-formed, proceed to Step 2. For multi-objective problems, list directives in priority order for lexicographic optimization. Example: minimize `x + y` subject to `x >= 1`, `y >= 2`, `x + y <= 10`: ```smtlib (declare-const x Int) (declare-const y Int) (assert (>= x 1)) (assert (>= y 2)) (assert (<= (+ x y) 10)) (minimize (+ x y)) (check-sat) (get-model) ``` # Step 2: Run the optimizer Action: Invoke optimize.py with the formula or file path. Expectation: The script prints `sat` with the optimal assignment, `unsat`, `unknown`, or `timeout`. A run entry is logged to z3agent.db. Result: On `sat`: proceed to Step 3 to read the optimal values. On `unsat` or `timeout`: check constraints for contradictions or simplify. ```bash python3 scripts/optimize.py --file scheduling.smt2 python3 scripts/optimize.py --formula "<inline smt-lib2>" --debug ``` # Step 3: Interpret the output Action: Parse the objective value and satisfying assignment from the output. Expectation: `sat` with a model containing the optimal value, `unsat` indicating infeasibility, or `unknown`/`timeout`. Result: On `sat`: report the optimal value and assignment. On `unsat`: the constraints are contradictory, no feasible solution exists. On `unknown`/`timeout`: relax constraints or try **simplify**. # Parameters | Parameter | Type | Required | Default | Description | |-----------|------|----------|---------|-------------| | formula | string | no | | SMT-LIB2 formula with minimize/maximize | | file | path | no | | path to .smt2 file | | timeout | int | no | 60 | seconds | | z3 | path | no | auto | path to z3 binary | | debug | flag | no | off | verbose tracing | | db | path | no | .z3-agent/z3agent.db | logging database |