| name | optimize |
| description | Solve constrained optimization problems using Z3. Supports minimization and maximization of objective functions over integer, real, and bitvector domains. |
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:
(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.
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 |
