SMT-based Verification Applied to Non-convex Optimization Problems

Abstract

This paper presents a novel, complete, and flexible optimization algorithm, which relies on recursive executions that re-constrains a model-checking procedure based on Satisfiability Modulo Theories (SMT). This SMT-based optimization technique is able to optimize a wide range of functions, including non-linear and non-convex problems using fixed-point arithmetic. Although SMT-based optimization is not a new technique, this work is the pioneer in solving non-linear and non-convex problems based on SMT; previous applications are only able to solve integer and rational linear problems. The proposed SMT-based optimization algorithm is compared to other traditional optimization techniques. Experimental results show the efficiency and effectiveness of the proposed algorithm, which finds the optimal solution in all evaluated benchmarks, while traditional techniques are usually trapped by local minima.

Counterexample guided inductive optimization based on satisfiability modulo theories

“…This study extends the previous work of Araújo et al [13] and presents three variants of a counterexample guided inductive optimization approach based on SMT solvers, which improve the technique performance for specific class of functions. Furthermore, the experimental evaluation is largely expanded, since the algorithms are executed for additional optimization problems and the performance of each proposed algorithm is compared to six well-known optimization techniques.…”

“…The generalized algorithm can be used for any constrained optimization problem and presents minor improvements w.r.t. Araújo et al [13]. The simplified algorithm is faster than the generalized one and can be employed if information about the minima location is provided, e.g., the cost function is semi-definite positive.…”

Counterexample guided inductive optimization applied to mobile robots path planning

“…In particular, CEGIO relies on iterative executions to constrain a verification procedure, in order to perform inductive generalization, based on counterexamples extracted from SAT and SMT solvers. CEGIO is able to successfully optimize a wide range of functions, including non-linear and non-convex optimization problems based on SAT and SMT solvers, in which data provided by counterexamples are employed to guide the verification engine, thus reducing the optimization domain [13]. The function evaluation and the search for the optimal solution are performed by means of an iterative execution of successive verifications based on counterexamples extracted from SAT and SMT solvers.…”

“…The verification process consists of three steps: modeling, especification, and verification [13]. Thus, the optimization problem described in section III-A is encoded as shown in Figure 1.…”

“…The smoothness is not required from the path planning algorithm, but it is provided by a trajectory planning algorithm that computes the curves between the points of the path, i.e., a trajectory planning Define the constraint J(L (i) ) < J(L (i−1) ) with directive ASSUME; 11 Verify the satisfiability of J optimal given by Eq. (7); 12 Update L * = L (i) e J(L * ) = J(L (i) ) based on the counterexample; 13 Do i = i + 1; 14 while ¬J optimal is satisfiable; 15 if ¬J optimal is not consecutively satisfiable then algorithm is responsible for interpolating the points found by the path planning.…”