Um novo método de otimização baseado em teorias de satisfatibilidade

Abstract

This work presents a new method of optimization applied to different classes of problems, such as non-convex and convex. The methodology consists in the use the counterexample generated from the model checking technique based on Boolean satisfiability theory (SAT) and satisfiability modulo theory (SMT), to guide the optimization process. Three algorithms of optimization are developed: Generic Algorithm, applied to any class of optimization problem, it will be used in the optimization of non-convex functions, Simplified Algorithm, used in the optimization of functions in which there is some previous knowledge, e. g., semi-defined or defined positive functions and Fast Algorithm, used to optimize convex functions. In addition, convergence proofs are provided for the respective algorithms. The algorithms are implemented using two model verifiers, CBMC which uses the SAT-based MiniSAT solver as back-end, and the ESBMC, which supports SMT-based solvers, such as Z3, Boolector and MathSAT. For perfomance evaluation, the algorithms are applied to a set of thirty functions taken from the literature and used to test optimization algorithms, they are also compared with traditional optimization algorithms usually used in solving non-convex optimization problems, such as genetic algorithm, particle swarm, pattern search, simulated annealing and nonlinear programming. Through the analysis of the results it can be concluded that the developed algorithms are suitable the classes of functions for which they were developed and have a higher rate of success in the search for the optimal value in comparison with the other algorithms. Finally, the developed methodology is applied to solve optimization problems in the context of the two-dimensional path planning for autonomous mobile robots.