Combine & Conquer: Genetic Algorithm and CP for Optimization

Abstract

We introduce a new optimization method based on a Genetic Algorithm (GA) combined with Constraint Satisfaction Problem (CSP) techniques. The approach is designed for combinatorial problems whose search spaces are too large and/or objective functions too complex for usual CSP techniques and whose constraints are too complex for conventional genetic algorithm. The main idea is the handling of sub-domains of the CSP variables by the genetic algorithm. The population of the genetic algorithm is made up of strings of sub-domains whose adaptation are computed through the resolution of the corresponding ¤b-CSPs’ which are somehow much easier than the original problem. We provide basic and dedicated recombination and mutation operators with various degrees of robustness. The first set of experimentations adresses a naÏve formulation of a Vehicle Routing Problem (VRP). The results are quite encouraging as we outperform CSP techniques and genetic algorithm alone on these formulations

Genetic algorithms are well suited to the quick and global exploration of a large search space to optimize any objective function (even a “black box” one, i.e. no hypothesis is required on the function) and are able to provide several solutions of “good quality”.

Constraints satisfaction techniques are fitted to highly constrained problems for which the exhaustive exploration of their search spaces are conceivable. Such a method provides naturally feasible solutions

We suggest to take advantage of the two approaches by combining hybridizing them:

• use of constraint satisfaction to compute feasible solutions on a subspace of the search space

• use of a genetic algorithm to explore the space formed by the set of these subspaces and perform the optimization

• The ratio ρ of the size of a subspace to the size of the whole search space is the essential parameter of the hybridization: one can continuously pass from a pure CSP search (ρ = 1) to a pure stochastic search (ρ = 0, i.e a subspace is reduced to a single value).