Constrained genetic operators preserving feasibility of solutions in genetic algorithms

Most real-world optimisation problems consist of various nontrivial constraints that are difficult to handle in standard genetic algorithms (GAs). It prompted many researches to investigate this problem and many constraint handling methods have been proposed for GAs. Although these methods have successfully been used in a number of optimisation problems, they usually are computationally expensive or problem domain specific. In the paper we present an approach for preserving feasible solutions in GAs with the use of problem independent genetic operators for the search spaces that can be constrained with various types of constraint. It is based on the use of general purpose constraint consistency techniques to prune dynamically the search space that in general can be discontinuous and/or not convex, to its feasible portion simultaneously with the search process. The paper details a number of constrained genetic operators that extend standard genetic operators to take advantage of the provided constraint consistency in the search space. It includes constrained uniform initialization, constrained m-point and uniform crossovers, and constrained uniform and boundary mutations. The constrained genetic operators are illustrated for an example of combinatorial optimisation problems, generalized assignment problem.