Hybridizing constraint consensus methods with evolutionary algorithms for constrained optimization

Abstract

Solving Constrained Optimization Problems (COPs) has been an important research topic in the optimization, operation research, and computer science domains. In COPs, an optimal solution must satisfy some feasibility condition which makes them harder when solving as compared to their unconstrained counterpart. In the literature, many Evolutionary Algorithms (EAs) have been reported for solving COPs. In those algorithms, the constraint handling is recognized as a very important component. However, almost all algorithms deal with constraints indirectly. Basically, in every generation, the constraint violation information is used to rank the individuals. Once the selection has been completed for crossover and mutation, those methodologies have no influence on the search process for constraint handling. This may be the reason for the slow convergence and the tendency to become trapped in local optima, when solving COPs using EAs. In this research, a Hybrid Evolutionary Algorithm (HEA), that combines EAs with Constraint Consensus (CC) methods, has been proposed. The CC methods are well-known search approaches that direct infeasible solutions towards the feasible space. Moreover, in the literature, there are many different CC methods with different characteristics. Such methods can rapidly improve the feasibility of individuals. So when combined with EAs, they can help the algorithm convergence faster. This thesis develops the HEAs that use either a single or a mix of three different CC methods with EAs. Two different EAs, namely Differential Evolution (DE) and Genetic Algorithm (GA), are tested with the CC methods. In addition, to show the applicability of the developed algorithm, a real world problem has been solved. HEA uses an adaptive mechanism to decide the appropriate mix of the CC methods in every generation. For further enhancement of the performance of HEA, a local search algorithm has also been included and tested. All of the above algorithms were run to solve a well-known set of 24 benchmark constrained problems. The experimental results show that the inclusion of CC methods with EAs, not only improves the quality of solutions, but also reduces the computational time. Overall, they are thus either better, or competitive, when compared with the state-of-the-art algorithms.