Multi-objective adaptive differential evolution algorithm for combinatorial optimisation

In this paper we propose an adaptive metaheuristic algorithm based on differential evolution (DE) for solving combinatorial optimization problems. DE is a heuristic method that has yielded promising results for solving complex optimization problems. The potentialities of DE are its simple structure, easy use, convergence property, quality of solution, and robustness. In order to avoid the difficult task of parameter setting, an adaptive feature is introduced into the algorithm. The resulting adaptive DE algorithm is built with typical features like Pareto dominance, density estimation, and an external archive to store the non-dominated solutions in order to handle multiple objectives. The performance of the proposed multi-objective adaptive DE algorithm is demonstrated by solving a hybrid laminate composite pressure vessel problem subjected to both combinatorial as well as design constraints. Further, the proposed algorithm is compared with three state-of-the-art multi-objective optimizers: Non-dominated sorting Genetic Algorithm (NSGA-II), Pareto Archived Evolutionary Strategy (PAES) and multi-objective particle swarm optimisation(MPSO). The studies presented in this paper indicate that proposed algorithm produces very competitive Pareto fronts according to the applied convergence metric and it clearly outperforms the other three algorithms.