Multi-objective Optimisation by Co-operative Co-evolution

This paper presents the integration between a co-operative co-evolutionary genetic algorithm (CCGA) and four evolutionary multiobjective optimisation algorithms (EMOAs): a multi-objective genetic algorithm (MOGA), a niched Pareto genetic algorithm (NPGA), a nondominated sorting genetic algorithm (NSGA) and a controlled elitist nondominated sorting genetic algorithm (CNSGA). The resulting algorithms can be referred to as co-operative co-evolutionary multi-objective optimisation algorithms or CCMOAs. The CCMOAs are benchmarked against the EMOAs in seven test problems. The first six problems cover different characteristics of multi-objective optimisation problems, namely convex Pareto front, non-convex Pareto front, discrete Pareto front, multimodality, deceptive Pareto front and non-uniformity of solution distribution. In contrast, the last problem is a two-objective real-world problem, which is generally referred to as the continuum topology design. The results indicate that the CCMOAs are superior to the EMOAs in terms of the solution set coverage, the average distance from the non-dominated solutions to the true Pareto front, the distribution of the non-dominated solutions and the extent of the front described by the non-dominated solutions.