Improving solution diversity on NSGA-II for multi-objective clustering problems

Multi-objective optimization algorithms produce a set of solutions that are incomparable to each other in terms of solution quality. For some problems, the relationship between the decision and the optimization space does not guarantee that distant solutions in one of the spaces will also be distant in the other. So, solutions in a Pareto frontier can be similar in decision space. NSGA-II is one of the most used multi-objective evolutionary algorithms (MOEA). Its operator's decisions are based purely on the optimization space, so a diverse set of solutions in the Pareto frontier is not guaranteed. In this paper, we introduce modifications to NSGA-II operators to improve the solution diversity of the Pareto frontier for the gene expression multi-objective clustering problem. We propose two algorithms based on these modified operators DNSGA-II (Diverse NSGA-II) and DMNSGA-II (Diverse memetic NSGA-II). The algorithms were tested on four literature gene expression datasets. The results show that our proposals outperform NSGA-II in terms of solution diversity. Quality in most cases is compromised, but we obtained one case with high diversity and quality of solutions. The algorithms were also compared with other algorithms in literature from the applied area, finding better quality solutions in our proposal.