A Delaunay Triangulation Based Density Measurement for Evolutionary Multi-objective Optimization Yutao Qi 1( ✉ ) , Minglei Yin 1 , and Xiaodong Li 2 1 School of Computer Science and Technology, Xidian University, Xi’an, China ytqi@xidan.edu.cn 2 School of Computer Science and IT, RMIT University, Melbourne, Australia Abstract. Diversity preservation is a critical issue in evolutionary multi- objective optimization algorithms (MOEAs), it has significant influence on the quality of final solution set. In this wok, a crowding density measurement is developed for preserving diversity in MOEAs by using the Delaunay triangulation mesh built on the population in the objective space. Base on the property of the Delaunay triangulation, the new density measurement considers both the Eucli‐ dean distance and the relative position between individuals, and thus provide a more accurate estimation of the density around a specific individual within the population. Experimental results indicate that the suggested density measurement help to improve the performance of MOEAs significantly. Keywords: Evolutionary multi-objective optimization · Diversity preservation · Delaunay triangulation · Density measurement 1 Introduction Multi-objective optimization problem (MOP) is a category of problems that optimize two or more conflicting objectives simultaneously [1]. Different from single-objective optimization problems, a MOP usually has no unique solution that meets all the objec‐ tives. Instead, there exist some trade-off solutions which are known as the Pareto optimal solutions. The collection of all the Pareto optimal solutions in the decision space is termed as the Pareto set (PS) whose image in the objective space is called the Pareto front (PF). As it is time-consuming or even impossible to obtain the whole PF, the aim of a multi-objective optimizer is to find a representative set of non-dominated solutions that approximates the PF as closely as possible and spreads evenly along the PF. Provided with an approximated set of the PF, a decision maker would have a better understanding of the target MOP and thus make more reasonable decisions. Among existing multi-objective optimization approaches, multi-objective optimi‐ zation evolutionary algorithms (MOEAs) are recognized as one of the most successful techniques. By evolving a population of solutions, MOEAs can provide a required set of non-dominated solutions in a single run, which is significant advantage over tradi‐ tional approaches [2]. Since the pioneer work by Schaffer [3] who first combined the traditional multi-objective optimization technique with evolutionary computation, many © Springer International Publishing Switzerland 2016 T. Ray et al. (Eds.): ACALCI 2016, LNAI 9592, pp. 183–192, 2016. DOI: 10.1007/978-3-319-28270-1_16