Evolutionary multi and many-objective optimization via clustering for environmental selection

An improved differential evolution algorithm for multi-modal multi-objective optimization

Multi-modal multi-objective problems (MMOPs) have gained much attention during the last decade. These problems have two or more global or local Pareto optimal sets (PSs), some of which map to the same Pareto front (PF). This article presents a new affinity propagation clustering (APC) method based on the Multi-modal multi-objective differential evolution (MMODE) algorithm, called MMODE_AP, for the suit of CEC'2020 benchmark functions. First, two adaptive mutation strategies are adopted to balance exploration and exploitation and improve the diversity in the evolution process. Then, the affinity propagation clustering method is adopted to define the crowding degree in decision space (DS) and objective space (OS). Meanwhile, the non-dominated sorting scheme incorporates a particular crowding distance to truncate the population during the environmental selection process, which can obtain well-distributed solutions in both DS and OS. Moreover, the local PF membership of the solution is defined, and a predefined parameter is introduced to maintain of the local PSs and solutions around the global PS. Finally, the proposed algorithm is implemented on the suit of CEC'2020 benchmark functions for comparison with some MMODE algorithms. According to the experimental study results, the proposed MMODE_AP algorithm has about 20 better performance results on benchmark functions compared to its competitors in terms of reciprocal of Pareto sets proximity (rPSP), inverted generational distances (IGD) in the decision (IGDX) and objective (IGDF). The proposed algorithm can efficiently achieve the two goals, i.e., the convergence to the true local and global Pareto fronts along with better distributed Pareto solutions on the Pareto fronts.

Clustering Analysis for the Pareto Optimal Front in Multi-Objective Optimization

Bio-inspired algorithms are a suitable alternative for solving multi-objective optimization problems. Among different proposals, a widely used approach is based on the Pareto front. In this document, a proposal is made for the analysis of the optimal front for multi-objective optimization problems using clustering techniques. With this approach, an alternative is sought for further use and improvement of multi-objective optimization algorithms considering solutions and clusters found. To carry out the clustering, the methods k-means and fuzzy c-means are employed, in such a way that there are two alternatives to generate the possible clusters. Regarding the results, it is observed that both clustering algorithms perform an adequate separation of the optimal Pareto continuous fronts; for discontinuous fronts, k-means and fuzzy c-means obtain results that complement each other (there is no superior algorithm). In terms of processing time, k-means presents less execution time than fuzzy c-means.

An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering †

Previously, cluster-based multi or many objective function techniques were proposed to reduce the Pareto set. Recently, researchers proposed such techniques to find better solutions in the objective space to solve engineering problems. In this work, we applied a cluster-based approach for solution selection in a multiobjective evolutionary algorithm based on decomposition with bare bones particle swarm optimization for data clustering and investigated its clustering performance. In our previous work, we found that MOEA/D with BBPSO performed the best on 10 datasets. Here, we extend this work applying a cluster-based approach tested on 13 UCI datasets. We compared with six multiobjective evolutionary clustering algorithms from the existing literature and ten from our previous work. The proposed technique was found to perform well on datasets highly overlapping clusters, such as CMC and Sonar. So far, we found only one work that used cluster-based MOEA for clustering data, the hierarchical topology multiobjective clustering algorithm. All other cluster-based MOEA found were used to solve other problems that are not data clustering problems. By clustering Pareto solutions and evaluating new candidates against the found cluster representatives, local search is introduced in the solution selection process within the objective space, which can be effective on datasets with highly overlapping clusters. This is an added layer of search control in the objective space. The results are found to be promising, prompting different areas of future research which are discussed, including the study of its effects with an increasing number of clusters as well as with other objective functions.