A clustering multi-objective evolutionary algorithm based on orthogonal and uniform design

Abstract

Abstract-Designing efficient algorithms for difficult multiobjective optimization problems is a very challenging problem. In this paper a new clustering multi-objective evolutionary algorithm based on orthogonal and uniform design is proposed. First, the orthogonal design is used to generate initial population of points that are scattered uniformly over the feasible solution space, so that the algorithm can evenly scan the feasible solution space once to locate good points for further exploration in subsequent iterations. Second, to explore the search space efficiently and get uniformly distributed and widely spread solutions in objective space, a new crossover operator is designed. Its exploration focus is mainly put on the sparse part and the boundary part of the obtained non-dominated solutions in objective space. Third, to get desired number of well distributed solutions in objective space, a new clustering method is proposed to select the non-dominated solutions. Finally, experiments on thirteen very difficult benchmark problems were made, and the results indicate the proposed algorithm is efficient.

A multi-objective differential evolution approach based on ε-elimination uniform-diversity for mechanism design

“…The proposed algorithm executed 30 times for each test function and the average results obtained by MUDE are compared with the results of all the algorithms participating in the CEC 2009 competition (Zhang et al 2009b;Chen et al 2009;Huang et al 2009;Liu and Li 2009;Gao et al 2009;Kukkonen and Lampinen 2009;Qu and Suganthan 2009;Sindhya et al 2009;Tiwari et al 2009;Tseng and Chen 2009;Wang et al 2009;Zamuda et al 2009), as well as two other more recent multi-objective optimization algorithms (Venkata Rao and Patel 2013; Akbari and Ziarati 2012). The performance indicator used to quantify the quality of the obtained results is the IGD (Inverted Generational distance) Metric (Zhang et al 2009a).…”

An Evolutionary Algorithm with Double-Level Archives for Multiobjective Optimization

“…These efforts include clustering the candidate individuals [18], [19] to achieve highly spreading population, using multiple populations [15], quantizing the solution space for selection [46], using dynamic multiple populations [16], [17], devising new strategies to estimate the density of objective space, territory definition around each individual [35], and estimating the density of solution space [30].…”

“…Another group in this category designs population distribution strategies to achieve a good distribution of solutions. Strategies include, using multiple populations [15] and dynamic multiple populations [16], [17], clustering the candidate individuals [18], [19], and devising new strategies to estimate the density of objective space. In most algorithms that work at the problem level, the distribution of solutions on the PF is controlled implicitly at the multiobjective problem level with the optimization operators, and adapts to different shapes of PF.…”

An improved version of the multiple trajectory search for real value multi-objective optimization problems

“…The following algorithms were presented in this competition: MOEADGM (Chen, Chen, and Zhang 2009), OMOEAII (Gao et al 2009), OWMOSaDE (Huang et al 2009), GDE3 (Kukkonen and Lampinen 2009), LiuLi Algorithm , DMOEADD ), MOEA/D (Zhang, Liu, and Li 2009), MOEP (Qu and Suganthan 2009), NSGAII-LS (Sindhya et al 2009), AMGA (Tiwari et al 2009), multiple trajectory search (MTS) (Tseng and Chen 2009), ClusteringMOEA (Wang et al 2009) and DECMOSA-SQP (Zamuda et al 2009). In the competition on unconstrained multi-objective optimization, MOEA/D was the winner and MTS was ranked the second best.…”