Use of Reference Point Sets in a Decomposition-Based Multi-Objective Evolutionary Algorithm

In recent years, decomposition-based multi-objective evolutionary algorithms (MOEAs) have gained increasing popularity. However, these MOEAs depend on the consistency between the Pareto front shape and the distribution of the reference weight vectors. In this paper, we propose a decomposition-based MOEA, which uses the modified Euclidean distance (\(d^+\)) as a scalar aggregation function. The proposed approach adopts a novel method for approximating the reference set, based on an hypercube-based method, in order to adapt the reference set for leading the evolutionary process. Our preliminary results indicate that our proposed approach is able to obtain solutions of a similar quality to those obtained by state-of-the-art MOEAs such as MOMBI-II, NSGA-III, RVEA and MOEA/DD in several MOPs, and is able to outperform them in problems with complicated Pareto fronts.

[1]  Xin Yao,et al.  A benchmark test suite for evolutionary many-objective optimization , 2017 .

[2]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[3]  Carlos A. Coello Coello,et al.  IGD+-EMOA: A multi-objective evolutionary algorithm based on IGD+ , 2016, CEC.

[4]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[5]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[6]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[7]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[8]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[9]  Hisao Ishibuchi,et al.  Modified Distance Calculation in Generational Distance and Inverted Generational Distance , 2015, EMO.

[10]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[11]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

[12]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[13]  Carlos A. Coello Coello,et al.  A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm , 2004, MICAI.

[14]  Carlos A. Coello Coello,et al.  Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization , 2015, GECCO.

[15]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[16]  Carlos A. Coello Coello,et al.  MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator , 2013, 2013 IEEE Congress on Evolutionary Computation.