Towards a Better Balance of Diversity and Convergence in NSGA-III: First Results

Over the last few decades we have experienced a plethora of successful optimization concepts, algorithms, techniques and softwares. Each trying to excel in its own niche. Logically, combining a carefully selected subset of them may deliver a novel approach that brings together the best of some those previously independent worlds. The span of applicability of the new approach and the magnitude of improvement are completely dependent on the selected techniques and the level of perfection in weaving them together. In this study, we combine NSGA-III with local search and use the recently proposed Karush-Kuhn-Tucker Proximity Measure KKTPM to guide the whole process. These three carefully selected building blocks are intended to perform well on several levels. Here, we focus on Diversity and Convergence DC-NSGA-III, hence we use Local Search and KKTPM respectively, in the course of a multi/many objective algorithm NSGA-III. The results show how DC-NSGA-III can significantly improve performance on several standard multi- and many-objective optimization problems.

[1]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[2]  Kalyanmoy Deb,et al.  A Local Search Based Evolutionary Multi-objective Optimization Approach for Fast and Accurate Convergence , 2008, PPSN.

[3]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

[4]  Kalyanmoy Deb,et al.  Towards faster convergence of evolutionary multi-criterion optimization algorithms using Karush Kuhn Tucker optimality based local search , 2017, Comput. Oper. Res..

[5]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[6]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

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

[8]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[9]  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.

[10]  Kalyanmoy Deb,et al.  An Optimality Theory-Based Proximity Measure for Set-Based Multiobjective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[11]  Kalyanmoy Deb,et al.  Towards a Better Diversity of Evolutionary Multi-Criterion Optimization Algorithms using Local Searches , 2016, GECCO.

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

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

[14]  Kalyanmoy Deb,et al.  Approximate KKT points and a proximity measure for termination , 2013, J. Glob. Optim..

[15]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[16]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[17]  Joshua D. Knowles,et al.  M-PAES: a memetic algorithm for multiobjective optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[18]  Peter A. N. Bosman,et al.  On Gradients and Hybrid Evolutionary Algorithms for Real-Valued Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.