Comparison study of large-scale optimisation techniques on the LSMOP benchmark functions

In this paper, we study the performance of three popular large-scale optimisation algorithms on the recently proposed large-scale many-objective optimisation problems (LSMOP). We briefly explain the three methods (MOEA/DVA, LMEA and WOF) and give an overview of their use and performance in the literature. For the Weighted Optimization Framework (WOF), we propose a new transformation function to eliminate the parameter needed in its previous version. In our experiments, we compare the three algorithms on the LSMOP1-9 functions with 2 and 3 objectives and up to 1006 decision variables. The special focus of our study is on the convergence speed and behaviour, since MOEA/DVA and LMEA, in contrast to WOF, need huge computational budgets to obtain variable groups prior to optimisation. Our experiments show that MOEA/DVA and WOF perform significantly better than LMEA on almost all instances and WOF further outperforms MOEA/DVA significantly in most of the 1006-variable problems, in solution quality as well as convergence speed. In most instances the WOF only needs 0.1% to 10% of the total evaluations to outperform the final solution sets obtained by LMEA and MOEA/DVA.

[1]  Enrique Alba,et al.  SMPSO: A new PSO-based metaheuristic for multi-objective optimization , 2009, 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making(MCDM).

[2]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[3]  Carlos A. Coello Coello,et al.  Use of cooperative coevolution for solving large scale multiobjective optimization problems , 2013, 2013 IEEE Congress on Evolutionary Computation.

[4]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[5]  Ye Tian,et al.  PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] , 2017, IEEE Computational Intelligence Magazine.

[6]  Hisao Ishibuchi,et al.  A Framework for Large-Scale Multiobjective Optimization Based on Problem Transformation , 2018, IEEE Transactions on Evolutionary Computation.

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

[8]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

[9]  Markus Olhofer,et al.  Test Problems for Large-Scale Multiobjective and Many-Objective Optimization , 2017, IEEE Transactions on Cybernetics.

[10]  Xiaodong Li,et al.  Effective decomposition of large-scale separable continuous functions for cooperative co-evolutionary algorithms , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[11]  Yuan Sun,et al.  Extended Differential Grouping for Large Scale Global Optimization with Direct and Indirect Variable Interactions , 2015, GECCO.

[12]  Xin Yao,et al.  Large scale evolutionary optimization using cooperative coevolution , 2008, Inf. Sci..

[13]  Jun Zhang,et al.  A random-based dynamic grouping strategy for large scale multi-objective optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[14]  Fang Liu,et al.  A Multiobjective Evolutionary Algorithm Based on Decision Variable Analyses for Multiobjective Optimization Problems With Large-Scale Variables , 2016, IEEE Transactions on Evolutionary Computation.

[15]  Xiaodong Li,et al.  Cooperatively Coevolving Particle Swarms for Large Scale Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[16]  Xiaodong Li,et al.  A Cooperative Coevolutionary Multiobjective Algorithm Using Non-dominated Sorting , 2004, GECCO.

[17]  Xiaodong Li,et al.  Tackling high dimensional nonseparable optimization problems by cooperatively coevolving particle swarms , 2009, 2009 IEEE Congress on Evolutionary Computation.

[18]  An adaptive configuration of differential evolution algorithms for big data , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[19]  Hisao Ishibuchi,et al.  Mutation operators based on variable grouping for multi-objective large-scale optimization , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[20]  Hisao Ishibuchi,et al.  Weighted Optimization Framework for Large-scale Multi-objective Optimization , 2016, GECCO.

[21]  Ye Tian,et al.  A Decision Variable Clustering-Based Evolutionary Algorithm for Large-Scale Many-Objective Optimization , 2018, IEEE Transactions on Evolutionary Computation.

[22]  Jing Liu,et al.  A multi-objective memetic algorithm based on decomposition for big optimization problems , 2016, Memetic Comput..

[23]  Shahryar Rahnamayan,et al.  Metaheuristics in large-scale global continues optimization: A survey , 2015, Inf. Sci..

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

[25]  Xin Yao,et al.  An adaptive coevolutionary Differential Evolution algorithm for large-scale optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[26]  Zhenyu Yang,et al.  Large-Scale Global Optimization Using Cooperative Coevolution with Variable Interaction Learning , 2010, PPSN.

[27]  Abdullah Al Mamun,et al.  Evolutionary big optimization (BigOpt) of signals , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

[28]  Kenneth A. De Jong,et al.  A Cooperative Coevolutionary Approach to Function Optimization , 1994, PPSN.

[29]  Xiaodong Li,et al.  Cooperative Co-Evolution With Differential Grouping for Large Scale Optimization , 2014, IEEE Transactions on Evolutionary Computation.