A Dynamic Global Differential Grouping for Large-Scale Black-Box Optimization

Cooperative Co-evolution (CC) framework is an important method to tackle Large Scale Black-Box Optimization (LSBO) problem. One of the main step in CC is grouping for the decision variables, which affects the optimization performance. An ideal grouping result is that the relationship of decision variables in intra-group is stronger as possible and those in inter-groups is weaker as possible. Global Differential Grouping (GDG) is an efficient grouping method based on the idea of partial derivatives of multivariate functions, and it can automatically resolve the problem by maintaining the global information among variables. However, once the grouping result by GDG is determined, it will no longer be updated and will not be automatically adjusted with the evolution of the algorithm, which may affect the optimization performance of the algorithm. Therefore, based on GDG, a Dynamic Global Differential Grouping (DGDG) strategy is proposed for grouping the decision variables in this paper, which can update the grouping results with the evolution processing. DGDG works with Particle Swarm Optimization (PSO) algorithm in this paper, which is termed as CC-DGDG-PSO. The experimental results based on the LSBO benchmark functions from CEC’2010 show that DGDG algorithm can improve the performance of GDG.

[1]  Xin Yao,et al.  Differential evolution for high-dimensional function optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[2]  Xin Yao,et al.  Multilevel cooperative coevolution for large scale optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[3]  Xiaodong Li,et al.  A Competitive Divide-and-Conquer Algorithm for Unconstrained Large-Scale Black-Box Optimization , 2016, ACM Trans. Math. Softw..

[4]  Tom Schaul,et al.  Studies in Continuous Black-box Optimization , 2011 .

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

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

[7]  J. C. Townsend,et al.  Very Large Scale Optimization , 2000 .

[8]  Tapabrata Ray,et al.  Divide and Conquer in Coevolution: A Difficult Balancing Act , 2010 .

[9]  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).

[10]  Graham J. Williams,et al.  Big Data Opportunities and Challenges: Discussions from Data Analytics Perspectives [Discussion Forum] , 2014, IEEE Computational Intelligence Magazine.

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

[12]  Kenneth A. De Jong,et al.  Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents , 2000, Evolutionary Computation.

[13]  Antonio Mucherino,et al.  Variable Neighborhood Search for Robust Optimization and Applications to Aerodynamics , 2011, LSSC.

[14]  Xiaodong Li,et al.  Benchmark Functions for the CEC'2010 Special Session and Competition on Large-Scale , 2009 .

[15]  Ke Tang,et al.  Scaling Up Covariance Matrix Adaptation Evolution Strategy Using Cooperative Coevolution , 2013, IDEAL.

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

[17]  Xiaodong Li,et al.  Designing benchmark problems for large-scale continuous optimization , 2015, Inf. Sci..

[18]  Xiaodong Li,et al.  Cooperative Co-evolution for large scale optimization through more frequent random grouping , 2010, IEEE Congress on Evolutionary Computation.

[19]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[20]  Bernard De Baets,et al.  Zadeh’s Extension Principle for Continuous Functions of Non-Interactive Variables: A Parallel Optimization Approach , 2012, IEEE Transactions on Fuzzy Systems.

[21]  Tapabrata Ray,et al.  A cooperative coevolutionary algorithm with Correlation based Adaptive Variable Partitioning , 2009, 2009 IEEE Congress on Evolutionary Computation.