Differential Grouping Method Research Articles

An Enhanced Differential Grouping Method for Large-Scale Overlapping Problems

An Enhanced Differential Grouping Method for Large-Scale Overlapping Problems

An Efficient Recursive Differential Grouping for Large-Scale Continuous Problems

Cooperative co-evolution (CC) is an efficient and practical evolutionary framework for solving large-scale optimization problems. The performance of CC is affected by the variable decomposition. An accurate variable decomposition can help to improve the performance of CC on solving an optimization problem. The variable grouping methods usually spend many computational resources obtaining an accurate variable decomposition. To reduce the computational cost on the decomposition, we propose an efficient recursive differential grouping (ERDG) method in this article. By exploiting the historical information on examining the interrelationship between the variables of an optimization problem, ERDG is able to avoid examining some interrelationship and spend much less computation than other recursive differential grouping methods. Our experimental results and analysis suggest that ERDG is a competitive method for decomposing large-scale continuous problems and improves the performance of CC for solving the large-scale optimization problems.

A Three-Level Recursive Differential Grouping Method for Large-Scale Continuous Optimization

Cooperative co-evolution (CC) is widely used to solve large-scale continuous optimization problems, which divides a large-scale problem into several small-scale sub-problems via decomposition methods and then optimizes each sub-problem separately. However, the performance of CC mainly depends on the decomposition methods. A recently proposed bisection-based decomposition method, called recursive differential grouping (RDG), shows good performance when solving large-scale continuous optimization problems. In order to further improve the performance of RDG, this paper develops a novel decomposition method, called three-level recursive differential grouping (TRDG). In TRDG, when the interaction between two sets is detected, the variables in one of the sets are divided into three subsets based on the trichotomy method, and then the interaction between each subset and the other set is detected. Compared with RDG, TRDG can reduce the depth of recursion, thus saving the number of fitness evaluations (FEs). In addition, we devise a novel strategy to update adaptively the threshold for identifying the interactions between variables. The simulation experiment results on CEC’2010 and CEC’2013 benchmark functions show that the performance of TRDG is better than several existing decomposition methods in terms of the accuracy and the number of FEs. Furthermore, TRDG is embedded into two frameworks to tackle CEC’2010 large-scale continuous optimization problems.

Cooperative co-evolution with improved differential grouping method for large-scale global optimisation

The cooperative co-evolution (CC) framework has shown to be effective in dealing with large-scale global optimisation (LSGO). However, the performance of algorithms based on the CC framework is often affected by the chosen variable grouping method, i.e., how variables are grouped into different sub-components. In this study, an improved variable grouping strategy based on the differential grouping (DG) is proposed, namely e-based differential grouping (e-DG). The e-DG strategy can identify both direct and indirect interactions between variables. Moreover, a simple yet effective method is introduced in e-DG to identify the calculation error that is detrimental to variable grouping in the original DG method (which needs to set the threshold value appropriately). The e-DG is compared against the DG on the CEC 2010 LSGO benchmarks, and is found to perform better in terms of the grouping accuracy on almost all problems. Moreover, a CC-based differential evolution algorithm with the e-DG strategy shows good performance on the 2010 LSGO benchmarks.

Cooperative co-evolution with improved differential grouping method for large-scale global optimisation

The cooperative co-evolution (CC) framework has shown to be effective in dealing with large-scale global optimisation (LSGO). However, the performance of algorithms based on the CC framework is often affected by the chosen variable grouping method, i.e., how variables are grouped into different sub-components. In this study, an improved variable grouping strategy based on the differential grouping (DG) is proposed, namely ε-based differential grouping (ε-DG). The ε-DG strategy can identify both direct and indirect interactions between variables. Moreover, a simple yet effective method is introduced in ε-DG to identify the calculation error that is detrimental to variable grouping in the original DG method (which needs to set the threshold value appropriately). The ε-DG is compared against the DG on the CEC 2010 LSGO benchmarks, and is found to perform better in terms of the grouping accuracy on almost all problems. Moreover, a CC-based differential evolution algorithm with the ε-DG strategy shows good performance on the 2010 LSGO benchmarks.

Mixed second order partial derivatives decomposition method for large scale optimization

This paper focuses on decomposition strategies for large-scale optimization problems. The cooperative co-evolution approach improves the scalability of evolutionary algorithms by decomposing a single high dimensional problem into several lower dimension sub-problems and then optimizing each of them individually. However, the dominating factor for the performance of these algorithms, on large-scale function optimization problems, is the choice of the decomposition approach employed. This paper provides a theoretical analysis of the interaction between variables in such approaches. Three theorems and three lemma are introduced to investigate the relationship between decision variables, and we provide theoretical explanations on overlapping subcomponents. An automatic decomposition approach, based on the mixed second order partial derivatives of the analytic expression of the optimization problem, is presented. We investigate the advantages and disadvantages of the differential grouping (DG) automatic decomposition approach, and we propose one enhanced version of differential grouping to deal with problems which the original differential grouping method is unable to resolve. We compare the performance of three different grouping strategies and provide the results of empirical evaluations using 20 benchmark data sets.