Dynamic Interconnection Approach With BLX-Based Search Applied to Multi-Swarm Optimizer: An Empirical Analysis to Real Constrained Optimization

Daniel Leal Souza,Rodrigo Lisboa Pereira,Otavio Noura Teixeira,Mario T R Serra Neto,Marco A F Mollinetti,Roberto C L De Oliveira

doi:10.1109/access.2021.3119579

Abstract

The Multi-Swarm approach allows the use of multiple configurations between two or more populations of particles, where each one can present different approaches (e.g. lbest, gbest, Unified, Guaranteed-Convergence) directed towards improving the optimization process. This article presents a proposal for local/global stochastic interconnection applied to the context of the Multi-Swarm algorithm, as well as for incrementing a local search method for refining previously obtained solutions. Two proposals are introduced for this new Multi-Swarm PSO (MSO). The first one is the inclusion of “counterpart particles”, which establishes a sub-topology between inter-swarm particles, accessed by migration and evaluability rules. The other involves using customized crossover operators and is based on the BLX scheme (Blend Crossover) with direction information used as a reference for establish a subspace search around the particles. Performance and robustness of the new approaches were assessed by ten constrained engineering design optimization problems (COPs), as is compared to other solutions already published in the scientific literature. Results indicate significant performance improvements for all 10 COPs when compared to concurrent-based MSOs. By making available new references from other swarms, the counterpart particles approach tends to improve the optimization process in the search space, while an intermediate layer of local search based on a modified directed BLX crossover should provide an extra search around the particle, and thus, refining previously obtained solutions.

Highlights

S INCE their first publication in 1995 [1], Particle Swarm Optimization (PSO) and its variants have been important in solving a wide variety of problems [2], [3], as well as being one of the major references for global optimization in the field of Swarm Intelligence (SI) [3]–[6]
This article is divided into the following sections: Related works with the state of the art (Section 2); Theoretical Basis for the Classical Particle Swarms, MultiSwarm Optimization and presenting the mechanisms for the proposed FC-CPMSO3 algorithm besides its version with "variant particles,” generated by a modified crossover BLX: FC-CPMSO-V1/V24 (Section 3); Experiment setup, with description of the benchmark functions, as well as the thread organization in CUDA and the results obtained from the tests (Section 4); Final remarks and conclusion, with commentaries regarding the advantages and drawbacks related to the proposed algorithms (Section 5)
Several articles regarding the use of PSO for constrained optimization (COP) are briefly reviewed in this subsection, and the results show a good performance in solving problems associated with that class of problems [16], [44]–[46]

Summary

INTRODUCTION

S INCE their first publication in 1995 [1], Particle Swarm Optimization (PSO) and its variants have been important in solving a wide variety of problems [2], [3], as well as being one of the major references for global optimization in the field of Swarm Intelligence (SI) [3]–[6]. Six important characteristics make PSO a quite attractive metaheuristic in the search and optimization context [9], [10]: 1) Intrinsic memory associated with each solution (local); 2) Capacity for information exchanges; 3) Search based on references of good prior results; 4) High degree of parallelism; 5) implemented; 6) Rapid convergence. Because of those attributes, PSO has been succesfully applied to a diverse family of problems, with hybrid or derived versions being used in several fields of scientific knowledge (e.g. engineering, antenna design, robotics, machine learning) [11]. Considering the possibilities for improvements and customization capacity of Multi-swarm PSOs, as well as addition of techniques focused on sweeping the search space beyond the mechanisms found in the original PSO original, hybridizing particle swarms with crossover-based solutions for local search in subspaces presents a range of possibilities for allowing improvements in the optimization process

PROBLEM DISCUSSION

A BRIEF RETROSPECTIVE AND RELATED WORKS

PROPOSED MECHANISMS AND SOLUTIONS

MULTI-SWARM OPTIMIZATION

FINAL REMARKS AND CONCLUSION