Performance up-gradation of Symbiotic Organisms Search by Backtracking Search Algorithm

Abstract

Symbiotic Organisms Search (SOS) algorithm is characterized based on the framework of relationships among the ecosystem species. Nevertheless, it is suffering from wasteful discovery, little productivity, and slack convergence rate. These deficiencies cause stagnation at the local optimum, which is hazardous in deciding the genuine optima of the optimization problem. Backtracking Search Algorithm (BSA) is likewise another streamlining method for comprehending the non-direct complex optimization problem. Consequently, in the current paper, an endeavor has been made toward the expulsion of the downsides from the traditional SOS by proposing a novel ensemble technique called e-SOSBSA to overhaul the degree of intensification and diversification. In e-SOSBSA, firstly, the mutation operator of BSA with the self-adaptive mutation rate is incorporated to produce a mutant of population and leap out from the local optima. Secondly, the crossover operator of BSA with the adaptive component of mixrate is incorporated to leverage the entire active search regions visited previously. The suggested e-SOSBSA has been tested with 20 classical benchmark functions, IEEE CEC2014, CEC2015, CEC2017, and the latest CEC 2020 test functions. Statistical analyses, convergence analysis, and diversity analysis are performed to show the stronger search capabilities of the proposed e-SOSBSA in contrast with the component algorithms and several state-of-the-art algorithms. Moreover, the proposed e-SOSBSA is applied to find the optimum value of the seven problems of engineering optimization. The numerical investigations and examinations show that the proposed e-SOSBSA can be profoundly viable in tackling real-world engineering optimization problems.

Keywords: Backtracking Search Algorithm; CEC2014; CEC2015; CEC2017; CEC2020; Engineering Problem; Ensemble algorithm; Function optimization; Symbiotic Organisms Search.

Fig. 1

Variation of proposed mutation and mixrate parameter for sphere function

Fig. 2

Comparison of evolutionary trends on Diversity-A and Diversity-B with classical SOS, BSA, and proposed e-SOSBSA

Fig. 2

Comparison of evolutionary trends on Diversity-A and Diversity-B with classical SOS, BSA, and proposed e-SOSBSA

Fig. 2

Comparison of evolutionary trends on Diversity-A and Diversity-B with classical SOS, BSA, and proposed e-SOSBSA

Fig. 3

Convergence graphs for some selected functions

Fig. 3

Convergence graphs for some selected functions

Fig. 4

Mean rank of Friedman test on 20 classical test functions (Appendix A)

Fig. 5

Mean rank of Friedman test on 20 classical test functions (Appendix A) compared to FDR-PSO, FIPS, UPSO, CLPSO, CPSOH, HBSA, and e-SOSBSA

Fig. 6

Mean rank of Friedman test on CEC14 test functions compared to MFO, WOA, SSA, SSO, SCA, m-SCA, e-SOSBSA

Fig. 7

Mean rank of Friedman test on CEC15 test functions compared to ASOS_ABF1, ASOS_ABF2, ASOS_ABF1&2, I-SOS, SaISOS, ACoS-PSO, CPI-DE, e-SOSBSA

Fig. 8

Mean rank of Friedman test on CEC17 test functions compared to ABSA, IBSA, HBSA, ACoS-PSO, CPI-DE, SCA, HSCA, and e-SOSBSA

Fig. 9

Mean rank of Friedman test on CEC20 test functions compared to e-SOSBSA, JAYA, TLBO, TSA, SOA, COA, SHO, and EO

Fig. 10

Algorithm complexity of CEC2014, CEC2015, CEC2017, CEC2020 test function

Fig. 11

Welded beam design problem (Mirjalili and Lewis 2016)

Fig. 12

Tension/compression spring design problem

Fig. 13

Speed reducer design problem

Fig. 14

Three-bar truss design problem

Fig. 15

Pressure vessel design (Mirjalili and Lewis 2016)

Fig. 16

Cantilever beam design problem

Fig. 17

I-beam design problem (Mirjalili et al. 2017)