Performance analysis: Differential search algorithm based on randomization and benchmark functions

Differential search algorithm (DSA) is a new optimization, meta-heuristic algorithm. It simulates the Brownian-like, random-walk movement of an organism by migrating to a better position. The purpose of this paper is to analyze the performance analysis of DSA into two key parts: six random number generators (RNGs) and Benchmark functions (BMF) from IEEE World Congress on Evolutionary Computation (CEC, 2015). Noting that this study took problem dimensionality and maximum function evaluation (MFE) into account, various configurations were executed to check the parameters’ influence. Shifted rotated Rastrigin’s functions provided the best outcomes for the majority of RNGs, and minimum dimensionality offered the best average. Among almost all BMFs studied, Weibull and Beta RNGs concluded with the best and worst averages, respectively. In sum, 50,000 MFE provided the best results with almost RNGs and BMFs.

DSA was tested under six randomizers (Bernoulli, Beta, Binomial, Chisquare, Rayleigh, Weibull), two unimodal functions (rotated high conditioned elliptic function, rotated cigar function), three simple multi-modal functions (shifted rotated Ackley’s, shifted rotated Rastrigin’s, shifted rotated Schwefel’s functions) and three hybrid Functions (Hybrid Function 1 (n=3), Hybrid Function 2 (n=4,and Hybrid Function 3 (n=5)) at four problem dimensionalities (10D, 30D, 50D and 100D). According to the protocol of the CEC (2015) testbed, the stopping criteria are the MFEs, which are set to 10,000, 50,000 and 100,000. All algorithms mentioned were implemented on PC running Windows 8.1, i5 CPU at 1.60 GHz, 2.29 GHz and a 64-bit operating system.

The authors concluded the results based on RNGs as follows: F3 gave the best average results with Bernoulli, whereas F4 resulted in the best outcomes with all other RNGs; minimum and maximum dimensionality offered the best and worst averages, respectively; and Bernoulli and Binomial RNGs retained the best and worst averages, respectively, when all other parameters were fixed. In addition, the authors’ results concluded, based on BMFs: Weibull and Beta RNGs produced the best and worst averages with most BMFs; shifted and rotated Rastrigin’s function and Hybrid Function 2 gave rise to the best and worst averages. In both parts, 50,000 MFEs offered the best average results with most RNGs and BMFs.

Being aware of the advantages and drawbacks of DS enlarges knowledge about the class in which differential evolution belongs. Application of that knowledge, to specific problems, ensures that the possible improvements are not randomly applied. Strengths and weaknesses influenced by the characteristics of the problem being solved (e.g. linearity, dimensionality) and by the internal approaches being used (e.g. stop criteria, parameter control settings, initialization procedure) are not studied in detail. In-depth study of performance under various conditions is a “must” if one desires to efficiently apply DS algorithms to help solve specific problems. In this work, all the functions were chosen from the 2015 IEEE World Congress on Evolutionary Computation (CEC, 2015).