Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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).

中文翻译：

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性能分析：基于随机化和基准函数的差分搜索算法

目的

差分搜索算法（DSA）是一种新的优化、元启发式算法。它通过迁移到更好的位置来模拟生物体的类似布朗式的随机游走运动。本文的目的是将 DSA 的性能分析分为两个关键部分：6 个随机数生成器 (RNG) 和来自 IEEE 世界进化计算大会 (CEC, 2015) 的基准函数 (BMF)。注意到本研究考虑了问题维度和最大函数评估 (MFE)，执行了各种配置以检查参数的影响。移位旋转 Rastrigin 的函数为大多数 RNG 提供了最好的结果，最小维度提供了最好的平均值。在研究的几乎所有 BMF 中，Weibull 和 Beta RNG 分别以最佳和最差平均值结束。总之，50，

设计/方法/方法

DSA 在六个随机变量（伯努利、Beta、二项式、卡方、瑞利、威布尔）、两个单峰函数（旋转的高条件椭圆函数、旋转的雪茄函数）、三个简单的多峰函数（移位旋转阿克莱函数、移位旋转 Rastrigin 函数、在四个问题维度（10D、30D、50D 和 100D）上移位旋转 Schwefel 函数）和三个混合函数（混合函数 1（n =3）、混合函数 2（n =4，和混合函数 3（n =5）） . 根据 CEC (2015) 试验台的协议，停止标准是 MFE，设置为 10,000、50,000 和 100,000。提到的所有算法均在运行 Windows 8.1、i5 CPU 的 PC 上实现，频率为 1.60 GHz、2.29 GHz 和64 位操作系统。

发现

作者基于 RNG 得出的结果如下：F3 使用 Bernoulli 给出了最好的平均结果，而 F4 给出了所有其他 RNG 的最佳结果；最小和最大维度分别提供了最好和最差的平均值；当所有其他参数都固定时，伯努利和二项式 RNG 分别保留了最好和最差的平均值。此外，作者基于 BMF 得出的结论是：Weibull 和 Beta RNG 对大多数 BMF 产生了最好和最差的平均值；移动和旋转 Rastrigin 的函数和混合函数 2 产生了最好和最差的平均值。在这两个部分中，50,000 个 MFE 提供了大多数 RNG 和 BMF 的最佳平均结果。

原创性/价值

意识到 DS 的优缺点，可以扩大对差异进化所属类别的了解。将该知识应用于特定问题可确保不会随机应用可能的改进。没有详细研究受所解决问题的特征（例如线性度、维数）和所使用的内部方法（例如停止标准、参数控制设置、初始化程序）影响的优点和缺点。如果希望有效地应用 DS 算法来帮助解决特定问题，那么深入研究各种条件下的性能是“必须的”。在这项工作中，所有函数均选自 2015 年 IEEE 世界进化计算大会（CEC，2015）。