Bi-Attempted Based Optimization Algorithm For Numerical Optimization Problems

Abstract

Numerical optimization is one of the well-known problems in computer science. Day by day, new methods are developed by many researchers. Recently, optimization became an essential task for many disciplines, such as engineering, medicine, management and others. In many cases, optimization problems may require fast and efficient algorithms for real-time implementations. In this paper, a simple, fast and feasible algorithm is presented for the optimization of both uni-modal and multi-modal benchmark functions. A population based Bi-Attempted Based Optimization Algorithm (ABaOA) is a stochastic search method which searches a solution space with two fixed step-size displacement parameters and two mutation operators. The proposed algorithm is derived from Base Optimization Algorithm (BaOA) which uses basic arithmetic operations. The performance of ABaOA is tested on twenty well-known benchmark functions and the results are statistically compared with the seven well-known stochastic optimization algorithms. Three different statistical analyses were done on the results obtained from the ABaOA. Two non-parametric statistical comparisons with the mean values are performed by using Sign and Wilcoxon tests. The non-parametric statistical multiple comparisons of the proposed algorithm is performed by using the Friedman test. The non-parametric Friedman test of differences among repeated measures of these algorithms was conducted and referred a Chi-square value of 67.337, which was significant (p<0.05). Wilcoxon non-parametric pairwise comparison test was applied to analyze the difference of ABaOA statistically among the other algorithms. The test indicates that the introduced algorithm is statistically significant than other algorithms with a level of significance p < 0.05. The experimental results also show that the ABaOA is clearly superior to the compared stochastic optimization algorithms.

Performance Analysis of Bi-Attempted Based Optimization Algorithm on Numerical Optimization Functions

“…Bu çalışmada ABaOA'nın çözüm uzayında yakınsama performansı ayrıntılı olarak incelenmiştir. Nüfus tabanlı evrimsel bir algoritma olan ABaOA, rastgele üretilen bir nüfusu iki sabit adım boyutlu çoğaltma parametresi ve iki temel aritmetik işlem operatörü kullanan bir Evrimsel Algoritma'dır [42]. Algoritmanın kodlama akış şeması Şekil 1'de gösterilmiştir.…”

“…Algoritmanın kodlama akış şeması Şekil 1'de gösterilmiştir. Rastrigin fonksiyonunun ABaOA, BaOA, GA, BPSO ve PSO algoritmaları ile literatürdeki çözümü Çizelge 2'de özetlenmiştir [10,42].…”

“…Algoritma İsmi Medyan Standart Sapma ABaOA [42] 0.00E+00 0.00E+00 BaOA [42] 0.00E+00 2.05E+00 GA [42] 5.895E+01 1.825E+01 BPSO [10] 0,0012 0,3459 PSO [10] 0,9949 0,6633…”