Influence of randomization strategies and problem characteristics on the performance of Differential Search algorithm

Abstract

In this work, the influence of different random number generators, problem dimensionality, and number of function evaluations on the optimization efficiency of Differential Search algorithm is presented in detail. Two types of random number generators were taken into account: discrete and continuous. Different combinations between the dimensionality property and the number of function evaluation setting were tested on: i) a set of benchmark functions from the CEC 2013 special session on real parameter optimization; and ii) 2 chemical engineering problems (optimal operation of an alkylation unit and heat exchanger network design). Also, a comparison with other optimizers was performed. It was found that, in similar conditions, the performance of the algorithm (in terms of the best solutions) varies substantially depending on the distribution used. In case of the benchmark problems, the best solutions were obtained for Binomial and Weibull distribution. For the separable functions is was observed that, indifferent of the distribution used, the algorithm was not able to find acceptable solution within the constraint represented by the number of function evaluations. In the case of the alkylation problem the best solutions were obtained by the Weibull distribution, the performance of the Differential Search algorithm being comparable to other optimizers such as Differential Evolution. In the case of the heat exchanger, three different distribution provided near optimal solutions (Binomial, ChiSquare and Weibull).