Review of Differential Evolution population size

Abstract

Abstract Population size of Differential Evolution (DE) algorithms is often specified by user and remains fixed during run. During the first decade since the introduction of DE the opinion that its population size should be related to the problem dimensionality prevailed, later the approaches to DE population size setting diversified. In large number of recently introduced DE algorithms the population size is considered to be problem-independent and often fixed to 100 or 50 individuals, but alongside a number of DE variants with flexible population size have been proposed. The present paper briefly reviews the opinions regarding DE population size setting and verifies the impact of the population size on the performance of DE algorithms. Ten DE algorithms with fixed population size, each with at least five different population size settings, and four DE algorithms with flexible population size are tested on CEC2005 benchmarks and CEC2011 real-world problems. It is found that the inappropriate choice of the population size may severely hamper the performance of each DE algorithm. Although the best choice of the population size depends on the specific algorithm, number of allowed function calls and problem to be solved, some rough guidelines may be sketched. When the maximum number of function calls is set to classical values, i.e. those specified for CEC2005 and CEC2011 competitions, for low-dimensional problems (with dimensionality below 30) the population size equal to 100 individuals is suggested; population sizes smaller than 50 are rarely advised. For higher-dimensional artificial problems the population size should often depend on the problem dimensionality d and be set to 3d–5d. Unfortunately, setting proper population size for higher-dimensional real-world problems (d>40) turns out too problem and algorithm-dependent to give any general guide; 200 individuals may be a first guess, but many DE approaches would need a much different choice, ranging from 50 to 10d. However, quite clear relation between the population size and the convergence speed has been found, showing that the fewer function calls are available, the lower population sizes perform better. Based on the extensive experimental results the use of adaptive population size is highly recommended, especially for higher-dimensional and real-world problems. However, which specific algorithms with population size adaptation perform better depends on the number of function calls allowed.