Abstract
This paper proposes the real-world application of the Differential Evolution (DE) algorithm using, distance-based mutation-selection, population size adaptation, and an archive for solutions (DEDMNA). This simple framework uses three widely-used mutation types with the application of binomial crossover. For each solution, the most proper position prior to evaluation is selected using the Euclidean distances of three newly generated positions. Moreover, an efficient linear population-size reduction mechanism is employed. Furthermore, an archive of older efficient solutions is used. The DEDMNA algorithm is applied to three real-life engineering problems and 13 constrained problems. Seven well-known state-of-the-art DE algorithms are used to compare the efficiency of DEDMNA. The performance of DEDMNA and other algorithms are comparatively assessed using statistical methods. The results obtained show that DEDMNA is a very comparable optimiser compared to the best performing DE variants. The simple idea of measuring the distance of the mutant solutions increases the performance of DE significantly.
Highlights
The solving of global optimisation problems is frequently needed in many areas of research, industry, and engineering where minimal or maximal cost values are required
Note that where the CoDE variant [17] selects one of the three trial individuals evaluated by the cost function, the proposed DEDMNA uses the Euclidean distance between the coordinates of the points in the population
Two variants of the novel DEDMNA algorithm are compared with six state-of-the-art Differential Evolution (DE) variants when solving three engineering and 13 constrained problems
Summary
The solving of global optimisation problems is frequently needed in many areas of research, industry, and engineering where minimal or maximal cost values are required. A new individual yi is evaluated by a cost function and it replaces the parent individual xi in the population if it is better, f (yi ) ≤ f ( xi ) This evolutionary operation is known as selection. A new DE variant based on a distance-based selection of mutation individuals, using an archive of old-good solutions and a population-size reduction mechanism, was applied to real-world problems. The main motivation for using the new algorithm was derived from an attempt to control the speed of convergence in the DE by the proper selection of a mutation individual [10,11]. A DE variant with Distance-based Mutation-selection, population size (N) reduction, and the use of an archive of old-good solutions (DEDMNA) is introduced. The results of their experiments showed an increased efficiency in some classification problems
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