Study on modified Whitley model with different number and various methods of forming elite individuals

Abstract

Introduction. A comparative analysis of the modified Whitley model solutions through different methods of forming elite individuals is presented. The algorithms of Kron and Plotnikov-Zverev are used in the study for the formation of elite individuals. The work objectives are the development of the modified Whitley model involving the Kron’s and PlotnikovZverev’s algorithms to form elite individuals, as well as a software tool for solving the scheduling theory problem. It was necessary to obtain the best solution to this problem with various initial data followed by processing the results and identifying a modification of the Whitley model. The distribution problem which implies the search for the optimal distribution of work to the processors with the minimization of the maximum execution time is described. Materials and Methods. All the algorithms implemented under the development of the software tool for solving the optimization scheduling problem are considered. The following algorithms are presented: the modified Whitley model, the application of the elitism strategy, the Kron’s algorithm, the Plotnikov-Zverev’s algorithm. Research Results. A software tool is developed. It was applied to conduct a computational experiment with various initial data using one, two, three, and four elite individuals. The experiment was carried out for the most common data sets with a different number of elite individuals. Each Whitley model modification was launched a hundred times with each set of the source data. The comparative analysis of the results shows how the application of the considered elitism strategies in the developed modifications of the genetic algorithm (Whitley model) affects the accuracy of the solution to the homogeneous minimax problem with a different number of elite individuals. Discussion and Conclusions. The best results of the algorithms are determined; the utilization of elitism in the modified Whitley model when solving a homogeneous minimax problem of scheduling theory is estimated. The algorithm results are compared for one, two, three and four elite individuals.

Keywords

• genetic algorithms
• modified whitley model
• elitism
• scheduling theory
• kron’s algorithm
• plotnikov-zverev’s algorithm
• np-complete problems
• homogeneous minimax problem
• heuristic algorithms
• computational experiment