Improved discrete differential evolution algorithm in solving quadratic assignment problem for best solutions

Abstract

The combinatorial optimization problems are very important in the branch of optimization or in the field of operation research in mathematics. The quadratic assignment problem (QAP) is in the category of facilities location problems and is considered as one of the significant complex's combinatorial optimization problems since it has many applications in the real world. The QAP is involved in allocating N facilities to N locations with specified distances amid the locations and the flows between the facilities. The modified discrete differential evolution algorithm has been presented in this study based on the crossover called uniform like a crossover (ULX). The proposed algorithm used to enhance the QAP solutions through finding the best distribution of the N facilities to N locations with the minimized total cost. The employed criteria in this study for the evaluation of the algorithm were dependent on the accuracy of the algorithm by using the relative percent deviation (PRD). The proposed algorithm was applied to 41 different sets of the benchmark QAPLIB, while the obtained results indicated that the proposed algorithm was more efficient and accurate compared with Tabu Search, Differential Evolution, and Genetic algorithm.