Improved Discrete Differential Evolution Algorithm in Solving Quadratic Assignment Problem for best Solutions

Asaad Shakir Hameed,Burhanuddin Mohd,Ngo Hea,Modhi Lafta

doi:10.14569/ijacsa.2018.091261

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.

Highlights

There are several specific problems for COPs, such as the quadratic assignment problem (QAP), routing problem (RP), etc
The QAP was introduced by [1] and the model of this problem has been applied in many aspects of life and is famous on campus and in hospital layout QAP is a complex problem that has attracted the attention of researchers since its first formulation [2], [3], [4], [5], and [6]
The modified of discrete differential evolution (DDE) has been proposed, which includes the type of the crossover (ULX) [18] to get the diversity of the search space

Summary

Introduction

There are several specific problems for COPs, such as the quadratic assignment problem (QAP), routing problem (RP), etc. The methods that found solutions to the QAP problem were classified into two categories as follows: the category that obtains the exact solution to QAP was called the exact methods, including the bounded dynamic branches and processes, Lagrangian-based relaxation methods, linear and quantitative programming methods. In these methods, the size of the problem requires a long calculation period if there are more than 30 methods [8], [9], [10], and [11]. The approximate methods have been divided into three categories [12]: Local Search Algorithm, such as Tabu Search; Swarm Intelligence, such as Ant Colony Optimization; Evolutionary Algorithm, such as the differential evolution algorithm

Methods

Results

Conclusion