Review on the Methods to Solve Combinatorial Optimization Problems Particularly: Quadratic Assignment Model

Burhanuddin Mohd Aboobaider,Modhi Lafta Mutar,Ngo Hea Choon,Wassim Habib Bilal,Asaad Shakir Hameed

doi:10.14419/ijet.v7i3.20.18722

Burhanuddin Mohd Aboobaider, Modhi Lafta Mutar + Show 3 more

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https://doi.org/10.14419/ijet.v7i3.20.18722

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Abstract

The quadratic assignment problem (QAP) is one of the fundamental combinatorial optimization problem (COPs) in the branch of optimization or operation research in mathematics, from the category of the Facilities Location Problems (FLPs). The quadratic assignment problem (QAP) be appropriate to the group of NP-hard issues and is measured as a challenging problem of the combinatorial optimization. QAP in Location Theory considers one of the problems of facilities tracing which the rate of locating a facility be determined by the spaces between facilities as well as the communication among the further facilities. QAP was presented in 1957 by Beckman and Koopmans as they were attempting to model a problem of facilities location. To survey the researcher’s works for QAP and applied, the mapped research landscape outlines literature into a logical classification and discovers this field basic characteristics represented on the motivation to use the quadratic assignment problem applied in hospital layout and campus planning. This survey achieved a concentrated each QAP article search in three key databases: Web of Science, Science Direct, and IEEE Xplore. Those databases are regarded extensive adequate in covering QAP and the methods utilized in solving QAP.

Highlights

In theoretical computer science and applied mathematics contain problems of combinatorial optimization which are a subject that is made of finding an optimal object from a finite set of Objects [1]
We presented the first classification in fig. 4 the classification involves on 145 papers obtained through the use of search engines such as IEEE Xplore, Since Direct and Web of Sciences, the study selection, progression means looking for literature sources, subsequently iterated by screening and filtering
This section is a description of a survey of all methods that solve combinatorial optimization problems Quadratic Assignment Problem, this classification includes 145 papers for the methods which used to solve quadratic assignment problem (QAP) model was presented during the period from 2002 - 2018, we have found two main methods to solve QAP model in this classification the first method namely Exact Algorithms and the second method namely Approximate Algorithms as shown in fig

Summary

Introduction

In theoretical computer science and applied mathematics contain problems of combinatorial optimization which are a subject that is made of finding an optimal object from a finite set of Objects [1]. The problems in the real world are divided into two categories, called decision problems and optimization problem as shown in fig. There are many specific issues of combinatorial optimization for example Facilities Location Problems FLP, Scheduling Problem SP, and Routing Problem RP. The quadratic assignment problem (QAP) is regarded the essential problems for combinatorial optimization among the other problems in the branch of optimization or operations research in mathematics, among the type of the amenities problems of setting [3]. The classic Quadratic Assignment Problem (QAP) is one of the greatest thoughtprovoking and inspiring combinatorial optimization issues in actuality [4]. Among the various research applications, QAP is considered as one form of the NP-hardest problem category [5]

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