A Hybrid Method Integrating a Discrete Differential Evolution Algorithm with Tabu Search Algorithm for the Quadratic Assignment Problem: A New Approach for Locating Hospital Departments

Abstract

The facility layout problem (FLP) is a very important class of NP-hard problems in operations research that deals with the optimal assignment of facilities to minimize transportation costs. The quadratic assignment problem (QAP) can model the FLP effectively. One of the FLPs is the hospital facility layout problem that aims to place comprehensive clinics, laboratories, and radiology units within predefined boundaries in a way that minimizes the cost of movement of patients and healthcare personnel. We are going to develop a hybrid method based on discrete differential evolution (DDE) algorithm for solving the QAP. In the existing DDE algorithms, certain issues such as premature convergence, stagnation, and exploitation mechanism have not been properly addressed. In this study, we first aim to discover the issues that make the current problem worse and to identify the best solution to the problem, and then we propose to develop a hybrid algorithm (HDDETS) by combining the DDE and tabu search (TS) algorithms to enhance the exploitation mechanism in the DDE algorithm. Then, the performance of the proposed HDDETS algorithm is evaluated by implementing on the benchmark instances from the QAPLIB website and by comparing with DDE and TS algorithms on the benchmark instances. It is found that the HDDETS algorithm has better performance than both the DDE and TS algorithms where the HDDETS has obtained 42 optimal and best-known solutions from 56 instances, while the DDE and TS algorithms have obtained 15 and 18 optimal and best-known solutions out of 56 instances, respectively. Finally, we propose to apply the proposed algorithm to find the optimal distributions of the advisory clinics inside the Azadi Hospital in Iraq that minimizes the total travel distance for patients when they move among these clinics. Our application shows that the proposed algorithm could find the best distribution of the hospital’s rooms, which are modeled as a QAP, with reduced total distance traveled by the patients.

Appling the Roulette Wheel Selection Approach to Address the Issues of Premature Convergence and Stagnation in the Discrete Differential Evolution Algorithm

“…While EAs beneft from global exploration search, issues such as stagnation, premature convergence occur in the iterative operation and slow in the exploitation mechanisms. Although the exploitation issue in the DDE algorithm has been addressed by the recent study [36]; however, the critical reading of the literature indicates that stagnation, premature convergence issues have not been investigated in the DDE algorithm associated with EAs to solve the QAP. Terefore, further research is required to enhance the algorithm that accounts for current challenges, which is the area of contribution of our study, specifcally the avoidance of stagnation and premature convergence in the DDE algorithm.…”

Experimental Study of Hybrid Genetic Algorithms for the Maximum Scatter Travelling Salesman Problem

“…Thus, for finding better solution, within acceptable computational effort, to such type of problems, generally, heuristic/metaheuristic algorithms are applied. Tabu search [8], simulated annealing [9], ant colony algorithm [10], insertion heuristic [11], variable neighbourhood method [12], discrete differential evolution algorithm [13], genetic algorithms [14], etc., are some popular metaheuristic algorithms. Among them, genetic algorithms (GAs) are widely used algorithms, and so, we are using GAs to solve the MSTSP.…”

Assessment of Assignment Problem using Hungarian Method

“…With the mixed-integer nonlinear programming model, it had been linearized and developed with bound algorithm, beam search, and filtered beam search algorithms. In this recent study, the facility layout problem (FLP) dealt with optimal assignments which helped to minimize the transportation cost (Hameed et al 2021). It can be added to the hospital facility layout problem that targeted comprehensive clinics, laboratories, and radiology units.…”