A new hybrid approach based on discrete differential evolution algorithm to enhancement solutions of quadratic assignment problem

Abstract

The Combinatorial Optimization Problem (COPs) is one of the branches of applied mathematics and computer sciences, which is accompanied by many problems such as Facility Layout Problem (FLP), Vehicle Routing Problem (VRP), etc. Even though the use of several mathematical formulations is employed for FLP, Quadratic Assignment Problem (QAP) is one of the most commonly used. One of the major problems of Combinatorial NP-hard Optimization Problem is QAP mathematical model. Consequently, many approaches have been introduced to solve this problem, and these approaches are classified as Approximate and Exact methods. With QAP, each facility is allocated to just one location, thereby reducing cost in terms of aggregate distances weighted by flow values. The primary aim of this study is to propose a hybrid approach which combines Discrete Differential Evolution (DDE) algorithm and Tabu Search (TS) algorithm to enhance solutions of QAP model, to reduce the distances between the locations by finding the best distribution of N facilities to N locations, and to implement hybrid approach based on discrete differential evolution (HDDETS) on many instances of QAP from the benchmark. The performance of the proposed approach has been tested on several sets of instances from the data set of QAP and the results obtained have shown the effective performance of the proposed algorithm in improving several solutions of QAP in reasonable time. Afterwards, the proposed approach is compared with other recent methods in the literature review. Based on the computation results, the proposed hybrid approach outperforms the other methods.

A comprehensive investigation into the performance of genetic algorithm for effective shipyard topological layout

“…QAP was first proposed by Koopmans and Beckmann, 49 and has been successfully applied in many real-life problems such as backboard wiring, hospital layout, typewriter keyboards, control panel design, traveling salesman, touchscreen devices and campus layout. 50,51 Since QAP is an NP-Hard class combinatorial optimization problem, there is no definitive method for its solution, and efforts to overcome such problems with the help of meta-heuristic approaches remain a more active area of research. 51,52 International literature defines QAP as the problem of positioning departments in a specific area with minimum cost allocation.…”

A Novel Multistrategy-Based Differential Evolution Algorithm and Its Application

“…Sethanan et al [56] presented a novel hybrid DE with a genetic operator to solve the multitrip VRP with backhauls. Hameed et al [57] presented a hybrid algorithm based on discrete DE and TS for solving many instances of QAP. Liu et al [58] presented a mixed-variable DE for solving the hierarchical mixed-variable optimization problem.…”

A Systematic Review of Hyper-Heuristics on Combinatorial Optimization Problems

“…Traveling Salesman [92] Traveling Salesman [93] Multiple Traveling Salesman [94] Bottleneck Traveling Salesman [95] Cutting Stock [96] Cutting Stock [97] 2D Cutting [98] Packing [99] Packing [100] 2D Packing [101] Bin Packing [102] Knapsack [103] Knapsack [104] Subset Sum [105] Unbounded Knapsack [105] Bounded Knapsack [106] Multiple Knapsack [107] Quadratic Knapsack [108] Scheduling [109] Scheduling [110] Production Scheduling [111] Workforce Scheduling [112] Job-Shop Scheduling [113] Precedence Constrained Scheduling [114] Educational Timetabling [115] Educational Timetabling [116] Facility Location [117] Assignment [118] Quadratic Assignment [119] Spanning Tree [120] Maximum Leaf Spanning Tree [121] Degree Constrained Spanning Tree [122] Minimum Spanning Tree [123] Boolean Satisfiability [124] Boolean Satisfiability [125] Covering [126] Minimum Vertex Cover [127] Set Cover [128] Exact Cover [129] Minimum Edge Cover [130] Vehicle Routing [131] Vehicle Routing…”