A Sule’s Method initiated genetic algorithm for solving QAP formulation in facility layout design: A real world application

This paper considers the Quadratic Assignment Problem (QAP) as one of the most important issues in optimization. This NP-hard problem has been largely studied in the scientific literature, and exact and approximate (heuristic and meta-heuristic) approaches have been used mainly to optimize one or more objectives. However, most of these studies do not consider or are not tested in real applications. Hence, in this work, we propose the use of Sule’s Method and genetic algorithms, for a QAP (stated as a facility Layout Problem) in a real industry application in Colombia so that the total cost to move the required material between the facilities is minimized. As far as we know, this is the first work in which Sule’s Method and genetic algorithms are used simultaneously for this combinatorial optimization problem. Additionally the proposed approach was tested using well-known datasets from the literature in order to assure its efficiency

PasMoQAP: A Parallel Asynchronous Memetic Algorithm for solving the Multi-Objective Quadratic Assignment Problem

Multi-Objective Optimization Problems (MOPs) have attracted growing attention during the last decades. Multi-Objective Evolutionary Algorithms (MOEAs) have been extensively used to address MOPs because are able to approximate a set of non-dominated high-quality solutions. The Multi-Objective Quadratic Assignment Problem (mQAP) is a MOP. The mQAP is a generalization of the classical QAP which has been extensively studied, and used in several real-life applications. The mQAP is defined as having as input several flows between the facilities which generate multiple cost functions that must be optimized simultaneously. In this study, we propose PasMoQAP, a parallel asynchronous memetic algorithm to solve the Multi-Objective Quadratic Assignment Problem. PasMoQAP is based on an island model that structures the population by creating sub-populations. The memetic algorithm on each island individually evolve a reduced population of solutions, and they asynchronously cooperate by sending selected solutions to the neighboring islands. The experimental results show that our approach significatively outperforms all the island-based variants of the multi-objective evolutionary algorithm NSGA-II. We show that PasMoQAP is a suitable alternative to solve the Multi-Objective Quadratic Assignment Problem.Comment: 8 pages, 3 figures, 2 tables. Accepted at Conference on Evolutionary Computation 2017 (CEC 2017

An algorithm for multi-objective assignment problem.

Tse Hok Man.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 68-69).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Background Study --- p.4Chapter 2.1 --- Channel Assignment in Multicarrier CDMA Systems --- p.4Chapter 2.1.1 --- Channel Throughput --- p.5Chapter 2.1.2 --- Greedy Approach to Channel Assignment --- p.6Chapter 2.2 --- Generalised Assignment Problem --- p.7Chapter 2.2.1 --- Branch and Bound Approach for GAP --- p.8Chapter 2.2.2 --- Genetic Algorithm for GAP --- p.10Chapter 2.3 --- Negative Cycle Detection --- p.11Chapter 2.3.1 --- Labeling Method --- p.11Chapter 2.3.2 --- Bellman-Ford-Moore algorithm --- p.13Chapter 2.3.3 --- Amortized Search --- p.14Chapter 3 --- Multi-objective Assignment Problem --- p.15Chapter 3.1 --- Multi-objective Assignment Problem --- p.16Chapter 3.2 --- NP-Hardness --- p.18Chapter 3.3 --- Transformation of the Multi-objective Assignment Problem --- p.19Chapter 3.4 --- Algorithm --- p.23Chapter 3.5 --- Example --- p.25Chapter 3.6 --- A Special Case - Linear Objective Function --- p.32Chapter 3.7 --- Performance on the assignment problem --- p.33Chapter 4 --- Goal Programming Model for Channel Assignment Problem --- p.35Chapter 4.1 --- Motivation --- p.35Chapter 4.2 --- System Model --- p.36Chapter 4.3 --- Goal Programming Model for Channel Assignment Problem --- p.38Chapter 4.4 --- Simulation --- p.39Chapter 4.4.1 --- Throughput Optimization --- p.40Chapter 4.4.2 --- Best-First-Assign Algorithm --- p.41Chapter 4.4.3 --- Channel Swapping Algorithm --- p.41Chapter 4.4.4 --- Lower Bound --- p.43Chapter 4.4.5 --- Result --- p.43Chapter 4.5 --- Future Works --- p.50Chapter 5 --- Extended Application on the General Problem --- p.51Chapter 5.1 --- Latency Minimization --- p.52Chapter 5.2 --- Generalised Assignment Problem --- p.53Chapter 5.3 --- Quadratic Assignment Problem --- p.60Chapter 6 --- Conclusion --- p.65Bibliography --- p.6

An Efficient Implementation of the Robust Tabu Search Heuristic for Sparse Quadratic Assignment Problems

We propose and develop an efficient implementation of the robust tabu search heuristic for sparse quadratic assignment problems. The traditional implementation of the heuristic applicable to all quadratic assignment problems is of O(N^2) complexity per iteration for problems of size N. Using multiple priority queues to determine the next best move instead of scanning all possible moves, and using adjacency lists to minimize the operations needed to determine the cost of moves, we reduce the asymptotic complexity per iteration to O(N log N ). For practical sized problems, the complexity is O(N)