A hybrid Tabu search-simulated annealing method to solve quadratic assignment problem

Quadratic assignment problem (QAP) has been considered as one of the most complicated problems. The problem is NP-Hard and the optimal solutions are not available for large-scale problems. This paper presents a hybrid method using tabu search and simulated annealing technique to solve QAP called TABUSA. Using some well-known problems from QAPLIB generated by Burkard et al. (1997) [Burkard, R. E., Karisch, S. E., & Rendl, F. (1997). QAPLIB–a quadratic assignment problem library. Journal of Global Optimization, 10(4), 391-403.], two methods of TABUSA and TS are both coded on MATLAB and they are compared in terms of relative percentage deviation (RPD) for all instances. The performance of the proposed method is examined against Tabu search and the preliminary results indicate that the hybrid method is capable of solving real-world problems, efficiently

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

The single-finger keyboard layout problem

The problem of designing new keyboards layouts able to improve the typing speed of an average message has been widely considered in the literature of the Ergonomics domain. Empirical tests with users and simple optimization criteria have been used to propose new solutions. On the contrary, very few papers in Operations Research have addressed this optimization problem. In this paper we firstly resume the most relevant problems in keyboard design, enlightening the related Ergonomics aspects. Then we concentrate on keyboards that must be used witha single finger or stylus, like that of Portable Data Assistant, Smartphones and other small devices.We show that the underlying optimization problem is a generalization of the well known Quadratic Assignment Problem (QAP). We recall some of the most effective metaheuristic algorithms for QAP and we propose some non trivial extensions to the keyboard design problem. We compare the new algorithms through computational experiments with instances obtained from word lists of the English, French, Italian and Spanish languages. We provide on the web benchmark instances for each language and the best solutions we obtained

A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an itera- tive multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con- struction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solu- tion. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut prob- lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP)

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

Parallel hybrid chicken swarm optimization for solving the quadratic assignment problem

In this research, we intend to suggest a new method based on a parallel hybrid chicken swarm optimization (PHCSO) by integrating the constructive procedure of GRASP and an effective modified version of Tabu search. In this vein, the goal of this adaptation is straightforward about the fact of preventing the stagnation of the research. Furthermore, the proposed contribution looks at providing an optimal trade-off between the two key components of bio-inspired metaheuristics: local intensification and global diversification, which affect the efficiency of our proposed algorithm and the choice of the dependent parameters. Moreover, the pragmatic results of exhaustive experiments were promising while applying our algorithm on diverse QAPLIB instances . Finally, we briefly highlight perspectives for further research

AN INVESTIGATION OF METAHEURISTICS USING PATH- RELINKING ON THE QUADRATIC ASSIGNMENT PROBLEM

The Quadratic Assignment Problem (QAP) is a widely researched, yet complex, combinatorial optimization problem that is applicable in modeling many real-world problems. Specifically, many optimization problems are formulated as QAPs. To resolve QAPs, the recent trends have been to use metaheuristics rather than exact or heuristic methods, and many researchers have found that the use of hybrid metaheuristics is actually more effective. A newly proposed hybrid metaheuristic is path relinking (PR), which is used to generate solutions by combining two or more reference solutions. In this dissertation, we investigated these diversification and intensification mechanisms using QAP. To satisfy the extensive demands of the computational resources, we utilized a High Throughput Computing (HTC) environment and test cases from the QAPLIB (QAP test case repository). This dissertation consists of three integrated studies that are built upon each other. The first phase explores the effects of the parameter tuning, metaheuristic design, and representation schemes (random keys and permutation solution encoding procedures) of two path-based metaheuristics (Tabu Search and Simulated Annealing) and two population-based metaheuristics (Genetic Algorithms and Artificial Immune Algorithms) using QAP as a testbed. In the second phase of the study, we examined eight tuned metaheuristics representing two representation schemes using problem characteristics. We use problem size, flow and distance dominance measures, sparsity (number of zero entries in the matrices), and the coefficient of correlation measures of the matrices to build search trajectories. The third phase of the dissertation focuses on intensification and diversification mechanisms using path-relinking (PR) procedures (the two variants of position-based path relinking) to enhance the performance of path-based and population-based metaheuristics. The current research in this field has explored the unusual effectiveness of PR algorithms in variety of applications and has emphasized the significance of future research incorporating more sophisticated strategies and frameworks. In addition to addressing these issues, we also examined the effects of solution representations on PR augmentation. For future research, we propose metaheuristic studies using fitness landscape analysis to investigate particular metaheuristics\u27 fitness landscapes and evolution through parameter tuning, solution representation, and PR augmentation. The main research contributions of this dissertation are to widen the knowledge domains of metaheuristic design, representation schemes, parameter tuning, PR mechanism viability, and search trajectory analysis of the fitness landscape using QAPs