Solving the quadratic assignment problem by a Hybrid Algorithm

This paper presents a hybrid algorithm to solve the Quadratic Assignment Problem (QAP). The proposed algorithm involves using the Greedy Randomized Adaptive Search Procedure (GRASP) to obtain an initial solution, and then using a combined Simulated Annealing (SA) and Tabu Search (TS) algorithm to improve the solution. Experimental results  indicate that the hybrid algorithm is able to obtain good quality solutions for QAPLIB test problems within reasonable computation time

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)

EFFICIENT METAHEURISTIC ALGORITHMS FOR THE MULTI-STRIPE TRAVELLING SALESMAN PROBLEM

The Multi-stripe Travelling Salesman Problem (Ms-TSP) is an extension of the Travelling Salesman Problem (TSP). In the \textit{q}-stripe TSP with $q \geq 1$, the objective function sums the costs for travelling from one customer to each of the next \textit{q} customers along the tour. The resulting \textit{q}-stripe TSP generalizes the TSP and forms a special case of the Quadratic Assignment Problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The proposed algorithm has two main components, which are construction and improvement phases. The construction phase generates a solution using Greedy Randomized Adaptive Search Procedure (GRASP) while the optimization phase improves the solution with several variants of Variable Neighborhood Search, both coupled with a technique called Shaking Technique to escape from local optima. In addition, Adaptive Memory is integrated into our algorithms to balance between the diversification and intensification. To show the efficiency of our proposed metaheuristic algorithms, we extensively experiment on benchmark instances. The results indicate that the developed algorithms can produce efficient and effective solutions at a reasonable computation time

Consumer choice in competitive location models: Formulations and heuristics

A new direction of research in Competitive Location theory incorporates theories of Consumer Choice Behavior in its models. Following this direction, this paper studies the importance of consumer behavior with respect to distance or transportation costs in the optimality of locations obtained by traditional Competitive Location models. To do this, it considers different ways of defining a key parameter in the basic Maximum Capture model (MAXCAP). This parameter will reflect various ways of taking into account distance based on several Consumer Choice Behavior theories. The optimal locations and the deviation in demand captured when the optimal locations of the other models are used instead of the true ones, are computed for each model. A metaheuristic based on GRASP and Tabu search procedure is presented to solve all the models. Computational experience and an application to 55-node network are also presented.Distance, competitive location models, consumer choice behavior, GRASP, tabu

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

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