Comparative Performance of Tabu Search and Simulated Annealing Heuristics for the Quadratic Assignment Problem

For almost two decades the question of whether tabu search (TS) or simulated annealing (SA) performs better for the quadratic assignment problem has been unresolved. To answer this question satisfactorily, we compare performance at various values of targeted solution quality, running each heuristic at its optimal number of iterations for each target. We find that for a number of varied problem instances, SA performs better for higher quality targets while TS performs better for lower quality targets

Parallel Local Search on GPU

www.lifl.fr/~luongLocal search algorithms are a class of algorithms to solve complex optimization problems in science and industry. Even if these metaheuristics allow to significantly reduce the computational time of the solution exploration space, the iterative process remains costly when very large problem instances are dealt with. As a solution, graphics processing units (GPUs) represent an efficient alternative for calculations instead of traditional CPU. This paper presents a new methodology to design and implement local search algorithms on GPU. Methods such as tabu search, hill climbing or iterated local search present similar concepts that can be parallelized on GPU and then a general cooperative model can be highlighted. In addition to single-solution based metaheuristics on GPU, this model can be extended with a hybrid multi-core and multi-GPU approach for multiple local search methods such as multistart. The conclusions from both GPU and multi-GPU experiments indicate significant speed-ups compared to CPU approaches

A Heuristic Approach to the Theater Distribution Problem

Analysts at USTRANSCOM are tasked with providing vehicle mixtures that will support the distribution of requirements as provided in the form of TPFDD. An integer programming model exists to search for optimal solutions to these problems, but it is fairly time consuming, and produces only one of potentially several good quality solutions. This research constructs a number of heuristic approaches to solving the TDP. Two distinct shipping methods are examined and applied through both constructive and probabilistic vehicle assignment processes. Multistart metaheuristic approaches are designed and used in conjunction with the constructive and probabilistic approaches. Random TPFDDs of size 20, 100 and 1000 are tested, and solutions are compared to those obtained by the integer programming approach. The heuristic models implemented in this research develop feasible solutions to the notional TPFDDs in less time than the integer program. They can very quickly identify a number of good quality solutions to the same problem

Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem

Copyright @ 2000 INFORMSThe multisource Weber problem is to locate simultaneously m facilities in the Euclidean plane to minimize the total transportation cost for satisfying the demand of n fixed users, each supplied from its closest facility. Many heuristics have been proposed for this problem, as well as a few exact algorithms. Heuristics are needed to solve quickly large problems and to provide good initial solutions for exact algorithms. We compare various heuristics, i.e., alternative location-allocation (Cooper 1964), projection (Bongartz et al. 1994), Tabu search (Brimberg and Mladenovic 1996a), p-Median plus Weber (Hansen ct al. 1996), Genetic search and several versions of Variable Neighbourhood search. Based on empirical tests that are reported, it is found that most traditional and some recent heuristics give poor results when the number of facilities to locate is large and that Variable Neighbourhood search gives consistently best results, on average, in moderate computing time.This study was supported by the Department of National Defence (Canada) Academic Research; Office of Naval Research Grant N00014-92-J-1194, Natural Sciences and Engineering Research Council of Canada Grant GPO 105574 and Fonds pour la Formation des Chercheurs et l’Aide a la Recherche Grant 32EQ 1048; and by an International Postdoctoral Fellowship of the Natural Sciences and Engineering Research Council of Canada, Grant OGPOO 39682

Benchmarking a wide spectrum of metaheuristic techniques for the radio network design problem

The radio network design (RND) is an NP-hard optimization problem which consists of the maximization of the coverage of a given area while minimizing the base station deployment. Solving RND problems efficiently is relevant to many fields of application and has a direct impact in the engineering, telecommunication, scientific, and industrial areas. Numerous works can be found in the literature dealing with the RND problem, although they all suffer from the same shortfall: a noncomparable efficiency. Therefore, the aim of this paper is twofold: first, to offer a reliable RND comparison base reference in order to cover a wide algorithmic spectrum, and, second, to offer a comprehensible insight into accurate comparisons of efficiency, reliability, and swiftness of the different techniques applied to solve the RND problem. In order to achieve the first aim we propose a canonical RND problem formulation driven by two main directives: technology independence and a normalized comparison criterion. Following this, we have included an exhaustive behavior comparison between 14 different techniques. Finally, this paper indicates algorithmic trends and different patterns that can be observed through this analysis.Publicad

Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing problem into a travelling salesman problem and uses the assignment problem as a lower bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational experiments show that we are able to exactly solve large test instances with up to 1000 customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups of instances. We wanted to determine how far the difference is between the best feasible solution obtained by VNS and the value of optimal solution in order to use the output of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions

DOTcvpSB, a software toolbox for dynamic optimization in systems biology

<p>Abstract</p> <p>Background</p> <p>Mathematical optimization aims to make a system or design as effective or functional as possible, computing the quality of the different alternatives using a mathematical model. Most models in systems biology have a dynamic nature, usually described by sets of differential equations. Dynamic optimization addresses this class of systems, seeking the computation of the optimal time-varying conditions (control variables) to minimize or maximize a certain performance index. Dynamic optimization can solve many important problems in systems biology, including optimal control for obtaining a desired biological performance, the analysis of network designs and computer aided design of biological units.</p> <p>Results</p> <p>Here, we present a software toolbox, DOTcvpSB, which uses a rich ensemble of state-of-the-art numerical methods for solving continuous and mixed-integer dynamic optimization (MIDO) problems. The toolbox has been written in MATLAB and provides an easy and user friendly environment, including a graphical user interface, while ensuring a good numerical performance. Problems are easily stated thanks to the compact input definition. The toolbox also offers the possibility of importing SBML models, thus enabling it as a powerful optimization companion to modelling packages in systems biology. It serves as a means of handling generic black-box models as well.</p> <p>Conclusion</p> <p>Here we illustrate the capabilities and performance of DOTcvpSB by solving several challenging optimization problems related with bioreactor optimization, optimal drug infusion to a patient and the minimization of intracellular oscillations. The results illustrate how the suite of solvers available allows the efficient solution of a wide class of dynamic optimization problems, including challenging multimodal ones. The toolbox is freely available for academic use.</p

A Parallel Tabu Search for the Large-scale Quadratic Assignment Problem

International audienceParallelization is an important paradigm for solving massive optimization problems. Understanding how to fully benefit form the aggregated computing power and what makes a parallel strategy successful is a difficult issue. In this study, we propose a simple parallel iterative tabu search (PITS) and study its effectiveness with respect to different experimental settings. Using the quadratic assignment problem (QAP) as a case study, we first consider different small-and medium-size instances from the literature and then tackle a large-size instance that was rarely considered due the its inherent solving difficulty. In particular, we show that a balance between the number of function evaluations each parallel process is allowed to perform before resuming the search is a critical issue to obtain an improved quality

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

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