Instance generators and test suites for the multiobjective quadratic assignment problem

We describe, and make publicly available, two problem instance generators for a multiobjective version of the well-known quadratic assignment problem (QAP). The generators allow a number of instance parameters to be set, including those controlling epistasis and inter-objective correlations. Based on these generators, several initial test suites are provided and described. For each test instance we measure some global properties and, for the smallest ones, make some initial observations of the Pareto optimal sets/fronts. Our purpose in providing these tools is to facilitate the ongoing study of problem structure in multiobjective (combinatorial) optimization, and its effects on search landscape and algorithm performance.

Some reformulations for the quadratic assignment problem

Kombinatorisk optimering handlar om att hitta en bra eller rent av den bästa möjliga lösningen från ett känt antal lösningar eller kombinationer. Ofta är antalet lösningar så enormt att en genomgång av alla olika lösningar inte är möjlig. En av huvudorsakerna till att det forskas inom kombinatorisk optimering är att liknande frågeställningar eller problem uppkommer inom så många olika områden. Påståendet stämmer speciellt bra för kvadratiska tilldelningsproblem(eng. Quadratic Assignment Problem). Sådana problem uppstår då man försöker beskriva en stor mängd tillämpade frågeställningar. Vilken gate skall väljas för flygen på större flygplatser för att minimera den totala väg människorna behöver gå och bagaget förflyttas? Var skall olika avdelningar på en fabrik placeras för att minimera materialförflyttningar mellan avdelningarna? Hur ser ett optimalt tangentbord ut för olika språk? Var skall komponenterna placeras på ett kretskort? De här är alla frågor som kan besvaras genom att lösa kvadratiska tilldelningsproblem. Kvadratiska tilldelningsproblem är dock mycket svåra att lösa. Det beror på att problemet i den standardform det matematiskt formuleras i huvudsak består av produkter av binära variabler. I denna avhandling har problemet omformulerats till en linjär diskret form som innehåller färre variabler. Med omformuleringen har bland annat flera tidigare olösta kvadratiska tilldelningsproblem kunnat lösas till globalt optimum, den bästa möjliga lösningen, för första gången någonsin.

Quadratic assignment problem /

Includes bibliographies (p. 14).

Statistical bound of genetic solutions to quadratic assignment problems

Quadratic assignment problems (QAPs) are commonly solved by heuristic methods, where the optimum is sought iteratively. Heuristics are known to provide good solutions but the quality of the solutions, i.e., the confidence interval of the solution is unknown. This paper uses statistical optimum estimation techniques (SOETs) to assess the quality of Genetic algorithm solutions for QAPs. We examine the functioning of different SOETs regarding biasness, coverage rate and length of interval, and then we compare the SOET lower bound with deterministic ones. The commonly used deterministic bounds are confined to only a few algorithms. We show that, the Jackknife estimators have better performance than Weibull estimators, and when the number of heuristic solutions is as large as 100, higher order JK-estimators perform better than lower order ones. Compared with the deterministic bounds, the SOET lower bound performs significantly better than most deterministic lower bounds and is comparable with the best deterministic ones. 

Approche efficace pour la conception des architectures multiprocesseurs sur puce électronique

Les systèmes multiprocesseurs sur puce électronique (On-Chip Multiprocessor [OCM]) sont considérés comme les meilleures structures pour occuper l'espace disponible sur les circuits intégrés actuels. Dans nos travaux, nous nous intéressons à un modèle architectural, appelé architecture isométrique de systèmes multiprocesseurs sur puce, qui permet d'évaluer, de prédire et d'optimiser les systèmes OCM en misant sur une organisation efficace des nœuds (processeurs et mémoires), et à des méthodologies qui permettent d'utiliser efficacement ces architectures. Dans la première partie de la thèse, nous nous intéressons à la topologie du modèle et nous proposons une architecture qui permet d'utiliser efficacement et massivement les mémoires sur la puce. Les processeurs et les mémoires sont organisés selon une approche isométrique qui consiste à rapprocher les données des processus plutôt que d'optimiser les transferts entre les processeurs et les mémoires disposés de manière conventionnelle. L'architecture est un modèle maillé en trois dimensions. La disposition des unités sur ce modèle est inspirée de la structure cristalline du chlorure de sodium (NaCl), où chaque processeur peut accéder à six mémoires à la fois et où chaque mémoire peut communiquer avec autant de processeurs à la fois. Dans la deuxième partie de notre travail, nous nous intéressons à une méthodologie de décomposition où le nombre de nœuds du modèle est idéal et peut être déterminé à partir d'une spécification matricielle de l'application qui est traitée par le modèle proposé. Sachant que la performance d'un modèle dépend de la quantité de flot de données échangées entre ses unités, en l'occurrence leur nombre, et notre but étant de garantir une bonne performance de calcul en fonction de l'application traitée, nous proposons de trouver le nombre idéal de processeurs et de mémoires du système à construire. Aussi, considérons-nous la décomposition de la spécification du modèle à construire ou de l'application à traiter en fonction de l'équilibre de charge des unités. Nous proposons ainsi une approche de décomposition sur trois points : la transformation de la spécification ou de l'application en une matrice d'incidence dont les éléments sont les flots de données entre les processus et les données, une nouvelle méthodologie basée sur le problème de la formation des cellules (Cell Formation Problem [CFP]), et un équilibre de charge de processus dans les processeurs et de données dans les mémoires. Dans la troisième partie, toujours dans le souci de concevoir un système efficace et performant, nous nous intéressons à l'affectation des processeurs et des mémoires par une méthodologie en deux étapes. Dans un premier temps, nous affectons des unités aux nœuds du système, considéré ici comme un graphe non orienté, et dans un deuxième temps, nous affectons des valeurs aux arcs de ce graphe. Pour l'affectation, nous proposons une modélisation des applications décomposées en utilisant une approche matricielle et l'utilisation du problème d'affectation quadratique (Quadratic Assignment Problem [QAP]). Pour l'affectation de valeurs aux arcs, nous proposons une approche de perturbation graduelle, afin de chercher la meilleure combinaison du coût de l'affectation, ceci en respectant certains paramètres comme la température, la dissipation de chaleur, la consommation d'énergie et la surface occupée par la puce. Le but ultime de ce travail est de proposer aux architectes de systèmes multiprocesseurs sur puce une méthodologie non traditionnelle et un outil systématique et efficace d'aide à la conception dès la phase de la spécification fonctionnelle du système.

A public transport bus assignment problem: parallel metaheuristics assessment

Combinatorial Optimization Problems occur in a wide variety of contexts and generally are NP-hard problems. At a corporate level solving this problems is of great importance since they contribute to the optimization of operational costs. In this thesis we propose to solve the Public Transport Bus Assignment problem considering an heterogeneous fleet and line exchanges, a variant of the Multi-Depot Vehicle Scheduling Problem in which additional constraints are enforced to model a real life scenario. The number of constraints involved and the large number of variables makes impracticable solving to optimality using complete search techniques. Therefore, we explore metaheuristics, that sacrifice optimality to produce solutions in feasible time. More concretely, we focus on the development of algorithms based on a sophisticated metaheuristic, Ant-Colony Optimization (ACO), which is based on a stochastic learning mechanism. For complex problems with a considerable number of constraints, sophisticated metaheuristics may fail to produce quality solutions in a reasonable amount of time. Thus, we developed parallel shared-memory (SM) synchronous ACO algorithms, however, synchronism originates the straggler problem. Therefore, we proposed three SM asynchronous algorithms that break the original algorithm semantics and differ on the degree of concurrency allowed while manipulating the learned information. Our results show that our sequential ACO algorithms produced better solutions than a Restarts metaheuristic, the ACO algorithms were able to learn and better solutions were achieved by increasing the amount of cooperation (number of search agents). Regarding parallel algorithms, our asynchronous ACO algorithms outperformed synchronous ones in terms of speedup and solution quality, achieving speedups of 17.6x. The cooperation scheme imposed by asynchronism also achieved a better learning rate than the original one.

A simulation-based algorithm for solving the resource-assignment problem in satellite telecommunication networks

This paper proposes an heuristic for the scheduling of capacity requests and the periodic assignment of radio resources in geostationary (GEO) satellite networks with star topology, using the Demand Assigned Multiple Access (DAMA) protocol in the link layer, and Multi-Frequency Time Division Multiple Access (MF-TDMA) and Adaptive Coding and Modulation (ACM) in the physical layer.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

Referee Assignment Problem Case: Italian Volleyball Championships

This thesis addresses the formulation of a referee assignment problem for the Italian Volleyball Serie A Championships. The problem has particular constraints such as a referee must be assigned to different teams in a given period of times, and the minimal/maximal level of workload for each referee is obtained by considering cost and profit in the objective function. The problem has been solved through an exact method by using an integer linear programming formulation and a clique based decomposition for improving the computing time. Extensive computational experiments on real-world instances have been performed to determine the effectiveness of the proposed approach.

An alternative formulation for the fuzzy assignment problem

The existing assignment problems for assigning n jobs to n individuals are limited to the considerations of cost or profit measured as crisp. However, in many real applications, costs are not deterministic numbers. This paper develops a procedure based on Data Envelopment Analysis method to solve the assignment problems with fuzzy costs or fuzzy profits for each possible assignment. It aims to obtain the points with maximum membership values for the fuzzy parameters while maximizing the profit or minimizing the assignment cost. In this method, a discrete approach is presented to rank the fuzzy numbers first. Then, corresponding to each fuzzy number, we introduce a crisp number using the efficiency concept. A numerical example is used to illustrate the usefulness of this new method. © 2012 Operational Research Society Ltd. All rights reserved.

Genetic Algorithm Approach for Solving the Task Assignment Problem

This research was partially supported by the Serbian Ministry of Science and Ecology under project 144007. The authors are grateful to Ivana Ljubić for help in testing and to Vladimir Filipović for useful suggestions and comments.

Solving the Task Assignment Problem with a Variable Neighborhood Search

In this paper a variable neighborhood search (VNS) approach for the task assignment problem (TAP) is considered. An appropriate neighborhood scheme along with a shaking operator and local search procedure are constructed specifically for this problem. The computational results are presented for the instances from the literature, and compared to optimal solutions obtained by the CPLEX solver and heuristic solutions generated by the genetic algorithm. It can be seen that the proposed VNS approach reaches all optimal solutions in a quite short amount of computational time.