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Improving group role assignment problem by incremental assignment algorithm

The Assignment Problem is a basic combinatorial optimization problem. In a weighted bipartite graph, the Assignment Problem is to find a largest sum of weights matching. The Hungarian method is a well-known algorithm which is combinatorial optimization. Adding a new row and a new column to a weighted bipartite graph is called the Incremental Assignment Problem (IAP). The maximum weighted matching (the optimal solution) of the weighted bipartite graph has been given. The algorithm of the Incremental Assignment Problem utilizes the given optimal solution (the maximum weighted matching) and the dual variables to solve the matrix after extended bipartite graph. This thesis proposes an improvement of the Incremental Assignment Algorithm (IAA), named the Improved Incremental Assignment Algorithm. The improved algorithm will save the operation time and operation space to find the optimal solution (the maximum weighted matching) of the bipartite graph. We also present the definition of the Incremental Group Role Assignment Problem that based on the Group Role Assignment Problem (GRAP) and Incremental Assignment Problem (IAP). A solution has been designed to solve it by using the Improved Incremental Assignment Algorithm (IIAA). In this thesis, simulation results are presented. We utilize the tests to compare the algorithm of the Incremental Assignment Problem and the Improved Incremental Assignment Algorithm (IIAA) to show the advantages of IIAA.Master of Science (MSc) in Computational Science

Resolution Search et problèmes d'optimisation discrète

Les problèmes d optimisation discrète sont pour beaucoup difficiles à résoudre, depar leur nature combinatoire. Citons par exemple les problèmes de programmationlinéaire en nombres entiers. Une approche couramment employée pour les résoudreexactement est l approche de Séparation et Évaluation Progressive. Une approchedifférente appelée Resolution Search a été proposée par Chvátal en 1997 pourrésoudre exactement des problèmes d optimisation à variables 0-1, mais elle restemal connue et n a été que peu appliquée depuis.Cette thèse tente de remédier à cela, avec un succès partiel. Une première contributionconsiste en la généralisation de Resolution Search à tout problème d optimisationdiscrète, tout en introduisant de nouveaux concepts et définitions. Ensuite,afin de confirmer l intérêt de cette approche, nous avons essayé de l appliquer enpratique pour résoudre efficacement des problèmes bien connus. Bien que notrerecherche n ait pas abouti sur ce point, elle nous a amené à de nouvelles méthodespour résoudre exactement les problèmes d affectation généralisée et de localisationsimple. Après avoir présenté ces méthodes, la thèse conclut avec un bilan et desperspectives sur l application pratique de Resolution Search.The combinatorial nature of discrete optimization problems often makes them difficultto solve. Consider for instance integer linear programming problems, which arecommonly solved using a Branch-and-Bound approach. An alternative approach,Resolution Search, was proposed by Chvátal in 1997 for solving 0-1 optimizationproblems, but remains little known to this day and as such has seen few practicalapplications.This thesis attempts to remedy this state of affairs, with partial success. Itsfirst contribution consists in the generalization of Resolution Search to any discreteoptimization problem, while introducing new definitions and concepts. Next, wetried to validate this approach by attempting to solve well-known problems efficientlywith it. Although our research did not succeed in this respect, it lead usto new methods for solving the generalized assignment and uncapacitated facilitylocation problems. After presenting these methods, this thesis concludes with asummary of our attempts at practical application of Resolution Search, along withfurther perspectives on this matter.AVIGNON-Bib. numérique (840079901) / SudocSudocFranceF