Local search heuristics for the multidimensional assignment problem

The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a large number of applications. We consider several known neighborhoods, generalize them and propose some new ones. The heuristics are evaluated both theoretically and experimentally and dominating algorithms are selected. We also demonstrate that a combination of two neighborhoods may yield a heuristics which is superior to both of its components

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