Assignment problem

About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.

An effective invasive weed optimization algorithm for scheduling semiconductor final testing problem

Abstract: In this paper, we address a semiconductor final testing problem from the semiconductor manufacturing process We aim to determine both the assignment of machines and the sequence of operations on all the machines so as to minimize makespan We present a cooperative co-evolutionary invasive weed optimization (CCIWO) algorithm which iterates with two coupled colonies, one of which addresses the machine assignment problem and the other deals with the operation sequence problem To well balance the search capability of the two colonies, we adopt independent size setting for each colony We design the reproduction and spatial dispersal methods for both the colonies by taking advantage of the information collected during the search process and problem-specific knowledge Extensive experiments and comparison show that the proposed CCIWO algorithm performs much better than the state-of-the-art algorithms in the literature for solving the semiconductor final testing scheduling problem with makespan criteria

A parallel shortest augmenting path algorithm for the assignment problem

Abstract: : We describe a parallel version of the shortest augmenting path algorithm for the assignment problem. While generating the initial dual solution and partial assignment in parallel does not require substantive changes in the sequential algorithm, using several augmenting paths in parallel does require a new dual variable recalculation method. The parallel algorithm was tested on a 14-processor Butterfly Plus computer, on problems with up to 900 million variables. The speedup obtained increases with problem size. The algorithm was also embedded into a parallel branch and bound procedure for the traveling salesman problem on a directed graph, which was test on the Butterfly Plus on problems involving up to 7,500 cities. To our knowledge, these are the largest assignment problems and traveling salesman problems solved so far.

New approaches for solving the block-to-train assignment problem

Abstract: Railroad planning involves solving two optimization problems: (i) the blocking problem, which determines what blocks to make and how to route traffic over these blocks; and (ii) the train schedule design problem, which determines train origins, destinations, and routes. Once the blocking plan and train schedule have been obtained, the next step is to determine which trains should carry which blocks. This problem, known as the block-to-train assignment problem, is considered in this paper. We provide two formulations for this problem: an arc-based formulation and a path-based formulation. The latter is generally smaller than the former, and it can better handle practical constraints. We also propose exact and heuristic algorithms based on the path-based formulation. Our exact algorithm solves an integer programming formulation with CPLEX using both a priori generation and dynamic generation of paths. Our heuristic algorithms include a Lagrangian relaxation-based method as well as a greedy construction method. We present computational results of our algorithms using the data provided by a major US railroad. We show that we can obtain an optimal solution of the block-to-train assignment problem within a few minutes of computational time, and can obtain heuristic solutions with 1–2p deviations from the optimal solutions within a few seconds. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008

Competitive Weighted Matching in Transversal Matroids

Abstract: Consider a bipartite graph with a set of left-vertices and a set of right-vertices. All the edges adjacent to the same left-vertex have the same weight. We present an algorithm that, given the set of right-vertices and the number of left-vertices, processes a uniformly random permutation of the left-vertices, one left-vertex at a time. In processing a particular left-vertex, the algorithm either permanently matches the left-vertex to a thus-far unmatched right-vertex, or decides never to match the left-vertex. The weight of the matching returned by our algorithm is within a constant factor of that of a maximum weight matching.