Topic
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.
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TL;DR: This paper discusses how to adequately characterize the features of a problem instance that have impact on difficulty in terms of algorithmic performance, and how such features can be defined and measured for various optimization problems.
175 citations
27 Feb 2003
TL;DR: In this article, it was shown that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for the maximum matching problem, although the algorithm does not employ the idea of augmenting paths.
Abstract: Randomized search heuristics like evolutionary algorithms are mostly applied to problems whose structure is not completely known but also to combinatorial optimization problems. Practitioners report surprising successes but almost no results with theoretically well-founded analyses exist. Such an analysis is started in this paper for a fundamental evolutionary algorithm and the well-known maximum matching problem. It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths. Moreover, for very simple graphs it is proved that the expected optimization time of the algorithm is polynomially bounded and bipartite graphs are constructed where this time grows exponentially.
174 citations
TL;DR: This work examines the classic on-line bipartite matching problem studied by Karp, Vazirani, and VazIRani and provides a simple proof that the Ranking algorithm for this problem achieves a competitive ratio of 1 -- 1/e.
Abstract: We examine the classic on-line bipartite matching problem studied by Karp, Vazirani, and Vazirani [8] and provide a simple proof of their result that the Ranking algorithm for this problem achieves a competitive ratio of 1 -- 1/e.
171 citations
TL;DR: It is found that as the problem size grows, the IP model size quickly expands to an extent that the ILOG CPLEX Solver can hardly manage, and two meta-heuristic approaches, Tabu Search (TS) and genetic algorithm (GA) are proposed.
171 citations
TL;DR: In this article, the optimal assignment of n men to n jobs, so as to maximize the total expected reward is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy.
Abstract: Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a “p” man is assigned to an “X = x” job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs, so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if p1 ≦ p2 ≦ ⋯ ≦ pn the optimal choice in the initial stage of an n stage assignment problem is to use pi if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected)...
171 citations