Topic

# Quadratic assignment problem

About: Quadratic assignment problem is a research topic. Over the lifetime, 3491 publications have been published within this topic receiving 116582 citations. The topic is also known as: QAP.

##### Papers published on a yearly basis

##### Papers

More filters

••

TL;DR: In this paper, algorithms for the solution of the general assignment and transportation problems are presen, and the algorithm is generalized to one for the transportation problem.

Abstract: In this paper we presen algorithms for the solution of the general assignment and transportation problems. In Section 1, a statement of the algorithm for the assignment problem appears, along with a proof for the correctness of the algorithm. The remarks which constitute the proof are incorporated parenthetically into the statement of the algorithm. Following this appears a discussion of certain theoretical aspects of the problem. In Section 2, the algorithm is generalized to one for the transportation problem. The algorithm of that section is stated as concisely as possible, with theoretical remarks omitted.

3,918 citations

••

[...]

TL;DR: Computational results on the Traveling Salesman Problem and the Quadratic Assignment Problem show that MM AS is currently among the best performing algorithms for these problems.

2,739 citations

•

01 Jan 1983

TL;DR: In this article, problem complexity and method efficiency in optimisation are discussed in terms of problem complexity, method efficiency, and method complexity in the context of OO optimization, respectively.

Abstract: (1984). Problem Complexity and Method Efficiency in Optimization. Journal of the Operational Research Society: Vol. 35, No. 5, pp. 455-455.

2,382 citations

••

TL;DR: This paper defines the various components comprising a GRASP and demonstrates, step by step, how to develop such heuristics for combinatorial optimization problems.

Abstract: Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

2,370 citations

••

TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.

Abstract: L. G. Khachiyan recently published a polynomial algorithm to check feasibility of a system of linear inequalities. The method is an adaptation of an algorithm proposed by Shor for non-linear optimization problems. In this paper we show that the method also yields interesting results in combinatorial optimization. Thus it yields polynomial algorithms for vertex packing in perfect graphs; for the matching and matroid intersection problems; for optimum covering of directed cuts of a digraph; for the minimum value of a submodular set function; and for other important combinatorial problems. On the negative side, it yields a proof that weighted fractional chromatic number is NP-hard.

2,170 citations