Topic

# Linear bottleneck assignment problem

About: Linear bottleneck assignment problem is a research topic. Over the lifetime, 1477 publications have been published within this topic receiving 45034 citations. The topic is also known as: LBAP.

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TL;DR: This paper has always been one of my favorite children, combining as it does elements of the duality of linear programming and combinatorial tools from graph theory, and it may be of some interest to tell the story of its origin this article.

Abstract: This paper has always been one of my favorite “children,” combining as it does elements of the duality of linear programming and combinatorial tools from graph theory. It may be of some interest to tell the story of its origin.

11,096 citations

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TL;DR: In this article, the equivalence of the Koopmans-beckmann problem to a linear assignment problem with certain additional constraints is demonstrated, and a method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions.

Abstract: This paper presents a formulation of the quadratic assignment problem, of which the Koopmans-Beckmann formulation is a special case. Various applications for the formulation are discussed. The equivalence of the problem to a linear assignment problem with certain additional constraints is demonstrated. A method for calculating a lower bound on the cost function is presented, and this forms the basis for an algorithm to determine optimal solutions. Further generalizations to cubic, quartic, N-adic problems are considered.

867 citations

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TL;DR: A collection of electronically available data instances for the Quadratic Assignment Problem are described, indicating whether or not the problem is solved to optimality and the best known bounds for the problem are supplied.

Abstract: A collection of electronically available data instances for the Quadratic Assignment Problem is described. For each instance, we provide detailed information, indicating whether or not the problem is solved to optimality. If not, we supply the best known bounds for the problem. Moreover we survey available software and describe recent dissertations related to the Quadratic Assignment Problem.

826 citations

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TL;DR: A discrete time model is presented for dynamic traffice assignment with a single destination and can be solved for a global optimum using a one-pass simplex algorithm---branch-and-bound is not required.

Abstract: A discrete time model is presented for dynamic traffice assignment with a single destination. Congestion is treated explicitly in the flow equations. The model is a nonlinear and nonconvex mathematical programming problem. A piecewise linear version of the model, with additional assumptions on the objective function, can be solved for a global optimum using a one-pass simplex algorithm---branch-and-bound is not required. The piecewise linear program has a staircase structure and can be solved by decomposition techniques or compactification methods for sparse matrices.

656 citations

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TL;DR: The effectiveness of the proposed PSO-based algorithm is demonstrated by comparing it with the genetic algorithm, which is well-known population-based probabilistic heuristic, on randomly generated task interaction graphs.

649 citations