A Linear Algorithm for a Minimax Location of a Path-Shaped Facility with a Specific Length in a Weighted Tree Network

Aboutahoun, Abdallah W.; El-Safty, Fatma

doi:10.1504/ijor.2021.10016889

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“…Most of papers study the problem of locating a path on a tree which minimizes either the sum of weighted distances from all vertices to the path (median criterion) or minimizes the maximum weighted distance from the vertices to the path (the center criterion). The path which satisfies the first criterion is called a median path [4,5,19,20,22,34], and the path which satisfies the second criterion is called a central path [1,2,7,28,33]. The median criterion is used to reduce the total cost of the service systems.…”

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confidence: 99%

An algorithm for solving the bi-objective median path-shaped facility on a tree network

Aboutahoun

El-Safty

2020

J Egypt Math Soc

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In this paper, an algorithm for the bi-objective median path (BMP) problem on a tree network is considered. The algorithm is based on the two-phase method which can compute all Pareto solutions for the BMP problem. The first phase is applied to find supported Pareto solutions by solving the uni-objective problem D(P, λ). The second phase is used to compute the unsupported Pareto solutions by applying a k-best algorithm which computes the k-best Pareto solutions in order of their objective values.

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