Abstract
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.
Highlights
The problem of locating a path on a tree network has been receiving a lot of attention in the literature since it has many applications including the design of pipe lines, public transit line, and railroad lines
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 or minimizes the maximum weighted distance from the vertices to the path
The problem of siting special types of subgraphs such as trees and paths of the underlying network is considered as an extensive facility location problem
Summary
The problem of locating a path on a tree network has been receiving a lot of attention in the literature since it has many applications including the design of pipe lines, public transit line, and railroad lines. Becker et al [6] studied the problem of finding a path on a tree by considering both the median and the center criterion. They solved two problems, and each one was about finding a path of bounded length which minimizes one criterion with a restriction on the other criterion. They gave O(n log n) algorithms for both problems
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