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The Shortest Path Problems

1970
The first image that comes to mind when the word ‘network’ is mentioned is a traffic network, whether it be road or air traffic. Most of us are familiar with such networks since one rarely travels from one location to another without consulting a ‘map’, which is, in our terminology, a ‘network’.
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Shortest Paths with Shortest Detours

Journal of Optimization Theory and Applications, 2017
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Carolin Torchiani   +3 more
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On the Forward Shortest Path Tour Problem

2017
This paper addresses the Forward Shortest Path Tour Problem (FSPTP). Given a weighted directed graph, whose nodes are partitioned into clusters, the FSPTP consists of finding a shortest path from a source node to a destination node and which crosses all the clusters in a fixed order.
Carrabs, Francesco   +3 more
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Computation of the Reverse Shortest-Path Problem

Journal of Global Optimization, 2003
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Yixun Lin, J. Z. Zhang
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Fuzzy shortest path problem

Computers & Industrial Engineering, 1994
Abstract We discuss the problem of finding the shortest paths from a fixed origin to a specified nodes in a network with arcs represented as intervals on real line. As a preliminary, we define the order relation between intervals by using two parameters.
Mitsuo Gen, Shinkoh Okada
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Fuzzy Shortest Path Problem

2007
In this chapter we consider the shortest route problem where distances/costs are not known precisely and are modeled using fuzzy numbers. The fuzzy shortest route problem is outlined in the next section. We have previously used an evolutionary algorithm to solve an example problem (Section 6.5.1 of [2] and [3]).
James J. Buckley, Leonard J. Jowers
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Shortest Path Problems in Hydrogeology

Groundwater, 1978
ABSTRACTMany aspects of ground water involve shortest paths between two points and shortest round trips to many points. These problems are included in network theory which is not easily available to ground‐water specialists. This paper introduces some of the techniques which can be solved by hand for fairly small projects.
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A multi-objective shortest path problem

Mathematical Methods of Operations Research, 2001
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A note on the problem of updating shortest paths

Networks, 1981
AbstractThe problem of updating shortest paths from all the vertices to a set of vertices when the length function is decreased was considered by S. Goto and A. Sangiovanni‐Vincentelli and a solution algorithm was presented based on the LU‐factorization of the measure matrix and a matrix inversion formula.
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Shortest and longest path problems

Optimization, 1996
This paper considers a wide class of shortest path problems in acyclic digraphs, where path lengths are given by the multiplicatively additive value. The problems are solved through bynamic programming, [4]. The bynamic programming formulation for the class has a system of two interrelated recursive equations. By solving the system, simultaneously both
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