WEIGHT OF SHORTEST PATH ANALYSES FOR THE OPTIMAL LOCATION PROBLEM

Weight of Shortest Path Analyses for the Optimal Location Problem

In this paper we consider the shortest path counting problem ( S P C P ) : how many shortest paths contain each edge of the network N = (V, E) with the vertex set V and the edge set E? There are n[n 1) shortest paths in the network with \V\ = n, so among all these shortest paths the S P C P requires us to count the number of shortest paths passing each edge. Defining the weight of shortest path...

The weight-constrained shortest path problem

In this class project, we investigate certain aspects of the Weight Constrained Shortest Path Problem. The problem is known NP-Hard, but there are algorithms, both exact and approximate, that attempt to solve it. We analyze two of the important exact methods label setting on graphs and Lagrangean relaxation of the constraint, and evaluate how they perform with different graph sizes, and differe...

Two optimal algorithms for finding bi-directional shortest path design problem in a block layout

In this paper, Shortest Path Design Problem (SPDP) in which the path is incident to all cells is considered. The bi-directional path is one of the known types of configuration of networks for Automated Guided Vehi-cles (AGV).To solve this problem, two algorithms are developed. For each algorithm an Integer Linear Pro-gramming (ILP) is determined. The objective functions of both algorithms are t...

Approximation Solutions for Time-Varying Shortest Path Problem

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

The Shortest Path Problem Revisited: Optimal Routing for Electric Vehicles