Solving resource constrained shortest path problems with LP-based methods

Abstract

In the resource constrained shortest path problem (RCSPP) there is a directed graph along with a source node and a destination node, and each arc has a cost and a vector of weights specifying its requirements from a set of resource types with finite capacities. A minimum cost source-destination directed path is sought such that the total consumption of the arcs from each resource type does not exceed the capacity of the resource. In this paper we investigate LPbased branch-and-bound methods and introduce new cutting planes, separation procedures, variable fixing, and primal heuristic methods for solving RCSPP to optimality. We provide detailed computational experiments, and a comparison to other methods in the literature.

An exact bidirectional A⋆ approach for solving resource‐constrained shortest path problems

“…Lozano and Medaglia demonstrate improved performance relative to Santos et al and Zhu and Wilhelm . Horváth and Kis present a linear‐programming‐based approach for the RCSPP and demonstrate comparable performance to Lozano and Medaglia and outperforms the reference‐point approach presented in Di Puglia Pugliese and Guerriero . Sedeño Noda and Alonso‐Rodríguez present a method based on k ‐shortest paths and the pruning strategies of Lozano and Medaglia .…”

Approximate algorithm for searching shortest path in multiservice network with constrained resource

“…В настоящее время выделяют три класса методов и соответствующих им алгоритмов, способных находить точное или приближённое решение задачи RCSP: 1) методы ранжирования путей [2], 2) методы маркировки вершин [1,3,4] и 3) методы лагранжевой релаксации [5,6]. Первые два класса основаны на теоретико-графовой постановке задачи, в то время как методы третьего класса исходят из постановки задачи RCSP на языке целочисленного линейного программирования.…”

“…К сожалению, большинство существующих алгоритмов решения задачи RCSP медленно работают на сетях большой размерности, для многих современных приложений совершенно неприемлемы временные характеристики данных алгоритмов и их многочисленных усовершенствованных версий [3]. Поэтому остаётся актуальной разработка приближённых алгоритмов решения задачи RCSP, способных быстро находить решение на сетях большой размерности [3,6].…”

An Algorithm of Searching for the Shortest Path

“…The algorithm with less simulation time and higher prediction accuracy can serve as a fast and reliable tool for fire prediction [5]. Markó Horváth et al investigate LP-based branch-and-bound methods and introduce new cutting planes, separation procedures, variable fixing, and primal heuristic methods for solving RCSPP, in which there is a directed graph along with a source node and a destination node, and each arc has a cost and a vector of weights specifying its requirements from a set of resource types with finite capacities, to optimality [6]. Rafael Castro de Andrade considers a directed graph G=(V, A ) with a set of nodes V and a set of arcs A , and let c u v denote the length of an arc uv ∈ A .…”