Multi-objective Shortest Path Problem Research Articles

An ant colony optimization algorithm for the bi-objective shortest path problem

Multi-objective shortest path problem (MOSP) is an extension of a traditional single objective shortest path problem that seeks for the efficient paths satisfying several conflicting objectives between two nodes of a network. MOSP is one of the most important problems in network optimization with wide applications in telecommunication industries, transportation and project management. This research presents an algorithm based on multi-objective ant colony optimization (ACO) to solve the bi-objective shortest path problem. To analyze the efficiency of the algorithm and check for the quality of solutions, experimental analyses are conducted. Two sets of small and large sized problems that generated randomly are solved. Results on the set problems are compared with those of label correcting solutions that is the most known efficient algorithm for solving MOSP. To compare the Pareto optimal frontiers produced by the suggested ACO algorithm and the label correcting algorithm, some performance measures are employed that consider and compare the distance, uniformity distribution and extension of the Pareto frontiers. The results on the set of instance problems show that the suggested algorithm produces good quality non-dominated solutions and time saving in computation of large-scale bi-objective shortest path problems.

On the selection of k efficient paths by clustering techniques

In the multi-objective shortest path problem usually there is not just one single path that simultaneously minimises r > 1 objective functions (costs); that is why the problem consists in finding the set of efficient paths of the given network. The number of such paths is often very large, while from an application point of view one is generally interested in selecting a given (small) number k > 1 of efficient paths that are representative of the whole efficient path set. In this paper, we propose a clustering-based approach for selecting k efficient paths maximising their representativeness with respect to the cost vectors of all the efficient paths or w.r.t. the dissimilarity among the k selected paths. Computational results are given on random networks; a comparison with a known approach in the literature is also presented.

Path recovery in frontier search for multiobjective shortest path problems

Frontier search is a best-first graph search technique that allows significant memory savings over previous best-first algorithms. The fundamental idea is to remove from memory already explored nodes, keeping only open nodes in the search frontier. However, once the goal node is reached, additional techniques are needed to recover the solution path. This paper describes and analyzes a path recovery procedure for frontier search applied to multiobjective shortest path problems. Differences with the scalar case are outlined, and performance is evaluated over a random problem set.

Selected Multicriteria Shortest Path Problems: An Analysis of Complexity, Models and Adaptation of Standard Algorithms

Selected Multicriteria Shortest Path Problems: An Analysis of Complexity, Models and Adaptation of Standard AlgorithmsThe paper presents selected multicriteria (multiobjective) approaches to shortest path problems. A classification of multi-objective shortest path (MOSP) problems is given. Different models of MOSP problems are discussed in detail. Methods of solving the formulated optimization problems are presented. An analysis of the complexity of the presented methods and ways of adapting of classical algorithms for solving multiobjective shortest path problems are described. A comparison of the effectiveness of solving selected MOSP problems defined as mathematical programming problems (using the CPLEX 7.0 solver) and multi-weighted graph problems (using modified Dijkstra's algorithm) is given. Experimental results of using the presented methods for multicriteria path selection in a terrain-based grid network are given.

Toll Pricing and Heterogeneous Users: Approximation Algorithms for Finding Bicriterion Time-Dependent Efficient Paths in Large-Scale Traffic Networks

This paper presents both exact and approximation algorithms for finding extreme efficient time-dependent shortest paths for use with dynamic traffic assignment applications to networks with variable toll pricing and heterogeneous users (with different value of time preferences). A parametric least-generalized cost path algorithm is presented to determine a complete set of extreme efficient time-dependent paths that simultaneously consider travel time and cost criteria. However, exact procedures may not be practical for large networks. For this reason, approximation schemes are devised and tested. Based on the concept of ϵ-efficiency in multiobjective shortest path problems, a binary search framework is developed to find a set of extreme efficient paths that minimize expected approximation error, with the use of the underlying value of time distribution. Both exact and approximation schemes (along with variants) are tested on three actual traffic networks. The experimental results indicate that the computa...

Toll Pricing and Heterogeneous Users

This paper presents both exact and approximation algorithms for finding extreme efficient time-dependent shortest paths for use with dynamic traffic assignment applications to networks with variable toll pricing and heterogeneous users (with different value of time preferences). A parametric least-generalized cost path algorithm is presented to determine a complete set of extreme efficient time-dependent paths that simultaneously consider travel time and cost criteria. However, exact procedures may not be practical for large networks. For this reason, approximation schemes are devised and tested. Based on the concept of ε-efficiency in multiobjective shortest path problems, a binary search framework is developed to find a set of extreme efficient paths that minimize expected approximation error, with the use of the underlying value of time distribution. Both exact and approximation schemes (along with variants) are tested on three actual traffic networks. The experimental results indicate that the computation time and the size of the solution set are jointly determined by several key parameters such as the number of time intervals and the number of nodes in the network. The results also suggest that the proposed approximation scheme is computationally efficient for large-scale bi-objective time-dependent shortest path applications while maintaining satisfactory solution quality.

The determination of the path with minimum‐cost norm value

AbstractThe multiobjective shortest path problem (MSPP) consists of finding the best nondominated path linking two specified nodes in a network where k > 1 different criteria are considered for the arc costs. Solving the MSPP implies determining all the nondominated paths; there may be many such paths, making the selection process a very hard task to accomplish. A traditional way of dealing with such a difficulty is using a utility function where the parameters are aggregated with different weights. In this work, an alternative utility function based on the norm value associated with each path is considered. Two algorithms for solving the minimum‐cost norm path problem are then proposed and some computational results are presented. © 2003 Wiley Periodicals, Inc.

A multi-objective shortest path problem

We study a multi-objective shortest path problem. We formulate a multi-objective Markov decision process model for the problem and solve it by the policy improvement procedure. We first show by counter-examples the differences between the multi-objective shortest path problem and the single-objective one. We next introduce “locally efficient policies” and present an algorithm for finding all efficient paths from all nodes to the destination. Moreover, as an application, we consider a shortest path problem with a constraint. Last, the algorithm is illustrated by a numerical example.

Solving min-max shortest-path problems on a network

In this article we consider the problem of determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it. This problem has a direct application in scheduling. It also has indirect applications in a class of routing problems and when considering multiobjective shortest-path problems. We present a label-correcting procedure for this problem. We also develop two pruning techniques, which, when incorporated in the label-correcting algorithm, recognize and discard many paths that are not part of the optimal path. Our computational results indicate that these techniques are able to speed up the label-correcting procedure by many orders of magnitude for hard problem instances, thereby enabling them to be solved in a reasonable time. © 1992 John Wiley & Sons, Inc.