Shortest path problems with partial information: Models and algorithms for detecting dominance

In this work we focus on partial information models for the well-known shortest path problem, where we consider multiple instances of values for the parameters that determine the cost of each arc. This allows coping with the uncertainty about the future, the imprecision of data, the arbitrariness of some options, the evolving values of the decision makers (DMs) and/or the multiplicity of DMs (in group decision making). This paper proves some results and presents detailed algorithms to identify the set of non dominated paths, a concept from decision theory under partial information. We first address problems with a finite set of instances, then problems with a general (eventually not discrete) set of instances and finally we study a particular case of the latter, which complies with a condition that may hold in some situations. To deal with these partial information problems we propose a new use for existing multicriteria algorithms based on the ranking of shortest paths.http://www.sciencedirect.com/science/article/B6VCT-3Y9MCF4-2/1/08f0e5f69f786fbe024d2c68ad927ff

Dealing with imprecise information in group multicriteria decisions: a methodology and a GDSS architecture

This paper outlines a distributed GDSS suitable to be used over the Internet, based on the VIP Analysis methodology and software. VIP Analysis incorporates complementary approaches to deal with the aggregation of multicriteria performances by means of an additive value function under imprecise information. This proposed GDSS intends to support a decision panel forming a democratic decision unit, whose members wish to reach a final decision in a choice problem, based on consensus or on some majority rule. Its purpose is not to impose an aggregated model from the individual ones. Rather, the GDSS is designed to reflect to each member the consequences of his/her inputs, confronting them with analogous reflections of the group members' inputs. We propose aggregation procedures to provide a reflection of the group's inputs to each of its members, and an architecture for a GDSS implementing these procedures.http://www.sciencedirect.com/science/article/B6VCT-4B5JR15-7/1/ec69930c867d6cea3058a818f9f33fe

Finding non-dominated bicriteria shortest pairs of disjoint simple paths

http://www.sciencedirect.com/science/article/B6VC5-4VBDKNX-1/2/b7e59602a9fb4eb885f498b0d8c779c

A critical reflection on optimal decision

A discussion and critique of the ideological framework that led to the preponderance of the concepts of utility and optimum as critical referents of decision in the modern age. The result of this critique is an appreciation of the limits of classical operational research, which can only be overcome by adopting a constructivist perspective. In the author's view, this is the approach that will viabilise a contribution to meet the demands imposed by the civilisational process.http://www.sciencedirect.com/science/article/B6VCT-48NX8MJ-7/1/a34b610f33c1dc54289e24c24b5ed04

On computing ELECTRE's credibility indices under partial information

The ELECTRE family of decision aid methods is a well-known approach to help decision makers (DMs) advance in a decision process. Among the most recent methods in the family, ELECTRE IS, III, and TRI compute fuzzy indices for the credibility of a given action outranking some other. We consider the case when the DMs are unsure which values each parameter should take, which may result from insufficient, imprecise or contradictory information, as well as from different preferences among a group of DMs. In the framework of a robustness analysis approach, where DMs provide only partial information on the parameter values (through constraints on acceptable combinations), we study how to find whether an outranking among two actions in an ELECTRE method is robust. In this context, we study the resulting nonlinear problems of optimizing a credibility index (under the type of constraints that we consider to appear in practice) and present some examples. Copyright © 1999 John Wiley & Sons, Ltd

An approach to determine unsupported non-dominated solutions in bicriteria integer linear programs

In this paper, we introduce a method for finding both supported and unsupported non-dominated solutions of a bicriteria integer linear program (BCILP). One-phase and two-phase implementations of the method are described, and their interactive versions are outlined. The one-phase method and the second phase of the other are based on the minimization of weighted Chebyshev distances to well-chosen reference points. The dynamic change of reference point proposed here makes this method particularly suitable for interactive approaches. Computational experiments on random instances of three classes of BCILP are reported and discussed. The implementation of the proposed method as a method to approximate the set of non-dominated solutions is described and evaluated in computational terms

Additive aggregation with variable interdependent parameters: the VIP Analysis software

We consider the aggregation of multicriteria performances by means of an additive value function under imprecise information. The problem addressed here is the way an analysis may be conducted when the decision makers are not able to (or do not wish to) fix precise values for the importance parameters. These parameters can be seen as interdependent variables that may take several values subject to constraints. Firstly, we briefly classify some existing approaches to deal with this problem. We argue that they complement each other, each one having its merits and shortcomings. Then, we present a new decision support software - VIP analysis - which incorporates approaches belonging to different classes. It proposes a methodology of analysis based on the progressive reduction of the number of alternatives, introducing a concept of tolerance that lets the decision makers use some of the approaches in a more flexible manner

Internet packet routing: Application of a K-quickest path algorithm

This paper describes a study on the application of an algorithm to rank the K-quickest paths to the routing of data packets in Internet networks. For this purpose an experimental framework was developed by considering two types of random generated networks. To simulate values of the IP packet sizes, a truncated Pareto distribution was defined, having in mind to reflect a key feature of Internet traffic, namely its self-similar stochastic nature. Results concerning the average CPU times of the algorithm for the different sets of experiments will be presented and discussed.http://www.sciencedirect.com/science/article/B6VCT-4JW124S-B/1/595ef677356cef2b2c795e3eeabee5e

An automated reference point-like approach for multicriteria shortest path problems

Abstract In this paper we introduce a method of analysis for the automated ordering and selection of solutions of a multicriteria shortest path model. The method is based on a reference point approach, where the paths in a specific priority region are ranked by non-decreasing order of a Chebyshev metric. In order to list paths according with this objective function a labelling algorithm is proposed. The developed method is applied in a video-traffic routing context. Computational results are presented and analysed, for randomly generated networks of significant dimension