Interactive Search for Compromise Solutions in Multicriteria Graph Problems

Abstract

In this paper, the purpose is to adapt classical interactive methods to multicriteria combinatorial problems in order to explore the non-dominated solutions set. We propose an interactive procedure alternating a calculation stage determining the current best compromise solution and a dialogue stage allowing decision maker to specify his/her preferences. For the calculation stage, we propose an efficient procedure which relies on algorithms providing k-best solutions of a scalarized version of the problem. Moreover, we show how to exploit previous iterations to speed-up the interactive process. We provide numerical experiments of our method on multicriteria shortest path and spanning tree problems.

An Evaluation of Best Compromise Search in Graphs

“…We consider the problem of determining a best compromise path from an initial node to a goal node in a multiobjective graph with respect to the Chebyshev norm. Notice that partial solutions evaluated according to the Chebyshev norm do not satisfy Bellman's optimality principle [2]. We compare two main general approaches.…”

“…This approach is simple, but: (a) requires the calculation of the full Pareto set, (b) costly Pareto dominance tests must be performed during the search to compare the current subpaths and keep only the optimal ones. The second approach is an alternative algorithm based on single-objective k-shortest paths search [2]. The major insight is that it is possible to devise a weighted linear function that minorates the Chebyshev distance [2].…”

“…The second approach is an alternative algorithm based on single-objective k-shortest paths search [2]. The major insight is that it is possible to devise a weighted linear function that minorates the Chebyshev distance [2]. For any vector cost y ∈ R q , it can indeed be easily shown that,…”

“…The second one explores the use of k-shortest-path algorithms to avoid evaluating all Pareto optimal paths in the graph, as well as performing computationally costly Pareto dominance tests. Preliminary results [2] showed an advantage in performance for kA * against the naive Pareto search (NAMOA * ) on random graphs with an artificially calculated heuristic. This paper performs a more systematic evaluation of both approaches on sets of standard bicriterion route planning problems [9,6,5].…”

A Case of Pathology in Multiobjective Heuristic Search

“…In the first place, many graph search problems can benefit directly from multiobjective analysis (De Luca Cardillo & Fortuna, 2000;Gabrel & Vanderpooten, 2002;Refanidis & Vlahavas, 2003;Müller-Hannemann & Weihe, 2006;Dell'Olmo, Gentili, & Scozzari, 2005;Ziebart, Dey, & Bagnell, 2008;Wu, Campbell, & Merz, 2009;Delling & Wagner, 2009;Fave, Canu, Iocchi, Nardi, & Ziparo, 2009;Mouratidis, Lin, & Yiu, 2010;Caramia, Giordani, & Iovanella, 2010;Boxnick, Klöpfer, Romaus, & Klöpper, 2010;Klöpper, Ishikawa, & Honiden, 2010;Wu, Campbell, & Merz, 2011;Machuca & Mandow, 2011). On the other hand, other multicriteria preference models used in graph search typically look for a subset of Pareto-optimal solutions (Mandow & Pérez de la Cruz, 2003;Perny & Spanjaard, 2005;Galand & Perny, 2006;Galand & Spanjaard, 2007;Galand, Perny, & Spanjaard, 2010). Therefore, improvements in performance of multiobjective algorithms can guide the development of efficient algorithms for other multicriteria decision rules.…”