An Analysis of Some Algorithms and Heuristics for Multiobjective Graph Search

Abstract

Many real problems require the examination of an exponential number of alternatives in order to find the best choice. They are the so-called combinatorial optimization problems. Besides, real problems usually involve the consideration of several conflicting magnitudes. When multiple objectives must be simultaneously optimized, there is generally not an optimal value satisfying the requirements for all the criteria at the same time. Solving these multiobjective combinatorial problems commonly results in a large set of Pareto-optimal solutions, which define the optimal tradeoffs between the objectives under consideration. One of most recurrent multiobjective problems is considered in this thesis: the search for shortest paths in a graph, taking into account several objectives at the same time. Many practical applications of multiobjective search in different domains can be pointed out: routing in multimedia networks (Clímaco et al., 2003), satellite scheduling (Gabrel & Vanderpooten, 2002), transportation problems (Pallottino & Scutellà, 1998), routing in railway networks (Müller-Hannemann & Weihe, 2006), route planning in road maps (Jozefowiez et al., 2008), robot surveillance (delle Fave et al., 2009) or domain independent planning (Refanidis & Vlahavas, 2003). Multiobjective route planning over realistic road maps has been considered as a potential application scenario for the multiobjective algorithms and heuristics considered in this thesis. Hazardous material transportation (Erkut et al., 2007), another related multiobjective routing problem, has also been considered as an interesting potential application scenario. Single criterion shortest path methods are well known and have been widely studied. Heuristic Search allows the reduction of the space and time requirements of these methods, exploiting estimates of the actual distance to the goal. Multiobjective problems are much more complex than their single-objective counterparts, and require specific methods. These range from exact solution techniques to approximate ones, including the metaheuristic approximate methods usually found in the literature. This thesis is concerned with exact best-first algorithms, and particularly, with the use of heuristic information to improve their performance. This thesis contributes both formal and empirical analysis of algorithms and heuristics for multiobjective search. The formal characterization of algorithms is important for the field. However, empirical evaluation is also of great importance for the real application of these methods. Several well known classes of problems have been used to test their performance, including some realistic scenarios as described above. The results of this thesis provide a better understanding of which of the available methods are better in practical situations. Formal and empirical explanations of their behaviour are presented. Heuristic search is shown to reduce considerably space and time requirements in most situations. In particular, the first systematic results showing the advantages of the application of precalculated multiobjective heuristics are presented. The thesis also contributes an improved method for heuristic precalculation, and explores the convenience of more informed precalculated heuristics.