A note on the complexity of some multiobjective A* search algorithms

Authors:
Lawrence Mandow;José-Luis Pérez de la Cruz
Affiliations:
Universidad de Málaga, Spain, email: {lawrence,perez}@lcc.uma.es;Universidad de Málaga, Spain, email: {lawrence,perez}@lcc.uma.es
Venue:
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Year:
2010

Citing 3
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Abstract

This paper studies the complexity of two different algorithms proposed as extensions of A* for multiobjective search: MOA* and NAMOA*. It is known that, for any given problem, NAMOA* requires the consideration of no more alternatives than MOA* when provided with the same heuristic information. In this paper we show that, in fact, expansions performed by MOA* can be many more than those demanded by the problem, and hence than those performed by NAMOA*. More specifically, we show a sequence of problems whose size grows linearly such that the number of expansions performed by NAMOA* grows also linearly, but the number of expansions performed by MOA* grows exponentially. Therefore, there are problems where NAMOA* performs exponentially better than MOA*.