An Axiomatic Approach to Robustness in Search Problems with Multiple Scenarios

International audienceThis paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of robust solutions, we propose a new sophistication of A* specially designed to determine the set of robust paths in a state space graph. The behavior of the algorithm is illustrated on a small example. Finally, an axiomatic justification of the refinement of robustness by an OWA criterion is provided

Subjective Evaluation of Discomfort in Sitting Positions

International audienceWe study the modelling of the subjective sensation of discomfort for subjectsseated during a long time, in terms of local discomforts. The methodology usesfuzzy measures and integrals in a multicriteria decision making process,which enables the modelling of complex interaction between variables. Resultsof the experiment are detailed, giving models with respect to different kindsof discomfort, and to different macro-zones of the body

An axiomatic approach to robustness in search problems with multiple scenarios

This paper is devoted to the the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of robust solutions, we propose a new sophistication of A ∗ specially designed to determine the set of robust paths in a state space graph. The behavior of the algorithm is illustrated on a small example. Finally, an axiomatic justification of the refinement of robustness by an OWA criterion is provided.

State space search for risk-averse agents

We investigate search problems under risk in statespace graphs, with the aim of finding optimal paths for risk-averse agents. We consider problems where uncertainty is due to the existence of different scenarios of known probabilities, with different impacts on costs of solution-paths. We consider various non-linear decision criteria (EU, RDU, Yaari) to express risk averse preferences; then we provide a general optimization procedure for such criteria, based on a path-ranking algorithm applied on a scalarized valuation of the graph. We also consider partial preference models like second order stochastic dominance (SSD) and propose a multiobjective search algorithm to determine SSDoptimal paths. Finally, the numerical performance of our algorithms are presented and discussed.

Search for Compromise Solutions in Multiobjective State Space Graphs

The aim of this paper is to introduce and solve new search problems in multiobjective state space graphs. Although most of the studies concentrate on the determination of the entire set of Pareto optimal solution paths, the size of which can be, in worst case, exponential in the number of nodes, we consider here more specialized problems where the search is focused on Pareto solutions achieving a well-balanced compromise between the conflicting objectives. After introducing a formal definition of the compromise search problem, we discuss computational issues and the complexity of the problem. Then, we introduce two algorithms to find the best compromise solution-paths in a state space graph. Finally, we report various numerical tests showing that, as far as compromise search is concerned, both algorithms are very efficient (compared to MOA*) but they present contrasted advantages discussed in the conclusion.ouinonouirechercheInternationa