Caractérisation des instances difficiles de problèmes d'optimisation NP-difficiles

Valentin Weber 1
1 G-SCOP_ROSP - ROSP
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : The empirical study of algorithms is a crucial topic in the design of new algorithms because the context of evaluation inevitably influences the measure of the quality of algorithms. In this topic, we particularly focus on the relevance of instances forming testbeds. We formalize this criterion with the notion of 'instance hardness' that depends on practical performance of some resolution methods. The aim of the thesis is to introduce a tool to evaluate instance hardness. The approach uses benchmarking of instances against a testbed of algorithms. We illustrate our experimental methodology to evaluate instance classes through several applications to the traveling salesman problem. We also suggest possibilities to generate hard instances. They rely on operations that modify instances but that allow to easily find the optimal solution of one instance from the other. We theoretically and empirically study their impact on the performance of some resolution methods.
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Valentin Weber. Caractérisation des instances difficiles de problèmes d'optimisation NP-difficiles. Autre [cs.OH]. Université de Grenoble, 2013. Français. ⟨NNT : 2013GRENM014⟩. ⟨tel-00992388⟩

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