Probabilistic Combinatorial Optimization - Murat, Cécile; Paschos, Vangelis Th (Paradigms of Combinatorial Optimization: Problems and New Approaches, 2014)
This chapter presents a class of combinatorial optimization problems, defined in terms of graphs and in which random phenomena is introduced. Probabilistic combinatorial optimization allows to integrating random phenomena into the instance, to simulate disturbances that the instance could be subject to. The chapter presents significant functional expressions, giving an idea of the proof and a reference to the work in which the complete demonstration for each one can be found. The results obtained in the context of approximation in relation to probabilistic combinatorial optimization problems are of three kinds: the first type involves judging the quality of the a priori approximation, compared with the approximation that re‐optimizes each subgraph; the second type involves judging the evolution of the quality of the deterministic solutions when they are used as a priori solutions; and the last type involves judging the quality of a priori solutions explicitly constructed for the probabilistic problem.