Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Optimal Recombination in Genetic Algorithms

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results

Uncertainty of flow in porous media

The problem posed to the Study Group was, in essence, how to estimate the probability distribution of f(x) from the probability distribution of x. Here x is a large vector and f is a complicated function which can be expensive to evaluate. For Schlumberger's applications f is a computer simulator of a hydrocarbon reservoir, and x is a description of the geology of the reservoir, which is uncertain

Regret Models and Preprocessing Techniques for Combinatorial Optimization under Uncertainty

Ph.DDOCTOR OF PHILOSOPH