El MUNDO: Embedding Measurement Uncertainty in Decision Making and Optimization

Abstract

In this project we address the problem of modelling and solving constraint based problems permeated with data uncertainty, due to imprecise measurements or incomplete knowledge. It is commonly specified as bounded interval parameters in a constraint problem. For tractability reasons, existing approaches assume independence of the data, also called parameters. This assumption is safe as no solutions are lost, but can lead to large solution spaces, and a loss of the problem structure. In this paper we present two approaches we have investigated in the El MUNDO project, to handle data parameter dependencies effectively. The first one is generic whereas the second one focuses on a specific problem structure. The first approach combines two complementary paradigms, namely constraint programming and regression analysis, and identifies the relationships between potential solutions and parameter variations. The second approach identifies the context of matrix models and shows how dependency constraints over the data columns of such matrices can be modeled and handled very efficiently. Illustrations of both approaches and their benefits are shown.