A graph theory approach for scenario aggregation for stochastic optimisation

Abstract

The development of fast, robust and reliable computational tools capable of addressing process management under uncertain conditions is an active topic in the current literature, and more precisely for the process systems engineering one. Particularly, scenario reduction strategies have emerged as an alternative to overcome the traditional issues associated with large-scale scenario-based problems. This work proposes a novel and flexible scenario-reduction alternative that integrates data mining, graph theory and community detection concepts to represent the uncertain information as a network and identify the most efficient communities/clusters. The capabilities of the proposed approach were tested by solving a set of two-stage mixed-integer linear programming problems under uncertainty. For comparison and validation purposes, these problems were also solved using two available methods (SCENRED and OSCAR). This comparison demonstrates that the results obtained by using the proposed approach are at least as good or better, in terms of quality and accuracy, than the results obtained bu using SCENRED and OSCAR. Additionally, the practical advantage of the proposed parameter definition rule is demonstrated as a way to overcome the limitations of the current alternatives (i.e. arbitrary user-defined parameters).