A Chance Constrained Programming Based Multi-Criteria Decision Making under Uncertainty

Multi-criteria decision making under uncertainty is a common practice followed in industries and academia. Among several types of uncertainty handling techniques, Chance Constrained Programming (CCP) is considered as an efficient and tractable approach provided one has accessibility to distribution of the data for uncertain parameters. However, the assumption that the uncertain parameters must follow some well-behaved probability distribution is a myth for most of the practical applications. This paper proposes a methodology to amalgamate machine learning algorithms with CCP and thereby make it data-driven. A novel fuzzy clustering mechanism is implemented to transcript the uncertain space such that the exact regions of uncertainty are identified. Subsequently, density based boundary point detection and Delaunay triangulation based boundary construction enable intelligent Sobol based sampling in these regions for use in CCP. The Fuzzy clustering mechanism used in the proposed method transforms the existing fuzzy C-means technique such that the decision variables are significantly reduced. This enables evolutionary optimizers to obtain better approximations of the uncertain space by identifying the true clusters. A highly nonlinear real life model for continuous casting from steelmaking industries is considered as a case study for testing the efficiency of data based CCP along with a comprehensive comparison between conventional CCP approach using box uncertainty set and proposed methodology. As the resulting CCP problem is multi-objective in nature, the Pareto solutions are obtained by NSGA II