Towards Efficient Robust Optimization using Data based Optimal Segmentation of Uncertain Space

Abstract

Performing multi-objective optimization under uncertainty is a common requirement in industries and academia. Robust optimization (RO) is considered as an efficient and tractable approach provided one has access to behavioral data for the uncertain parameters. However, solutions of RO may be far from the real solution and less reliable due to inability to map the uncertain space accurately, especially when the data appears discontinuous and scattered in the uncertain domain. Amalgamating machine learning algorithms with RO, this paper proposes a data-driven methodology, where a novel fuzzy clustering mechanism is implemented along-with boundary construction, to transcript the uncertain space such that the specific regions of uncertainty are identified. Subsequently, using intelligent Sobol sampling, samples are generated in the mapped uncertain regions. Results of two test cases are presented along with a comprehensive comparison study. Considered case-studies include highly nonlinear model for continuous casting process from steelmaking industries, where a multi-objective optimization problem under uncertainty is solved to balance the conflict between productivity and energy consumption. The Pareto-optimal solutions of the resulting RO problem are obtained through Non-Dominated Sorting Genetic Algorithm – II, and ~23–29% improvement is observed in the uncertain objective function. Further, the spread and diversity metrics are enhanced by ~10–95% as compared to those obtained using other standard uncertainty sets.