Projection-based robust optimization with symbolic computation. (September 2021)

• Record Type: Journal Article
• Authors: Zheng, Chenglin; Zhao, Fei; Chen, Xi
• Is Part Of: Computers & chemical engineering. Volume 152(2021)
• Publication Date: 2021-09
• Subjects: Robust optimization -- Uncertainty set -- Max-max decision criterion -- Cylindrical algebraic decomposition; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2021.107380
• Languages: English
• ISSNs: 0098-1354

Abstract

Highlights: Propose a novel robust optimization method based on feasible space projection. Circumvent the problem of formulating the traditional robust counterparts. The explicit expressions of the objective function and uncertainty set are deduced. The robust solution is guaranteed to be located with the max-max decision criterion. Abstract: Robust counterpart reformulation is a common technique used to deal with data uncertainty in robust optimization (RO) problems. The derivation of the robust counterpart formulation using the duality theory is nontrivial, especially for complex uncertainty sets. To reduce the dependence on robust counterparts, a novel method is proposed in this article for RO problems. Based on the feasible space projection, the proposed method can locate robust solutions without formulating the robust counterparts. RO model can be reformulated as a semi-algebraic system and a modified cylindrical algebraic decomposition method is applied to project the high-dimensional feasible space on the low-dimensional space of the objective function and uncertainty parameters. By solving the maximization problem and using the max-max decision criterion, the final robust solution can be selected. The case studies, involving problems of nonlinear programming (NLP) and robust design optimization problems, show that the proposed method can obtain the robust solution effectively.