(461d) Derivation of Generalized Affine Decision Rules for Mixed Integer Linear, Quadratic and Nonlinear Adjustable Robust Optimization Problems By Multi-Parametric Programming
In this work we propose a novel method for the derivation of generalized affine decision rules for linear/quadratic/nonlinear and mixed-integer ARO problems through multi-parametric programming. The ARO problem is treated as a multi-level programming problem (4) and it is then solved using M-POP, which is a novel algorithm for the exact and global solution of multi-level mixed-integer linear or quadratic programming problems (5, 6). The main idea behind the proposed approach is to solve the lower optimization level of the ARO problem parametrically, by considering âhere-and-nowâ variables and uncertainties as parameters. This will result in a set of affine decision rules for the âwait-and-seeâ variables as a function of âhere-and-nowâ variables and uncertainties for their entire feasible space. A set of illustrative numerical examples are provided to demonstrate the potential of the proposed novel approach.
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