A unified framework for adjustable robust optimization with endogenous uncertainty

Abstract

This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (a) alter the uncertainty set, (b) affect the materialization of uncertain parameters, and (c) determine the time when the true values of uncertain parameters are observed. We provide a systematic analysis of the different types of

Multistage distributionally robust optimization for integrated production and maintenance scheduling

“…Compared with existing static and two‐stage models, a multistage formulation captures the actual sequential decision‐making process more adequately and can hence provide improved solutions. To this end, we apply a decision rule approach originally proposed by Georghiou and coworkers 26,27 and recently refined by Feng et al 28 Multistage formulations based on decision rules have mainly been applied in the context of adjustable robust optimization (ARO), with several successful applications in process scheduling 29–34 . However, the vast majority of these works only consider continuous recourse.…”

Robust Scheduling of Virtual Power Plant Under Exogenous and Endogenous Uncertainties

“…RO under decision-dependent uncertainties (RO-DDU) recently has drawn increasing attention in the optimization community. Literature regards RO-DDU as two categories: static RO-DDU [11]- [15] and adaptive RO-DDU (ARO-DDU) [16]- [18]. In [11]- [15], the linear decision-dependency of polyhedral uncertainty sets on decision variables is considered, rendering a static RO-DDU model.…”

“…Then, the robust counterpart, which is a mixed integer linear program (MILP), is derived by applying the strong duality theory and Mc-Cormick Envelopes convex relaxation. In [16]- [18], ARO-DDU models that concurrently incorporate wait-and-see decisions and endogenous uncertainties are studied. Due to the computational intractability raised by the complex coupling relationship between uncertainties and decisions in two stages, the current works make considerable simplifications on the model.…”

“…Due to the computational intractability raised by the complex coupling relationship between uncertainties and decisions in two stages, the current works make considerable simplifications on the model. Reference [16], [17] assume affine decision rules for the wait-and-see decisions, converting the two-stage RO problem into a static RO problem. To address a two-stage ARO-DDU problem without any assumption on affine policies, the extensively-used C&CG algorithm [19] may fail when the uncertainty set is decision-dependent.…”

“…The master problem at iteration k is formulated below: min x,y 0 f (x, y 0 ) (16a) 16) is a relaxation to (15). We solve MP (16) to derive a relaxed optimum of (15). Constraints (16c) are feasibility cuts to MP.…”