Robust de novo programming under different uncertainty sets and its application to the renewable energy sector

Abstract

This paper proposes robust models of de novo programming (R-DNP) using cardinality-constrained robustness with interval-based, ellipsoidal, and norm-based uncertainty sets. R-DNP has not been researched or explored, and we aim to fill this gap in the literature. In particular, we develop the robust counterpart of the weighted DNP (W-DNP), Chebyshev DNP (C-DNP), and extended DNP (E-DNP) models to incorporate different uncertainty sets and decision-makers’ preferences. Methodologically, the proposed approach extends the conventional DNP model to solve uncertain coefficients for each decision variable on the left-hand side of each objective function and on the total budget, overcoming the limitations of the current multicriteria solution procedure of the DNP approach. The proposed methods provide decision-makers with more flexibility to express their level of conservatism and preferences by setting priority weights and aspiration levels. The proposed method’s usefulness over the standard DNP is demonstrated by providing an illustrative example. Moreover, we validate the proposed formulations for solving real-world problems through a hypothetical application: optimizing onshore wind farm locations in Morocco. The work’s results confirm the validity of the proposed methodologies, showing that they can assist decision-makers in determining the optimal system design for sustainable electricity generation under uncertain conditions.