Scenario tree reduction for optimisation under uncertainty using sensitivity analysis

Abstract

This work addresses the optimal management of a system through a two-stage stochastic Non-Linear Programming (NLP) formulation. This approach uses a scenario-based mathematical formulation to tackle uncertain information. Accurate representation of uncertainty usually involves increased number of scenarios, which may result in large-scale optimisation models. Thus, the proposed formulation aims to reduce the number of scenarios through a sensitivity analysis approach. The proposed model investigates the use of scenario reduction techniques to reduce computational requirements while maintaining good quality of the final optimal solution.

Data-Driven Scenario Generation for Two-Stage Stochastic Programming

“…Nonetheless, the use of a wide range of alternative approaches for scenario generation have also been investigated in the literature. For instance, Silvente et al (2019) implement a sensitivity analysis approach to reduce the number of scenarios.…”

A Stackelberg Game-Based Approach for Transactive Energy Management in Smart Distribution Networks

“…According to these explanations, in this work, the combination of a fast backward/forward algorithm in the SCENRED2 tool of the GAMS software [31] is used to diminish the initial number of scenarios to 10. The reduction algorithm tries to retain a set of probable scenarios by minimizing the Kantorovich distance between the primary set of scenarios and the reduced ones [32]. The probabilities of the reduced scenarios are reported in Table 2.…”

“…The first, second, third, and fourth lines of Equation (32) are related to the first stage of the problem. The first and second terms are the costs of exchanged energy in the DA WEM and DA LEM, respectively.…”

A graph theory approach for scenario aggregation for stochastic optimisation

“…Recently, Chen and Yan (2018b) proposed a scenario tree reduction formulation to cluster nodes with the same parent node into a smaller number of nodes. More recently, Silvente et al (2019) proposed RedOpt which is a scenario reduction technique inspired by the Branch and Bound method that progressively evaluates the branches using a sensitivity analysis. The good performance of these algorithms not only has justified/boosted their application to address chance-constrained and mixed integer-two-stage stochastic programming problems but also has enlarged the scope of scenario reduction methods to address various practical application such as energy production Xu et al (2015), chemical processes Karuppiah et al (2010) and the pharmaceutical industry (Henrion et al, 2008(Henrion et al, , 2009.…”