Determining approximate Stackelberg strategies in carbon constrained energy planning using a hybrid fuzzy optimisation and adaptive multi-particle simulated annealing technique

Abstract

In recent years, there has been growing international concern about climate change as a result of greenhouse gas emissions from human activity. Various process integration techniques have thus been developed to assist in determining the optimal allocation of energy sources to sectoral or regional demands under carbon footprint constraints; for example, the source-sink representation of this problem has been solved using graphical and algebraic pinch analysis techniques as well as linear programming. This work presents an extension of the original problem by incorporating a game-theoretic, two-level decision framework, which is a more accurate representation of real-life energy planning applications. The upper level decision-maker (i.e., the government) seeks to minimise total costs to society by selecting appropriate emission limits for each sector as well as subsidy levels for clean energy sources; on the other hand, the lower level decision-maker (i.e., industry) seeks to minimize total energy-related costs subject to the emission limits set by the government. This problem is a static Stackelberg game which may be formulated as a fuzzy bi-level optimisation model. A numerical example from literature is used to illustrate the modeling approach. The case study is then solved using an adaptive multi-particle simulated annealing algorithm to yield an approximate Stackelberg solution.