Optimizing Environmental-Economic Power via Genetic Algorithms in Bilevel Programming

Abstract: This article presents a model for addressing the environmental-economic power generation and dispatch (EEPGD) challenge using a multiobjective bilevel programming (MOBLP) approach. The optimization is conducted through a genetic algorithm (GA) based fuzzy goal programming (FGP) applied within the operational system of a thermal power plant. The MOBLP formulation involves segregating the first objectives into two sets and allocating them to distinct hierarchical decision levels (top-level and bottom-level) for optimization. Each level encompasses one or more control variables associated with the power generation decision system. Fuzzy descriptions are employed in the optimization problems of both levels to capture the nuances inherent in the decision-making context. The FGP model formulation includes the design of membership n functions corresponding to defined fuzzy goals. These functions are then transformed into membership goals by assigning the highest membership value (unity) as the achievement level. Additionally, under- and over-deviational variables are introduced for each membership goal. The goal achievement function aims to minimize under-deviational variables of membership goals based on their weights of importance to attain an optimal solution in the decision environment. In solving the developed FGP model, a GA scheme is applied in two stages. The first stage involves the direct optimization of individual objectives for their fuzzy representation. In the second stage, the evaluation of the goal achievement function is performed to reach an optimal power generation decision. The efficacy of the proposed method is demonstrated through its application to the IEEE 6-generator 30-bus System. Keywords: Environmental-economic power generation, Fuzzy goal programming, Genetic algorithm, Membership function