An Exact Solution Algorithm for Integer Bilevel Programming with Application in Energy Market Optimization

Abstract

AbstractWe develop an exact cutting plane solution algorithm for a special class of bilevel programming models utilized for optimal price-bidding of energy producers in day-ahead electricity markets. The proposed methodology utilizes a suitable reformulation in which a key prerequisite for global optimality, termed bilevel feasibility, is relaxed. Solving the problem to global optimality involves finding the price-offers of the strategic producer (upper-level decision variables) which maximize his self-profit upon clearing of the market and identification of the optimal energy quantity distribution (lower-level decision variables). To exclude from consideration the encountered bilevel infeasible solutions, the algorithm employs a special type of valid cuts drawn from the theory of integer parametric programming. The generation of these cuts involves finding the truly optimal lower-level solution using the strategic price-offers at the bilevel infeasible solution subject to exclusion and devising range intervals for these offers such that the optimality of this solution is retained when each of them lies in its corresponding interval. Each cut imposes a suitable part of this solution, under the condition that each price-offer belongs to its associated interval, which renders the bilevel infeasible solution invalid. We establish the theoretical framework for the development of the proposed algorithm, we illustrate its application on a small case study, and we present extensive computational results demonstrating its behavior and performance on random problem instances. These results indicate that the algorithm is capable of solving to global optimality considerably larger problems than those that a previous elementary version of the same algorithm could solve. This constitutes significant research contribution, considering the lack of generic optimization software for bilevel programming, as well as the fact that the applicability of specialized algorithms on problems of realistic size is rather limited.