A deterministic bounding procedure for the global optimization of a bi-level mixed-integer problem

In this paper, a deterministic bounding procedure for the global optimization of mixed-integer bi-level programming problem is proposed. The aim has been to develop an efficient algorithm deal with case study in electricity retail market. problem, retailer wants define time-of-use tariff structure maximize profits, but he take into account consumers’ reaction by means re-scheduling appliance operation minimize costs. formulated as model. we propose uses optimal-value-function reformulations based on similar principles ones that have used other authors, which are adapted characteristics type (pricing optimization) problems where no upper (lower) level variables appear lower (upper) constraints. overall strategy consists generating series convergent bounds and upper-level objective function until difference between these below given threshold. Computational results presented well comparison hybrid approach combining particle swarm exact solver tackle lower-level previously developed address study. When model difficult, significant relative MIP gap unavoidable when solving algorithm's subproblems. Novel those subproblems using “elastic” proposed trying obtain meaningful lower/upper within acceptable computational time.