A differential evolution algorithm for bilevel problems including linear equality constraints

A differential evolution technique is proposed in order to tackle continuous bilevel optimization problems subject to linear equality constraints, in addition to general non-linear equality and inequality constraints. The idea is to exactly satisfy the linear equality constraints, while the remaining constraints are dealt with via standard constraint handling techniques for metaheuristics. A procedure is proposed in order to generate a random initial population which is feasible with respect to the linear equality constraints. Then a mutation scheme that maintains such feasibility is adopted. The procedure is applied at the lower level (follower) and tested in problems from the literature in order to assess its performance when compared with the case where the constraints are handled via a well known selection scheme for constraint handling. The procedure is applied to problems found in the literature and its performance is compared with the case where the constraints are handled via a well known selection scheme for constraint handling.