A memetic algorithm for solving bilevel optimization problems with multiple followers

Bilevel optimization constitutes a specific class of problems where optimization is done at two nested levels - upper (leader) and lower (follower). The two levels are coupled by the requirement of optimality at lower level for each upper level solution. A number of real life problems in engineering, logistics, economics, transportation etc. need to be modeled as bilevel optimization problems due to involvement of a hierarchy of decision makers, and thus the problem is of significant research interest. Ensuring lower level optimality for each solution makes the problem computationally intensive in terms of number of function evaluations required. To reduce this computational effort while delivering competitive results, the authors proposed a bilevel memetic algorithm (BLMA) in their previous work, for problems with one leader and one follower. However, in a number of real-life problems, there could also exist multiple followers, which may or may not be dependent on each other. In this paper, we extend BLMA to solve problems with multiple followers. A number of benchmark multifollower problems from the literature are solved using the proposed algorithm, referred to as BLMAMF, and compared with recently reported results to demonstrate the efficacy of the approach.