Bilevel Multi-objective Optimization Problem Solving Using Progressively Interactive EMO

Abstract

Bilevel multi-objective optimization problems are known to be highly complex optimization tasks which require every feasible upper-level solution to satisfy optimality of a lower-level optimization problem. Multi-objective bilevel problems are commonly found in practice and high computation cost needed to solve such problems motivates to use multi-criterion decision making ideas to efficiently handle such problems. Multi-objective bilevel problems have been previously handled using an evolutionary multi-objective optimization (EMO) algorithm where the entire Pareto set is produced. In order to save the computational expense, a progressively interactive EMO for bilevel problems has been presented where preference information from the decision maker at the upper level of the bilevel problem is used to guide the algorithm towards the most preferred solution (a single solution point). The procedure has been evaluated on a set of five DS test problems suggested by Deb and Sinha. A comparison for the number of function evaluations has been done with a recently suggested Hybrid Bilevel Evolutionary Multi-objective Optimization algorithm which produces the entire upper level Pareto-front for a bilevel problem.