K-means cluster interactive algorithm-based evolutionary approach for solving bilevel multi-objective programming problems

Abstract

Solving bilevel multi-objective programming problems is one of the hardest tasks facing researchers in the optimization community. Bilevel multi-objective programming problems is an optimization problem consists of two interconnected hierarchical multi-objective programming problems: upper-level problem and lower-level problem. Difficulty in solving bilevel multi-objective programming problems is the need to solve lower-level multi-objective programming problem to know the feasible space of the upper-level problem. The proposed algorithm consists of two nested artificial multi-objective algorithms. One algorithm is for the upper-level problem and the other is for the lower-level problem. Also, the proposed algorithm is enriched with a k-means cluster scheme in two phases. The first phase is before starting two nested algorithms to help the algorithm to start with more appropriates solutions to the bi-level problem. The second phase is within the two nested algorithms to guide the algorithm to the most preferred solutions to the upper-level decision-maker. The performance of the proposed algorithm has been evaluated on different test problems including low dimension and high dimension test problems. The experimental results show that the proposed algorithm is a feasible and efficient method for solving the bilevel multi-objective programming problem.

Keywords

• Bilevel multi-objective programming
• Pareto optimal solution
• K-means clustering
• Evolutionary algorithms
• Genetic algorithm