Approximated set-valued mapping approach for handling multiobjective bilevel problems

A significant amount of research has been done on bilevel optimization problems both in the realm of classical and evolutionary optimization. However, the multiobjective extensions of bilevel programming have received relatively little attention from researchers in both the domains. The existing algorithms are mostly brute-force nested strategies, and therefore computationally demanding. In this paper, we develop insights into multiobjective bilevel optimization through theoretical progress made in the direction of parametric multiobjective programming. We introduce an approximated set-valued mapping procedure that would be helpful in the development of efficient evolutionary approaches for solving these problems. The utility of the procedure has been emphasized by incorporating it in a hierarchical evolutionary framework and assessing the improvements. Test problems with varying levels of complexity have been used in the experiments. HighlightsMultiobjective bilevel optimization algorithms have received only limited attention.Approximation of set-valued mapping has been used to solve the problem.Set-valued mapping has been approximated using multiple quadratic fibers.Significant computational savings have been achieved using the multi-fiber idea.

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