Multiobjective Bilevel Programming: Concepts and Perspectives of Development

Alves, Maria João; Antunes, Carlos Henggeler; Costa, João Paulo

doi:10.1007/978-3-030-11482-4_10

Cited by 6 publications

(2 citation statements)

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“…Many approaches have been developed for solving multi-objective bilevel problems. A particle swarm optimization algorithm is used to compute optimistic and pessimistic solutions in [19], who also developed a differential evolution algorithm to compute the four extreme solutions in [20]. Ref.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Objective BiLevel Optimization by Bayesian Optimization

Dogan,

Prestwich

2024

Algorithms

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In a multi-objective optimization problem, a decision maker has more than one objective to optimize. In a bilevel optimization problem, there are the following two decision-makers in a hierarchy: a leader who makes the first decision and a follower who reacts, each aiming to optimize their own objective. Many real-world decision-making processes have various objectives to optimize at the same time while considering how the decision-makers affect each other. When both features are combined, we have a multi-objective bilevel optimization problem, which arises in manufacturing, logistics, environmental economics, defence applications and many other areas. Many exact and approximation-based techniques have been proposed, but because of the intrinsic nonconvexity and conflicting multiple objectives, their computational cost is high. We propose a hybrid algorithm based on batch Bayesian optimization to approximate the upper-level Pareto-optimal solution set. We also extend our approach to handle uncertainty in the leader’s objectives via a hypervolume improvement-based acquisition function. Experiments show that our algorithm is more efficient than other current methods while successfully approximating Pareto-fronts.

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Section: Introductionmentioning

confidence: 99%

“…[25] use a multiobjective particle swarm optimization algorithm and efficiently computes lower-level solutions (OMOPSO-BL). More details can be found in [20] on optimistic multi-objective bilevel problems.…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective BiLevel Optimization by Bayesian Optimization

Dogan,

Prestwich

2024

Algorithms

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New concepts and an algorithm for multiobjective bilevel programming: optimistic, pessimistic and moderate solutions

2019

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Bilevel optimization deals with hierarchical mathematical programming problems in which two decision makers, the leader and the follower, control different sets of variables and have their own objective functions subject to interdependent constraints. Whenever multiple objective functions exist at the lower-level problem, the leader should cope with the uncertainty pertaining to the follower's reaction. The leader can adopt a more optimistic or more pessimistic stance regarding the follower's choice within his efficient region, which is restricted by the leader's choice. Moreover, the leader may also have multiple objective functions. This paper presents new concepts associated with solutions to problems with multiple objective functions at the lowerlevel and a single or multiple objective functions at the upper-level, exploring the optimistic and pessimistic leader's perspectives and their interplay with the follower's choices. Extreme solutions (called optimistic/deceiving and pessimistic/rewarding) and a moderate solution, resulting from the risk the leader is willing to accept, are defined for problems with a single objective at the upper-level (semivectorial problems). Definitions of optimistic and pessimistic Pareto fronts are proposed for problems with multiple objective functions at the upper-level. These novel concepts are illustrated emphasizing the difficulties associated with the computation of those solutions. In addition, a differential evolution algorithm, approximating the extreme and moderate solutions for the semivectorial problem, is presented. Illustrative results of this algorithm further stress the challenges and pitfalls associated with the computation and interpretation of results in this kind of problems, which have not been properly addressed in literature and may lead to misleading conclusions.

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