A Nested Differential Evolution Based Algorithm for Solving Multi-objective Bilevel Optimization Problems

Islam, Monjurul; Singh, Hemant Kumar; Ray, Tapabrata

doi:10.1007/978-3-319-28270-1_9

Cited by 7 publications

(3 citation statements)

References 32 publications

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“…More details can be found for the metric in [42]. The IGD values of the DBMA algorithm are not reported [21] but we compare the results with the HV metric. Both HV and IGD measure the convergence and the spread of the obtained set of solutions.…”

Section: Performance Measuresmentioning

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: Performance Measuresmentioning

confidence: 99%

“…Ref. [21] develop a nested differential evolution-based algorithm for multi-objective bilevel problems (DBMA). However, the necessary number of function evaluations is high, due to the nature of evolutionary algorithms.…”

Section: Introductionmentioning

confidence: 99%

Multi-Objective BiLevel Optimization by Bayesian Optimization

Dogan,

Prestwich

2024

Algorithms

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“…Evolutionary algorithms (EAs) have been used to solve MBOPs [10,11] because they do not depend on the mathematical characteristics of MBOPs. The existing EAs for solving MBOPs can be classified into three types: single-level reduction methods [12][13][14][15][16][17] , surrogate-model-based methods [6,18,19] , and nested-based methods [10,[20][21][22] .…”

Section: Introductionmentioning

confidence: 99%

A cluster-based co-evolutionary optimization method for bilevel multi-objective optimization

Hu,

Li,

Huang

et al. 2024

Journal of Smart Environments and Green Computing

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The research motivation of multi-objective bilevel optimization mainly stems from the need to solve practical problems and improve decision-making efficiency. On the one hand, bilevel optimization helps to solve the complexity and uncertainty in real life, thereby improving decision-making efficiency and robustness. On the other hand, by promoting the development and application of AI technology, bilevel optimization also provides support for sustainable development. Although the application of bilevel optimization has proven to be beneficial in addressing various real-life problems. However, recent studies indicate that achieving both high speed and high-quality optimization through existing algorithms remains challenging. This difficulty arises due to the NP-hard nature of the bilevel optimization problem. The nested structure method, commonly used to tackle this problem, involves each upper level solution independently performing the lower level optimization task. This approach significantly increases the number of evaluations for the lower level. To address this issue, our proposed method leverages the similarity in lower level optimization to group upper level solutions, enabling co-evolution of lower level solutions within the same group. Consequently, this approach substantially reduces the number of evaluations required for lower level solutions. Additionally, our method pairs parents and offspring, the optimized lower level solutions of the parents are utilized to optimize the lower level solutions of the offspring. This approach accelerates the optimization process for the lower level. To validate the effectiveness of our algorithm, we have applied it to a suite of test problems, demonstrating satisfactory performance.

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