A Knee Point Driven Evolutionary Algorithm for Multiobjective Bilevel Optimization.

Area of Science:

• Optimization
• Operations Research
• Computational Mathematics

Background:

• Bilevel optimization problems (BLOPs) involve nested optimization tasks, making them computationally intensive.
• Multiobjective BLOPs (MBLOPs) add complexity, as solutions must balance multiple objectives at both levels.
• Existing methods often expend resources on suboptimal lower-level solutions irrelevant to the MBLOP's Pareto front.

Purpose of the Study:

• To develop an efficient algorithm for solving multiobjective bilevel optimization problems (MBLOPs).
• To address the computational challenges and resource limitations in MBLOP solving.
• To improve the focus on high-performance solutions within the MBLOP feasible region.

Main Methods:

• A novel multiobjective bilevel optimization solving routine integrating a knee point driven algorithm.
• A two-stage approach: first, rapidly identify feasible solutions respecting lower-level constraints.
• Second, concentrate computational efforts on refining solutions with superior performance.

Main Results:

• Development of diverse MBLOP test problems with varying characteristics (scalability, deception, convexity, continuity).
• Validation of the proposed algorithm on a real-world petroleum refining problem involving environmental and operational objectives.
• Demonstration of the algorithm's effectiveness in solving MBLOPs through comprehensive experiments.

Conclusions:

• The proposed knee point driven algorithm efficiently solves MBLOPs by prioritizing feasible and high-performance solutions.
• The algorithm's effectiveness is proven on both synthetic test cases and a practical petroleum refining application.
• This approach offers a more resource-conscious strategy for tackling complex nested optimization challenges.