An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems.

Area of Science:

• Operations Research
• Computer Science
• Applied Mathematics

Background:

• Bilevel optimization involves nested problems with upper and lower-level objectives.
• Real-world applications in engineering, logistics, and economics often exhibit this structure.
• Existing algorithms face challenges with the computational cost of large-scale bilevel problems.

Purpose of the Study:

• To develop and evaluate a novel Memetic Algorithm (MA) for solving bilevel optimization problems.
• To investigate the efficacy of combining global and local search strategies within a bilevel framework.
• To address the high computational effort typically required for bilevel optimization.

Main Methods:

• Introduction of a nested Bilevel Memetic Algorithm (BLMA).
• Integration of global and local search methods at both upper and lower levels of the optimization hierarchy.
• Performance evaluation using twenty-five standard test problems and two real-life applications.

Main Results:

• The proposed BLMA demonstrates efficacy in solving bilevel optimization problems.
• The algorithm achieves solutions with reduced computational cost (fewer function evaluations).
• Comparative analysis shows competitive performance against established algorithms.

Conclusions:

• The Bilevel Memetic Algorithm (BLMA) offers an efficient approach to tackling complex bilevel optimization challenges.
• BLMA effectively balances global exploration and local exploitation for improved optimization.
• This method shows promise for practical applications requiring efficient bilevel optimization solutions.