A Reference Point-Based Evolutionary Algorithm Solves Multi and Many-Objective Optimization Problems: Method and...

Area of Science:

• Computational Intelligence
• Multi-objective Optimization
• Decision Support Systems

Background:

• Evolutionary multi-objective optimization (EMO) research increasingly integrates decision-maker preferences.
• Existing preference-based methods like R-NSGA-II use Euclidean distance, which has limitations in determining solution convergence.
• The challenge lies in accurately identifying Pareto-optimal solutions within a specific region of interest (ROI).

Purpose of the Study:

• To modify the R-NSGA-II algorithm for improved preference-based evolutionary multi-objective optimization.
• To replace the Euclidean distance metric with a more effective proximity measure for better convergence prediction.
• To enhance the ability to find solutions in the ROI and control the size of preferred regions.

Main Methods:

• Modified the reference point-based non-dominated sorting genetic (R-NSGA-II) algorithm.
• Replaced the Euclidean distance metric with the simplified Karush-Kuhn-Tucker proximity measure (S-KKTPM).
• Conducted extensive experiments on 2-10 objective problems using standard benchmark instances.

Main Results:

• The S-KKTPM-based R-NSGA-II algorithm demonstrates high competitiveness against state-of-the-art preference-based EMO methods.
• The proposed method effectively identifies preferred solutions within the specified region of interest (ROI).
• The algorithm successfully controls the size of individual preferred regions simultaneously.

Conclusions:

• The S-KKTPM metric provides a superior approach for preference-based EMO compared to Euclidean distance.
• The modified R-NSGA-II algorithm offers enhanced performance in finding desired Pareto-optimal solutions.
• This advancement facilitates more precise control over solution selection in multi-objective optimization problems.