An improved differential evolution algorithm for multi-modal multi-objective optimization.

Area of Science:

• Optimization Algorithms
• Computational Intelligence
• Multi-objective Optimization

Background:

• Multi-modal multi-objective problems (MMOPs) feature multiple Pareto optimal sets (PSs), posing challenges for convergence and diversity.
• Existing multi-modal multi-objective differential evolution (MMODE) algorithms struggle with effectively identifying and maintaining diverse solutions across all PSs.

Purpose of the Study:

• To introduce a novel MMODE algorithm incorporating Affinity Propagation Clustering (APC) for improved performance on MMOPs.
• To enhance the MMODE_AP algorithm's ability to converge to both global and local Pareto fronts while ensuring well-distributed solutions.

Main Methods:

• Developed MMODE_AP by integrating APC to define crowding degrees in decision and objective spaces.
• Employed adaptive mutation strategies to balance exploration and exploitation, improving evolutionary process diversity.
• Utilized a modified non-dominated sorting scheme with crowding distance for population truncation and solution distribution.

Main Results:

• MMODE_AP demonstrated superior performance on CEC'2020 benchmark functions compared to existing MMODE algorithms.
• Achieved approximately 20% better results in terms of reciprocal of Pareto sets proximity (rPSP) and inverted generational distances (IGD).
• Showcased efficient convergence to true local and global Pareto fronts with well-distributed solutions.

Conclusions:

• The proposed MMODE_AP algorithm effectively addresses the challenges of multi-modal multi-objective optimization.
• APC integration significantly improves the identification and distribution of solutions across multiple Pareto optimal sets.
• MMODE_AP offers a robust approach for achieving both convergence and diversity in complex optimization landscapes.