Multimodal multi-objective optimization algorithm based on hierarchical environment selection strategy.

Area of Science:

• Computational intelligence
• Optimization algorithms
• Evolutionary computation

Background:

• Current multimodal multi-objective optimization algorithms struggle with Pareto optimal set (PS) completeness and convergence.
• Existing methods often lack strategies to ensure both diversity and convergence effectively.

Purpose of the Study:

• To propose a novel optimization algorithm addressing deficiencies in current multimodal multi-objective optimization.
• To enhance the completeness and convergence of Pareto optimal sets (PSs) and Pareto fronts (PFs).

Main Methods:

• The algorithm is based on a differential evolutionary algorithm (DE) framework.
• A neighborhood-based individual variation strategy using special crowding distance is employed to ensure diversity.
• A hierarchical environment selection strategy sorts and selects non-dominated individuals layer by layer.
• Adaptive mutation strategies are utilized during individual evolution based on population characteristics.

Main Results:

• The proposed algorithm demonstrates superior performance compared to several existing algorithms on 13 test problems.
• It effectively obtains more diverse and uniformly distributed Pareto optimal sets (PSs) and Pareto fronts (PFs).
• The strategies employed prevent premature convergence and maintain the algorithm's searchability.

Conclusions:

• The developed optimization algorithm with hierarchical selection effectively improves the convergence and diversity of Pareto optimal sets.
• The approach offers a promising solution for complex multimodal multi-objective optimization problems.
• The algorithm exhibits robust performance and better distribution of solutions.