Hyperplane Assisted Evolutionary Algorithm for Many-Objective Optimization Problems

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Evolutionary Computation

Background:

• Many-objective optimization problems (MaOPs) present challenges in balancing convergence and diversity for evolutionary algorithms.
• The increasing number of objectives in MaOPs makes it difficult to maintain selection pressure toward the Pareto-optimal front.
• Existing methods struggle with the sharp increase in nondominated solutions as objectives grow.

Purpose of the Study:

• To address the challenges in environmental selection for MaOPs.
• To introduce a new definition of "prominent solutions" to better distinguish nondominated solutions.
• To propose a novel environmental selection strategy and a corresponding algorithm (hpaEA) for MaOPs.

Main Methods:

• Defined "prominent solutions" based on hyperplanes formed by neighboring solutions to identify those with clear Pareto-optimal front tendencies.
• Developed a two-criterion environmental selection strategy to prioritize prominent solutions and balance convergence/diversity.
• Proposed the hyperplane assisted evolutionary algorithm (hpaEA) incorporating the new selection strategy.

Main Results:

• Conducted extensive experiments comparing hpaEA with five state-of-the-art algorithms on 36 benchmark instances.
• Demonstrated the superiority of hpaEA in solving MaOPs.
• hpaEA significantly outperformed compared algorithms on 20 out of 36 benchmark instances.

Conclusions:

• The proposed definition of prominent solutions and the novel selection strategy effectively enhance evolutionary algorithms for MaOPs.
• hpaEA shows significant performance improvements over existing methods, particularly in challenging many-objective scenarios.
• The hyperplane-assisted approach offers a promising direction for future research in many-objective optimization.