On the Norm of Dominant Difference for Many-Objective Particle Swarm Optimization

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Evolutionary Computation

Background:

• Multiobjective particle swarm optimization (PSO) often uses Pareto-based techniques.
• These methods face scalability challenges in many-objective optimization problems (MaOPs) due to poor Pareto optimality discrimination.
• This limitation affects leader selection and algorithm effectiveness.

Purpose of the Study:

• To propose a new scheme for discriminating solutions in objective space for MaOPs.
• To introduce a novel algorithm, many-objective PSO based on the norm of dominant difference (MOPSO/DD), to address scalability and discrimination issues.

Main Methods:

• Proposed the concept of 'dominant difference' of a solution to demonstrate its dominance across all dimensions.
• Investigated the norm of dominant difference within the population to indirectly obtain discriminability for hard-to-distinguish solutions.
• Integrated this into PSO, creating MOPSO/DD, and incorporated an Lp-norm-based density estimator for improved convergence, diversity, and reduced complexity.

Main Results:

• MOPSO/DD demonstrates effective discrimination of solutions in objective space, even for difficult cases in MaOPs.
• The algorithm exhibits good convergence and diversity properties.
• MOPSO/DD achieves lower computational complexity compared to existing methods.

Conclusions:

• The proposed dominant difference scheme and MOPSO/DD algorithm offer a competitive and effective approach for many-objective optimization problems.
• The Lp-norm-based density estimator contributes to the algorithm's efficiency and performance.
• MOPSO/DD shows promise compared to state-of-the-art multiobjective evolutionary algorithms.