Diversity comparison of Pareto front approximations in many-objective optimization

Area of Science:

• Optimization
• Computational Science
• Artificial Intelligence

Background:

• Diversity assessment of Pareto front approximations is crucial in stochastic multiobjective optimization.
• Existing diversity indicators often become infeasible or unworkable with a large number of objectives.

Purpose of the Study:

• To propose a novel Diversity Comparison Indicator (DCI) for assessing Pareto front approximations in many-objective optimization.
• To develop a computationally efficient indicator that scales well with an increasing number of objectives.

Main Methods:

• The DCI utilizes a grid environment to categorize solutions into hyperboxes.
• It evaluates the relative quality of different Pareto front approximations by considering their contributions to non-empty hyperboxes.
• The indicator exhibits quadratic time complexity, independent of grid divisions.

Main Results:

• The DCI demonstrates effectiveness in assessing diversity across artificial and real-world Pareto front approximations with varying numbers of objectives.
• Empirical and analytical comparisons show favorable performance against existing diversity indicators.
• Parametric investigations provide insights into grid division settings.

Conclusions:

• The proposed DCI is a viable and efficient tool for evaluating the diversity of Pareto front approximations, particularly in many-objective scenarios.
• Its computational efficiency makes it suitable for complex optimization problems.
• The indicator offers practical guidance for users with diverse preferences.