IGD Indicator-based Evolutionary Algorithm for Many-objective Optimization Problems (1802.08792v1)

Abstract: Inverted Generational Distance (IGD) has been widely considered as a reliable performance indicator to concurrently quantify the convergence and diversity of multi- and many-objective evolutionary algorithms. In this paper, an IGD indicator-based evolutionary algorithm for solving many-objective optimization problems (MaOPs) has been proposed. Specifically, the IGD indicator is employed in each generation to select the solutions with favorable convergence and diversity. In addition, a computationally efficient dominance comparison method is designed to assign the rank values of solutions along with three newly proposed proximity distance assignments. Based on these two designs, the solutions are selected from a global view by linear assignment mechanism to concern the convergence and diversity simultaneously. In order to facilitate the accuracy of the sampled reference points for the calculation of IGD indicator, we also propose an efficient decomposition-based nadir point estimation method for constructing the Utopian Pareto front which is regarded as the best approximate Pareto front for real-world MaOPs at the early stage of the evolution. To evaluate the performance, a series of experiments is performed on the proposed algorithm against a group of selected state-of-the-art many-objective optimization algorithms over optimization problems with $8$-, $15$-, and $20$-objective. Experimental results measured by the chosen performance metrics indicate that the proposed algorithm is very competitive in addressing MaOPs.

• The paper proposes a novel IGD indicator method that balances convergence and diversity in many-objective optimization problems.
• It incorporates efficient decomposition, dominance comparison, and proximity distance assignment strategies to enhance computational efficiency.
• It outperforms traditional MOEAs on benchmark problems, particularly excelling on concave Pareto fronts.

Essay on "IGD Indicator-based Evolutionary Algorithm for Many-objective Optimization Problems"

The paper "IGD Indicator-based Evolutionary Algorithm for Many-objective Optimization Problems" by Yanan Sun et al. addresses the computational challenges associated with optimizing many-objective problems (MaOPs). Traditional multi-objective evolutionary algorithms (MOEAs) often struggle with scalability when more than three objectives are involved, making efficient algorithms for MaOPs crucial. This research proffers a novel approach grounded in the Inverted Generational Distance (IGD) indicator to simultaneously optimize the convergence and diversity of solutions for MaOPs.

Overview

The IGD has been esteemed as a reliable metric for gauging the convergence and diversity in the context of multi-objective optimization. This paper introduces an IGD indicator-based evolutionary algorithm designed explicitly for MaOPs. One of the core mechanisms is leveraging the IGD indicator in each generation to prioritize solutions that strike a favorable balance between convergence and diversity. The algorithm incorporates a computationally efficient dominance comparison mechanism, new proximity distance assignments, and a linear assignment-based selection process to ensure a globally consistent perspective on solutions.

Key Contributions

1. Decomposition-based Nadir Point Estimation: The proposed method estimates nadir points to help adequately compute the IGD indicator. It is notably efficient, converting an $m$-objective problem to $m$ single-objective problems and is less computationally intensive than other estimation methods.
2. Enhanced Dominance Comparison Scheme: Unlike traditional MOEAs, which compare all population members, this approach assesses only the dominance relations relative to a set of reference points, enhancing computational efficiency.
3. Proximity Distance Assignment Mechanisms: The algorithm introduces distance calculations tailored to each solution's rank, enhancing the algorithm's alignment with Pareto compliance and improving convergence pressure.
4. Global Selection Mechanism: Solutions are selected through linear assignment, balancing convergence and diversity simultaneously by allowing an expansive vantage point of the population.

Numerical Results

The algorithm was tested on standard benchmark problems (DTLZ and WFG suites) with 8, 15, and 20 objectives, and it was compared against notable MOEAs like NSGA-III, MOEA/D, HypE, RVEA, and KnEA. The proposed algorithm generally performed competitively, especially in addressing MaOPs with complex objective spaces. In particular, its performance on problems with concave Pareto fronts was noticeably superior, benefiting from the effective balancing of diversity and convergence.

Implications and Future Directions

The proposed evolutionary algorithm successfully addresses the dual challenges of convergence and diversity in MaOP optimization, validating the use of IGD as a central performance metric.

The results suggest that further advancements could result from:

• Adaptive Reference Point Generation: Future research might explore adaptive methods in constructing Utopian Pareto fronts, refining reference generation for dynamic environments.
• Scalable Decomposition Strategies: Investigating scalable decomposition strategies could further enhance the efficacy and application of the algorithm in large-scale real-world problems.
• Hybrid Methodologies: Integrating this IGD-based approach with other techniques in deep learning and other computational domains may offer compounded benefits.

Overall, this paper expands the repertoire of tools available to researchers in the field of evolutionary computation, providing a robust framework adaptable to the intricate nature of many real-world optimization tasks.