# IGD Indicator-based Evolutionary Algorithm for Many-objective Optimization Problems

## TL;DR

This paper introduces an IGD indicator-based evolutionary algorithm for many-objective optimization that improves solution convergence and diversity through novel selection, ranking, and reference point estimation methods, showing competitive performance.

## Contribution

The paper proposes a new evolutionary algorithm utilizing IGD for solution selection, a fast dominance comparison, and an efficient nadir point estimation for better MaOP handling.

## Key findings

- The algorithm outperforms state-of-the-art methods on 8-, 15-, and 20-objective problems.
- It effectively balances convergence and diversity in many-objective optimization.
- Experimental results demonstrate its high competitiveness and robustness.

## 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.