# Reference Point and Grid Method-Based Evolutionary Algorithm with Entropy for Many-Objective Optimization Problems

## TL;DR

This paper introduces RGEA, a new algorithm that combines reference points and grids with entropy to better solve complex many-objective optimization problems.

## Contribution

The novel RGEA algorithm uses entropy to adaptively switch between reference point and grid methods for improved performance on many-objective problems.

## Key findings

- RGEA outperforms existing algorithms on both regular and irregular Pareto front problems.
- Entropy helps RGEA determine whether to use reference points or grids based on the problem's shape.
- Extensive experiments show RGEA's effectiveness across 3-to-10 objective problems.

## Abstract

In everyday scenarios, there are many challenges involving multi-objective optimization. As the count of objective functions rises to four or beyond, the problem’s complexity intensifies considerably, often making it challenging for traditional algorithms to arrive at satisfactory solutions. The non-dominated sorting evolutionary reference point-based (NSGA-III) and the grid-based evolutionary algorithms (GrEA) are two prevalent algorithms for many-objective optimization. These two algorithms preserve population diversity by employing reference point and grid mechanisms, respectively. However, they still have limitations when addressing many-objective optimization problems. Due to the uniform distribution of reference points, the reference point-based methods do not obtain good performance on problems with an irregular Pareto front, while grid-based methods do not achieve good results on problems with a regular Pareto front because of the uneven partition of grids. To address the limitations of reference point-based algorithms and grid-based approaches in tackling both regular and irregular problems, a reference point- and grid-based evolutionary algorithm with entropy is proposed for many-objective optimization, denoted as RGEA, which aims to solve both regular and irregular many-objective optimization problems. Entropy is introduced to measure the shape of the Pareto front of a many-objective optimization problem. In RGEA, a parameter α is introduced to determine the interval for calculating the entropy value. By comparing the current entropy value with the maximum entropy value, the reference point-based method or the grid-based method can be determined. In order to verify the performance of the proposed algorithm, a comprehensive experiment was designed on some popular test suites with 3-to-10 objectives. In addition, RGEA was compared against six algorithms without adaptive technology and six algorithms with adaptive technology. A great number of experimental results were obtained showing that RGEA can obtain good results.