A knowledge-learning-and-transfer-aided differential evolution for nonlinear equation systems

Abstract

Nonlinear equation systems (NESs) are common in practical applications, and solving them is an important task in numerical computation. Evolutionary algorithms (EAs) for handling NESs have received considerable attention. EAs generate a large amount of data, which reflect the evolutionary behavior. However, there are still deficiencies in the mining and use of these data. Inspired by the ability of humans to acquire knowledge from past historical experience, this paper proposes a knowledge-learning-and-transfer-aided hybrid niching-based differential evolution (HNDE/KLT). HNDE/KLT aims to acquire knowledge from historical experiences and use them to guide the evolution. The HNDE/KLT include two main features: i) artificial neural networks are embedded in EAs, so the algorithm can learn from successful historical evolutionary information and obtain the relationship between the current individual’s position and the optimal evolutionary direction; ii) a knowledge-transfer-based technique is designed to perform information exchange between different subpopulations, enhancing exploitation efficiency. Experimental results show that the HNDE/KLT can better solve NESs, indicating that learning plus transfer can make problem solving more intelligent. Additionally, we employed our algorithm to solve two real-world problems, and obtained good results.