A Novel Detection-and-Replacement-Based Order-Operator for Differential Evolution in Solving Complex Bound Constrained Optimization Problems

Sichen Tao (), Sicheng Liu, Shoya Ohta, Ruihan Zhao, Zheng Tang and Yifei Yang ()
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Sichen Tao: Faculty of Engineering, University of Toyama, Toyama-shi 930-8555, Japan
Sicheng Liu: Faculty of Engineering, Yantai Vocational College, Yantai 264670, China
Shoya Ohta: Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8560, Japan
Ruihan Zhao: School of Engineering and Design, Technical University Munich, 85748 Garching, Germany
Zheng Tang: Faculty of Engineering, University of Toyama, Toyama-shi 930-8555, Japan
Yifei Yang: Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8560, Japan

Mathematics, 2025, vol. 13, issue 9, 1-40

Abstract: The design of differential evolution (DE) operators has long been a key topic in the research of metaheuristic algorithms. This paper systematically reviews the functional differences between mechanism improvements and operator improvements in terms of exploration and exploitation capabilities, based on the general patterns of algorithm enhancements. It proposes a theoretical hypothesis: operator improvement is more directly associated with the enhancement of an algorithm’s exploitation capability. Accordingly, this paper designs a new differential operator, DE/current-to-pbest/order, based on the classic DE/current-to-pbest/1 operator. This new operator introduces a directional judgment mechanism and a replacement strategy based on individual fitness, ensuring that the differential vector consistently points toward better individuals. This enhancement improves the effectiveness of the search direction and significantly strengthens the algorithm’s ability to delve into high-quality solution regions. To verify the effectiveness and generality of the proposed operator, it is embedded into two mainstream evolutionary algorithm frameworks, JADE and LSHADE, to construct OJADE and OLSHADE. A systematic evaluation is conducted using two authoritative benchmark sets: CEC2017 and CEC2011. The CEC2017 set focuses on assessing the optimization capability of theoretical complex functions, covering problems of various dimensions and types; the CEC2011 set, on the other hand, targets multimodal and hybrid optimization challenges in real engineering contexts, featuring higher structural complexity and generalization requirements. On both benchmark sets, OLSHADE demonstrates outstanding solution quality, convergence efficiency, and result stability, showing particular advantages in high-dimensional complex problems, thus fully validating the effectiveness of the proposed operator in enhancing exploitation capability. In addition, the operator has a lightweight structure and is easy to integrate, with good portability and scalability. It can be embedded as a general-purpose module into more DE variants and EAs in the future, providing flexible support for further performance optimization in solving complex problems.

Keywords: metaheuristics; evolutionary computation; differential evolution; order-operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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