A neural network with strong interpretability for solving optimization problems

• Published in: Applied soft computing Vol. 170; p. 112688
• Main Authors: Fan, Jianhan, Liao, Yiming, Zou, Jianxiao, Liao, Kaiji, Fan, Shicai
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2025
• Subjects: Metaheuristic; OPSN; Optimization problem; Optimization problem solving network; Optimization problem solving network; OPSN; Metaheuristic; Optimization problem
• ISSN: 1568-4946
• DOI: 10.1016/j.asoc.2024.112688

Accurate and rapid solutions to optimization problems are crucial in scientific and engineering fields. To address diverse optimization challenges, this paper proposes an Optimization Problem Solving Network (OPSN), a novel neural network with strong interpretability. By introducing the Lagrange multiplier method and Karush–Kuhn–Tucker (KKT) conditions, the theoretical conditions that must be satisfied to obtain the optimal solution are derived. Based on these conditions, OPSN is developed. The network structure of OPSN is similar to that of the backpropagation (BP) neural network; however, the forward computation formula is redesigned to incorporate the constraint information inherent in the optimization problem. By introducing the penalty coefficient, the activation functions of the network nodes are redefined to assess whether the constraints are satisfied. Additionally, a special node is added to capture information about the objective function. To reduce the adjustable parameters, the network input is fixed at 1, and the normalization algorithm has been developed based on the search range of each variable. The network is initialized with random weights as starting values. Extensive testing on 15 CEC2017 benchmark functions and six real-world engineering problems demonstrates OPSN’s superior performance, faster convergence, and broad applicability compared to five established optimization algorithms. •New meta-heuristic algorithm for solving optimization problems.•Neural network with strong interpretability.•New forward calculation formula and activation function.•CEC2017 and engineering problem test.