A multi-objective whale optimization for solving combinatorial optimization problems via Hopfield neural networks
摘要
Nowadays, researchers are focused on enhancing the learning phase in Discrete Hopfield Neural Network, but little attention has been given to simultaneously improving both the learning and retrieval phases. This study aims to address this gap by optimizing not only the learning phase but also the final neuron state retrieved by the network. This is achieved through the implementation of an Election Algorithm as a learning algorithm and a Hybrid Binary Whale Optimization Algorithm for optimizing the retrieved neuron states. This contributes to the achievement of multiple objectives including maximizing diverse solutions while maintaining a maximum global solution and minimizing similarity index values. The effectiveness of the model in achieving these multiple objectives is compared to various baseline metaheuristic algorithms and it is demonstrated that the proposed model outperforms these baseline algorithms in successfully fulfilling the specified multi-objectives. The performance analysis of these baseline algorithms show that the proposed algorithm achieves a 100% success rate in maximizing diversified solutions while maintaining a maximum global solution. Moreover, the proposed algorithm exhibits the highest total neuron variation at 80.73% and the lowest similarity index at 83%. Additionally, from the perspective of logic mining, this work could also be beneficial in solving real-life classification problems.