ABSTRACT
In humanitarian aid scenarios, the model of cumulative capacitated vehicle routing problem can be used in vehicle scheduling, aiming at delivering materials to recipients as quickly as possible, thus minimizing their wait time. Traditional approaches focus on this metric, but practical implementations must also consider factors such as driver labor intensity and the capacity for on-site decision-making. To evaluate driver workload, the operation times of relief vehicles are typically used, and multi-objective modeling is employed to facilitate on-site decision-making. This paper introduces a multi-objective cumulative capacitated vehicle routing problem considering operation time (MO-CCVRP-OT). Our model is bi-objective, aiming to minimize both the cumulative wait time of disaster-affected areas and the extra expenditures incurred by the excess operation time of rescue vehicles. Based on the traditional grey wolf optimizer algorithm, this paper proposes a dynamic grey wolf optimizer algorithm with floating 2-opt (DGWO-F2OPT), which combines real number encoding with an equal-division random key and ROV rules for decoding; in addition, a dynamic non-dominated solution set update strategy is introduced. To solve MO-CCVRP-OT efficiently and increase the algorithm's convergence speed, a multi-objective improved floating 2-opt (F2OPT) local search strategy is proposed. The utopia optimum solution of DGWO-F2OPT has an average value of two fitness values that is 6.22% lower than that of DGWO-2OPT. DGWO-F2OPT's average fitness value in the algorithm comparison trials is 16.49% less than that of NS-2OPT. In the model comparison studies, MO-CCVRP-OT is 18.72% closer to the utopian point in Euclidean distance than CVRP-OT.
ABSTRACT
INTRODUCTION: In recent years, the proliferation of Industrial Internet of Things (IIoT) devices has resulted in a substantial increase in data generation across various domains, including the nascent 6G networks. Digital Twins (DTs), serving as virtual replicas of physical entities, have gained popularity within the realm of IoT due to their capacity to simulate and optimize physical systems in a cost-effective manner. Nonetheless, the security of DTs and the safeguarding of the sensitive data they generate have emerged as paramount concerns. Fortunately, the Federated Fearning (FL) system has emerged as a promising solution to address the challenge of data privacy within DTs. Nonetheless, the requisite acquisition of a significant volume of labeled data for training purposes poses a formidable challenge, particularly in a DT environment that blends real and virtual data. OBJECTIVES: To tackle this challenge, this study presents an innovative Semi-supervised FL (SSFL) framework designed to overcome the scarcity of labeled data through the strategic utilization of pseudo-labels. METHODS: Specifically, our proposed SSFL algorithm, named SSFL-MBE, introduces a novel approach by combining Mix data augmentation and Bayesian Estimation consistency regularization loss, thereby integrating robust augmentation techniques to enhance model generalization. Furthermore, we introduce a Bayesian-estimated pseudo-label loss that leverages prior probabilistic knowledge to enhance model performance. Our investigation focuses particularly on a demanding scenario where labeled and unlabeled data are segregated across disparate locations, specifically, the server and various clients. RESULTS: Comprehensive evaluations conducted on CIFAR-10 and MNIST datasets conclusively demonstrate that our proposed algorithm consistently surpasses mainstream SSFL baseline models, exhibiting an enhancement in model performance ranging from 0.5% to 1.5%. CONCLUSION: Overall, this work contributes to the development of more efficient and secure approaches for model training in DT-empowered FL settings, which is crucial for the deployment of IIoTs in 6G-enabled environments.
