The traveling salesman problem (TSP) has been studied for many years. In particular, the multimodal optimization of the TSP is important for practical applications, because decision-makers can select the best candidate based on current conditions and requirements. In the Euclidean TSP, there are$n$points in$\mathbb {R}^{d}$space with Euclidean distance between any two points, that is,$d(x, y) =||x-y||_{2}$. The goal is to find a tour of minimum length visiting each point. In this article, we only focus on the case that$d=2$. Recently, in order to efficiently handle the multimodal optimization of the TSP, some methods have been developed to deal with it. Nevertheless, these methods usually perform poorly for large-scale cases. In this article, we propose a niching regression adaptive memetic algorithm (MA) to handle the multimodal optimization of the Euclidean TSP. We use the MA as the baseline algorithm and incorporate the neighborhood strategy to maintain the population diversity. In addition, we design a novel regression partition initialization and adaptive parameter control to enhance our algorithm, and propose the concept of the redundant individual to improve the search efficiency. To validate the performance of the proposed algorithm, we comprehensively conduct experiments on the multimodal optimization of TSP benchmark and the well-known TSPLIB library. The experimental results reveal that the proposed method outperforms other methods, especially for large-scale cases.

Cloud services are experiencing a remarkable increase in the number of users and the resource required over the past few years. Thus, it has become a great challenge for the internet vendors to make a robust framework to serve the customers with low cost and delay. Congestion control is one of the essential topics of routing algorithms in cloud data center networks. In this paper, we propose a weighted optimal scheduling scheme WSPR for congestion control in cloud data center networks which prevents the congestion in advance with the global view so that it can make good use of vacant network resources. We choose BCube as our network model and modify the network topology to fit software-defined networks so as to have a full view of the topology. First, we design the SP graph which contains all shortest paths between a source server and a destination server. Second, we propose WSPR to allocate the most appropriate path to each flow for congestion control. We implement a system to simulate a data center, and evaluate our proposed scheme WSPR by comparing WSPR with other classical methods. The experimental results demonstrate that our proposed scheme WSPR has the best performance in terms of the maximum delay, average delay, and throughput among all compared methods.