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Many time-varying problems have been solved using the zeroing neural network proposed by Zhang et al. In this article, nine types of time-varying problems, namely time-varying nonlinear equation system, time-varying linear equation system, time-varying convex nonlinear optimization under linear equalities, unconstrained time-varying convex nonlinear optimization, time-varying convex quadratic programming under linear equalities, unconstrained time-varying convex quadratic programming, time-varying nonlinear inequality system, time-varying linear inequality system, and time-varying division, are investigated to better understand the essence of zeroing neutral network. Discrete-form time-varying problems are studied by considering the nature of unknown future and the requirement of real-time computation for time-varying problems. A unified model is proposed in the frame of zeroing neural network to uniformly solve these time-varying problems on the basis of their connections and a newly developed discretization formula. Theoretical analyses and numerical experiments, including the tracking control of PUMA560 robot manipulator, verify the effectiveness and precision of the proposed unified model.

Network Function Virtualization (NFV) can provide the resource according to the request and can improve the flexibility of the network. It has become the key technology of the Internet of Things (IoT). Resource scheduling for the virtual network function service chain (VNF-SC) is the key issue of the NFV. Energy consumption is an important indicator for the IoT; we take the energy consumption into the objective and define a novel objective to satisfying different objectives of the decision-maker. Due to the complexity of VNF-SC deployment problem, through taking into consideration of the heterogeneity of nodes (each node only can provide some specific VNFs), and the limitation of resources in each node, a novel optimal model is constructed to define the problem of VNF-SC deployment problem. To solve the optimization model effectively, a weighted center opposition-based learning is introduced to brainstorm optimization to find the optimal solution (OBLBSO). To show the efficiency of the proposed algorithm, numerous of simulation experiments have been conducted. Experimental results indicate that OBLBSO can improve the accuracy of the solution than compared algorithm.

Elastic optical networks (EONs) virtualization can allow the virtual optical networks (VONs) to utilize all the physical resources of EONs, and can attain a high performance of the networks. However, the optimal scheme for VONs mapping should be determined. To tackle these challenges, a bi-level mathematical model is established. leader's and follower's objectives are to minimize energy consumption and the maximum index of used frequency slots, respectively. The bi-level mathematical model can determine the optimal schemes of VONs mapping. To solve the mathematical model effectively, a uniform design method is applied to generate initial population for the lower level problem. In addition, To solve the whole model effectively, a tailor-made encoding, population initialization, genetic operators and local search operator are designed. An efficient genetic algorithm with local search operator is proposed for the bi-level mathematical model. To evaluate the mathematical model and the designed algorithm, a large number of experiments are performed on three kinds of the widely used networks, and the experimental results indicate that the effectiveness of the proposed bi-level mathematical model and designed algorithms.

Time discretization is an important part of time-varying problems solving that determines convergence, real-time performance and accuracy for solution models. It is a challenging work compared with relatively simple derivative approximation due to unknown future information and stability constraint. To the best of the authors’s knowledge, no effective time discretization was developed other than Euler finite difference formula before recently development of ZeaD formulas. Existing work presents some ZeaD formulas including specific time-discretization formulas having third order accuracy. In this work, $N$ -instant general third-order-accuracy formula is proposed, and it leads to different general third-order-accuracy formulas when different instant number $N$ is considered. Stability and convergence are analyzed, and effective domains for parameters in 5-instant and 6-instant general third-order-accuracy formula are given to guarantee effective time discretization. Furthermore, $N$ -instant general third-order-accuracy formula is employed to solve time-varying optimization, and $N$ -instant general solution model is proposed. Finally, comparative experimental results are presented to substantiate the effectiveness and superiority of proposed general formulas and models.

The resource allocation for bag-of-tasks in the heterogeneous distributed system is to distribute the tasks to proper processors such that the makespan is minimized. It is a well-known NP-hard problem, and is even more complex and challenging when the processors have off-line time. To tackle this challenging problem, first, we set up a mathematical model for this problem which minimizes the makespan of the bag-of-tasks with the off-line time segment of the processors. Second, to solve the model efficiently, we propose two new algorithms: a new scheduling algorithm referred to as sorting-allocation-pulling scheduling algorithm which first allocate the tasks to available time segment on proper processors and then pulls them to the formerly available time segment for the sake of minimizing the makespan, and an effective genetic algorithm with a novel local search operator and a well-designed modify operator. Finally, the numerical simulation experiments are conducted, and the two proposed algorithms are compared. The experimental results indicate the effectiveness of the proposed model and algorithms.

Signcryption is a basic cryptographic primitive that simultaneously captures the functions of encryption and signature. To realize comprehensive information security against quantum computing attacks, lattice-based signcryption schemes have been successively proposed. However, the performance of signcryption schemes should be improved in the lattice setting. An efficient lattice-based signcryption scheme in the standard model is proposed in this paper. Under the ring learning with errors (RLWE) assumption and the ideal short integer solution (ISIS) assumption, the proposed signcryption scheme achieves indistinguishability against adaptive chosen ciphertext attacks (IND-CCA2) and existential unforgeability under an adaptive chosen-message attack (EUF-ACMA). Our scheme not only reduces the communication and computational overhead but also realizes a new design that combines the partitioning technique with the idea of tag-based key encapsulation. The performance analysis results show that our scheme is more efficient than previous lattice-based signcryption schemes in the standard model.

Network virtualization (NV) can provide the resource according to the request and can improve the flexibility of the network. It has become the key technology of 5G communication. Resource scheduling in virtual network mapping is an important problem faced by NV technology. To enhance the performance of the network, optimal resource scheduling schemes should be determined. In general, maximum index of frequency slots used, energy consumption, and the ratio of used frequency slots are three very important indicators for the network. Based on the previous research studies, we first take these three indicators into the objective of the mathematical model and define a novel multiobjective optimization model. Then, the three objectives are integrated into one objective to be minimized by using the sum weighted strategy. Finally, an efficient algorithm, which integrates the advantages of artificial raindrop algorithm (ARA), particle swarm optimization, and differential evolution, is proposed and denoted as IARA. Moreover, simulation experiments have been conducted in several experimental scenes with other compared algorithms. The experimental results show that the proposed algorithm IARA can obtain better scheduling schemes than the compared algorithms.

Network function virtualization (NFV) technology can realize on-demand distribution of network resources and improve network flexibility. It has become one of the key technologies for next-generation communications. Virtual network function service chain (VNF-SC) deployment is an important problem faced by network function virtualization technology. In this paper, the problem, VNF deployment for VNF-SC, is investigated. First, a two-objective mathematical model, which maximizes balancing and reliability of SFC, is established. In this model, VNFs are divided into two classes, i.e., part of required VNFs in each VNF-SC is dependent, others are independent. Second, harmony search-based MOEA/D (HS-MOEA/D) is proposed to solve the model effectively. In HS-MOEA/D, Chebyshev decomposition mechanism is used to transform multiobjective optimization problem into a series of single-objective optimization subproblems. A new evolutionary strategy is deeply studied in order to propose a new harmony search (HS) algorithm. Finally, to show high performance of the proposed algorithm, a large number of experiments are conducted. The simulation results show that the proposed algorithm enhances the reliability of SFC and reduces the end-to-end delay.

The risk measure plays an important role for portfolio selection problem. The lower partial risk (downside risk) measures have been considered to be more in line with investor’s attitude toward risk. The purpose of this paper is to construct a portfolio selection model in the lower partial risk framework. First, semi-variance and semi-absolute deviation risk measures are used as double-risk measures simultaneously, which can overcome the shortcomings of both semi-variance risk measure and semi-absolute deviation risk measure and can provide additional strengths and flexibility. Second, to address a real portfolio selection problem, by considering the transaction cost and liquidity of portfolio, and regarding the returns of risk assets as LR-type fuzzy variables, we present a fuzzy multi-objective portfolio selection model. Third, in order to limit the proportion of the portfolio invested in assets with common characteristics and to avoid very small holdings, the quantity and class constraints are introduced into the model. Finally, to solve the proposed model efficiently, a new multi-objective evolutionary algorithm is designed. Furthermore, some experiments are conducted by using the data of Shanghai Stock Exchange, and the results indicate the efficiency and effectiveness of the proposed model and algorithm.

Manycast routing and spectrum assignment (RSA) in elastic optical networks (EONs) has become a hot research field. In this paper, the mathematical model and high efficient algorithm to solve this challenging problem in EONs is investigated. First, a multi-objective optimization model, which minimizes network power consumption, the total occupied spectrum, and the maximum index of used frequency spectrum, is established. To handle this multi-objective optimization model, we integrate these three objectives into one by using a weighted sum strategy. To make the population distributed on the search domain uniformly, a uniform design method was developed. Based on this, an improved grey wolf optimization method (IGWO), which was inspired by PSO (Particle Swarm Optimization, PSO) and DE (Differential Evolution, DE), is proposed to solve the maximum model efficiently. To demonstrate high performance of the designed algorithm, a series of experiments are conducted using several different experimental scenes. Experimental results indicate that the proposed algorithm can obtain better results than the compared algorithm.

Virtualization technology can greatly improve the efficiency of the networks by allowing the virtual optical networks to share the resources of the physical networks. However, it will face some challenges, such as finding the efficient strategies for virtual nodes mapping, virtual links mapping and spectrum assignment. It is even more complex and challenging when the physical elastic optical networks using multi-core fibers. To tackle these challenges, we establish a constrained optimization model to determine the optimal schemes of optical network mapping, core allocation and spectrum assignment. To solve the model efficiently, tailor-made encoding scheme, crossover and mutation operators are designed. Based on these, an efficient genetic algorithm is proposed to obtain the optimal schemes of the virtual nodes mapping, virtual links mapping, core allocation. The simulation experiments are conducted on three widely used networks, and the experimental results show the effectiveness of the proposed model and algorithm.

By adopting the orthogonal frequency division multiplexing technology, elastic optical networks can provide the flexible and variable bandwidth allocation to each connection request and get higher spectrum utilization. The routing and spectrum assignment problem in elastic optical network is a well-known NP-hard problem. In addition, information security has received worldwide attention. We combine these two problems to investigate the routing and spectrum assignment problem with the guaranteed security in elastic optical network, and establish a new optimization model to minimize the maximum index of the used frequency slots, which is used to determine an optimal routing and spectrum assignment schemes. To solve the model effectively, a hybrid genetic algorithm framework integrating a heuristic algorithm into a genetic algorithm is proposed. The heuristic algorithm is first used to sort the connection requests and then the genetic algorithm is designed to look for an optimal routing and spectrum assignment scheme. In the genetic algorithm, tailor-made crossover, mutation and local search operators are designed. Moreover, simulation experiments are conducted with three heuristic strategies, and the experimental results indicate that the effectiveness of the proposed model and algorithm framework.

Routing, spectrum assignment are key issues and the hot focus area in multi-domain elastic optical networks (EONs). When the EONs with multi-cores, more challenges will be faced, such as core allocation, crosstalk, etc. To tackle these challenges, we establish a mixed integer linear programming model with the maximum index used frequency slots (MIUFS) to be minimized, which is used to determine the optimal schemes of routing, core allocation and spectrum assignment for the multi-domain EONs with multi-cores. To solve the model efficiently, an efficient genetic algorithm with tailor-made crossover, mutation and local search operators is designed. To evaluate the model and the proposed algorithm, several simulation experiments are conducted on two different multi-domain EONs, and the experimental results show that the proposed algorithm has a higher performance than the compared algorithms.

In this paper, the problem of routing and spectrum assignment for static connection requests in elastic optical networks (EONs) is studied. Two different ratios of blocking formations are adopted, and a global constraint optimization model is established to minimize the ratio of blocking in the network. First, we propose an availability index of the frequency slots in the path. Second, a strategy of routing is designed by considering the two indexes of path length and availability index to judge the quality of the path. Then, a greedy strategy, which can obtain the largest availability index in the path after the frequency slot allocated, is proposed for the sake of assigning the spectra effectively. Simulation experiments were carried out in two network topologies. The two different ratios of blocking are obtained for different sorting strategy for connection requests and the number of connection requests. The experimental results show that the routing and spectrum assignment scheme designed in this paper can get a small ratio of blocking.

The routing and spectrum assignment problems in elastic optical networks are well-known NP-hard problem, and are even more complex and challenging when the energy consumption is taken into account. To tackle this challenging problem, we establish a bi-level programming model with the energy consumption of the optical networks and the maximum index of used frequency slots as the leader’s and follower’s objectives to be minimized, respectively, which are used to determine the optimal schemes of routing and spectrum assignments. To solve the model effectively, a hybrid genetic algorithm framework integrating a heuristic algorithm into a genetic algorithm is proposed. We use heuristic algorithm to sort the connection requests and design a genetic algorithm with tailor-made crossover, mutation and local search operator to look for an optimal routing and spectrum assignment scheme. Finally, simulation experiments are conducted, and the experimental results indicate the effectiveness of the proposed model and algorithms.

The routing, core allocation and spectrum assignment (RSA) problem in elastic optical networks with multi-core is a well-known NP-hard problem and the network information security is also an important problem in elastic optical networks. In this paper, we combine these two problems to investigate the routing, core allocation and spectrum assignment problem with the guaranteed secure level in elastic optical network with multi-core. We establish a new optimization model to determine an optimal routing, core allocation scheme with the guaranteed secure level by minimizing the maximum sequence number of frequency slots. To solve the model effectively, we propose a hybrid algorithm for routing and core allocation. First, the candidate secure paths, which can guarantee the required secure level for connection requests, are determined by using a heuristic algorithm. Then, to get an optimal routing and core allocation scheme, an effective genetic algorithm with a tailor-made crossover operator and a well-designed mutation operator is designed. Finally, simulation experiments are conducted, and the experimental results indicate that the effectiveness of the proposed model and algorithm.

The scheduling for divisible load in heterogeneous distributed system is a well known NP-hard problem. The problem is even more complex and challenging when its model has more than one objective, The difficulty is to satisfy multiple objectives that may be of conflicting nature. This paper investigates a multi-objective scheduling problem for divisible load in heterogeneous distributed systems. First, the cost of the system is taken into account and its quantitative formula is given. Second, a bi-objective optimization model, which minimizes the cost of system and the makespan of the load, is established. For the sake of solving the bi-objective optimization model efficiently, a novel effective bi-objective genetic algorithm combing the idea of MOEA/D is proposed. Finally, numerical simulation experiments are conducted, and the experimental results indicate that the effectiveness of the proposed model and algorithm.

In the past decades, divisible load scheduling has become an increasingly concerned field in the research of computer science. At the same time, the total system cost of data center has received worldwide attention, and the concept of green computing has been put forward. This paper investigates an cost-efficient divisible load scheduling using genetic algorithm. It focuses on finding an efficient scheduling strategy for distributed environment so that the total system cost is minimum. First, the system cost model is established when the start overheads are considered. Second, the optimization model has a time constraints for the sake of the make span can be tolerant for the user. Third, a novel and efficient generic algorithm is proposed. Finally, the experimental results demonstrate that the the proposed algorithm performs well.