A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling

In this paper, the no-wait flow shop scheduling problem under makespan and flowtime criteria is addressed. The no-wait flowshop is a variant of the well-known flowshop scheduling problem where all processes follow the previous one without any interruption for operations of a job. Owing to the problem is known to be NP-hard for more than two machines, a hybrid meta-heuristic algorithm based on ant colony optimization (ACO) and simulated annealing (SA) algorithm is improved. First, at each step, due to the characteristic of ACO algorithm that include solution construction and pheromone trail updating, some different areas of search space are checked and best solution is selected. Then, to enhance the quality and diversity of the solution and finding best neighbor of this solution, a novel SA is presented. Moreover, a new principle is applied for global pheromone update based on the probability function like SA algorithm. The proposed approach solution is compared with several the state-of-the-art algorithms in the literature. The reported results show that the proposed algorithms are effective and the new approach for local search in ACO algorithm is efficient for solving the no-wait flow shop problem. Then, we employed another hybrid ACO algorithm based on hybridization of ACO with variable neighborhood search (VNS) and compare the results given by two proposed algorithms. These results show that our new hybrid provides better results than ACO-VNS algorithm.

We consider general quantum random walks in a d-dimensional half-space. We first obtain a path integral formula for general quantum random walks in a d-dimensional space. Our path integral formula is valid for general quantum random walks on Cayley graphs as well. Then the path integral formula is applied to obtain the scaling limit of the exit distribution, the expectation of exit time and the asymptotic behaviour of the exit probabilities, for general quantum random walks in a half-space under some conditions on amplitude functions. The conditions are shown to be satisfied by both the Hadamard and Grover quantum random walks in two-dimensional half-spaces. For the two-dimensional case, we show that the critical exponent for the scaling limit of the hitting distribution is 1 as the lattice spacing tends to zero, i.e. the natural magnitude of the hitting position is of order O(1) if the lattice spacing is set to be 1/n. We also show that the rate of convergence of the total hitting probability has lower bound n−2 and upper bound n−2+ϵ for any ϵ > 0. For a quantum random walk with a fixed starting point, we show that the probability of hitting times at the hyperplane decays faster than that of the classical random walk. In both one and two dimensions, given the event of a hit, the conditional expectation of hitting times is finite, in contrast to being infinite for the classical case. In the one-dimensional case, we also obtain an exact order of the probability distribution of the hitting time at 0.

In order to improve the utilization of cloud computing resources, this paper studies cloud computing resource scheduling based on improved Ant Colony Optimization Algorithm (ACO) and Simulated annealing algorithm (SA). We apply ACO and SA to schedule the large-scale cloud computing resource data. This paper uses SA to prevent ACO falling into the local optimal solution, and accelerate the convergence speed of ACO. The experimental results show that the proposed method is more effective compared with the already existed approaches. Our proposed method can improve the resource utilization.

In order to solve the optimization of new energy bus line network, a new energy bus line network based on ant colony algorithm and low-carbon concept is proposed. Firstly, the model of public transport network is established combined with OD matrix, and the improved ant colony algorithm is used to iteratively optimize the initial suboptimal route set, optimize the objective function, and finally obtain the optimal public transport route set. Secondly, the improved ant colony algorithm based on simulated annealing solves the design of public transport network, and the optimization scheme greatly reduces the number of passenger transfers and the total travel time of passengers. Finally, simulated annealing algorithm, basic ant colony algorithm, and simulated annealing improved ant colony algorithm are used to optimize the objective function. It is proved that the improved ant colony algorithm of simulated annealing can find the optimal solution of the three algorithms when solving the problem of public transport network design, which is better than the solution of basic ant colony and simulated annealing algorithm. The solution efficiency is 10.6 times that of simulated annealing algorithm and 3.5 times that of basic ant colony algorithm.

Quantum walk mixing is faster than classical on periodic lattices

The crowd-creation space is a manifestation of the development of innovation theory to a certain stage. With the creation of the crowd-creation space, the problem of optimizing the resource allocation of the crowd-creation space has become a research hotspot. The emergence of cloud computing provides a new idea for solving the problem of resource allocation. Common cloud computing resource allocation algorithms include genetic algorithms, simulated annealing algorithms, and ant colony algorithms. These algorithms have their obvious shortcomings, which are not conducive to solving the problem of optimal resource allocation for crowd-creation space computing. Based on this, this paper proposes an In the cloud computing environment, the algorithm for optimizing resource allocation for crowd-creation space computing adopts a combination of genetic algorithm and ant colony algorithm and optimizes it by citing some mechanisms of simulated annealing algorithm. The algorithm in this paper is an improved genetic ant colony algorithm (HGAACO). In this paper, the feasibility of the algorithm is verified through experiments. The experimental results show that with 20 tasks, the ant colony algorithm task allocation time is 93ms, the genetic ant colony algorithm time is 90ms, and the improved algorithm task allocation time proposed in this paper is 74ms, obviously superior. The algorithm proposed in this paper has a certain reference value for solving the creative space computing optimization resource allocation.

Quantum biology seeks to explain biological phenomena via quantum mechanisms, such as enzyme reaction rates via tunnelling and photosynthesis energy efficiency via coherent superposition of states. However, less effort has been devoted to study the role of quantum mechanisms in biological evolution. In this paper, we used transcription factor networks with two and four different phenotypes, and used classical random walks (CRW) and quantum walks (QW) to compare network search behaviour and efficiency at finding novel phenotypes between CRW and QW. In the network with two phenotypes, at temporal scales comparable to decoherence time TD, QW are as efficient as CRW at finding new phenotypes. In the case of the network with four phenotypes, the QW had a higher probability of mutating to a novel phenotype than the CRW, regardless of the number of mutational steps (i.e. 1, 2 or 3) away from the new phenotype. Before quantum decoherence, the QW probabilities become higher turning the QW effectively more efficient than CRW at finding novel phenotypes under different starting conditions. Thus, our results warrant further exploration of the QW under more realistic network scenarios (i.e. larger genotype networks) in both closed and open systems (e.g. by considering Lindblad terms).

We present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.

We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. The number of steps of the quantum walk is quadratically smaller than the classical hitting time of any reversible random walk P on the graph.Our approach is new, simpler and more general than previous ones. We introduce a notion of interpolation between the walk P and the absorbing walk P′, whose marked states are absorbing. Then our quantum walk is simply the quantum analogue of the interpolation. Contrary to previous approaches, our results remain valid when the random walk P is not state-transitive, and in the presence of multiple marked vertices.As a consequence we make a progress on an open problem related to the spatial search on the 2D-grid.

In practical application scenarios such as logistics distribution and UAV cruise, the spherical multi-point path optimization problem has significant research value and practical significance. This research focuses on solving the spherical multi-point path optimization problem. The study first establishes a spherical distance calculation model, deriving the distance formula between any two points using spherical geometric principles. Taking eight specific points as research objects, the problem is transformed into a graph theory problem, and a single-objective linear programming model is constructed. The study employs Simulated Annealing Algorithm and Ant Colony Algorithm for comparative analysis. Through parameter optimization, the Simulated Annealing Algorithm achieved a shortest path length of 7.0381 kilometers. In comparison, the Ant Colony Algorithm obtained an optimal path (44-61-158-83-147-100-31-115) with a length of 4.0635 kilometers and a total time of 390.2 minutes, showing a 2.2% improvement in efficiency compared to the Simulated Annealing Algorithm. The results demonstrate that the Ant Colony Algorithm exhibits better performance and stability in this spherical multi-point path optimization problem.

Hybrid heuristic algorithm for cost-efficient QoS aware task scheduling in fog–cloud environment

This paper presents a methodology to solve the manufacturing cell creation and the production scheduling problems for designing virtual cellular manufacturing systems (VCMSs). The objective is to minimize the total materials and components travelling distance incurred. The methodology consists of (i) a mathematical model that describes the characteristics of a VCMS and includes constraints such as delivery due dates of products, maximum capacities of resources, critical tools limitation, and (ii) an ant colony optimization (ACO) algorithm for manufacturing cell formation and production scheduling. Since the proposed ACO algorithm does not indicate a feasible schedule explicitly, two simple heuristics are developed to assign workstations to the operations of the jobs, and to construct the final schedule. To demonstrate the effectiveness of the proposed methodology, both the ACO algorithm and the genetic algorithm are applied to design manufacturing cells for a company in China producing internal combustion engine components. Comparison of the results obtained with the results supplied by the company on the existing manufacturing system show that both the ACO algorithm and the genetic algorithm together with the virtual cellular manufacturing concept perform better than the current manufacturing practice in terms of average workstation utilization, product completion time and system throughput. Also, the results of a set of randomly generated numerical experiments show that the proposed ACO algorithm generates excellent final solutions in a much shorter computation time when compared with the genetic algorithm. Therefore, the mathematical model and the ACO algorithm proposed in this paper form a simple, but effective and efficient methodology to solve the manufacturing cell creation and production scheduling problems for designing VCMSs.

Cloud computing provides computing resources like software and hardware as a service by the network for several users. Task scheduling is one of the main problems to attain cost-effective execution. The main purpose of task scheduling is to allocate tasks to resources so that it can optimize one or more criteria. Since the problem of task scheduling is one of the Nondeterministic Polynomial-time (NP)-hard problems, meta-heuristic algorithms have been widely employed for solving task scheduling problems. One of the new bio-inspired meta-algorithms is Seagull Optimization Algorithm (SOA). In this paper, we proposed an energy-aware and cost-efficient SOA-based Task Scheduling (SOATS) algorithm. The aims of proposed algorithm to make a trade-off between five objectives (i.e., energy consumption, makespan, cost, waiting time, and load balancing) using a fewer number of iterations. The experiment results by comparing with several meta-heuristic algorithms (i.e., Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), and Whale Optimization Algorithm (WOA)) prove that the proposed technique performs better in solving task scheduling problem. Moreover, we compared the proposed algorithm with well-known scheduling methods: Cost-based Job Scheduling (CJS), Moth Search Algorithm based Differential Evolution (MSDE), and Fuzzy-GA (FUGE). In the heavily loaded environment, the SOATS algorithm improved energy consumption and cost saving by 10 and 25%, respectively.

In the optical quantum random walk system, phase fluctuation and beam splitter fluctuation are two unavoidable decoherence factors. These two factors degrade the performance of quantum random walk by destroying coherence, and even degrade it into a classical one. We propose a scheme for the simulation of quantum random walk using phase shifters, tunable beam splitters, and photodetectors. This proposed scheme enables us to analyze the effect of phase fluctuation and beam splitter fluctuation on two-photon quantum random walk. Furthermore, it is helpful to guide the control of phase fluctuation and beam splitter fluctuation in the experiment.

Traditional time series forecasting models are difficult to capture the nonlinear patterns. Support vector regression (SVR) is a powerful tool for modeling the inputs and output(s) of complex and nonlinear systems. However, parameters determination for a SVR model is competent to the forecasting accuracy. Several evolutionary algorithms, such as genetic algorithms and simulated annealing algorithms have been used to the parameters selection, however, these algorithms often suffer the problem of being trapped in local optimum. In this paper, a novel building cooling load forecasting approach combining support vector regression (SVR) and Ant colony algorithm (ACO) is proposed. ant colony (ACO) optimization was developed to optimize three parameters of SVR, including penalty parameter C, insensitive loss function ε and kernel function σ. SVR constructs hyperplane in high dimension space and fits the data in non-linear form. Normalized Mean square error (NMSE) of fitting result is used as target of ant colony optimization. ACO finds the best parameters which correspond to the NMSE. The results showed that the proposed approach, by comparing with back-propagation neural network model, was an efficient way to model building cooling load with good predictive accuracy. ACO and SVR provide a useful tool for maximizing the combustion efficiency of cooling load. Also, the method can be easily extended to other applications.