Quantum algorithm for minimum dominating set problem with circuit design

Using quantum algorithms to solve various problems has attracted widespread attention with the development of quantum computing.Researchers are particularly interested in using the acceleration properties of quantum algorithms to solve NP-complete problems.This paper focuses on the well-known NP-complete problem of finding the minimum dominating set in undirected graphs.To expedite the search process,a quantum algorithm employing Grover’s search is proposed.However,a challenge arises from the unknown number of solutions for the minimum dominating set,rendering direct usage of original Grover’s search impossible.Thus,a swap test method is introduced to ascertain the number of iterations required.The oracle,diffusion operators,and swap test are designed with achievable quantum gates.The query complexity is O(1.414^(n))and the space complexity is O(n).To validate the proposed approach,qiskit software package is employed to simulate the quantum circuit,yielding the anticipated results.

RESEARCH ON THE MINIMUM ZONE CYLINDRICITY EVALUATION BASED ON GENETIC ALGORITHMS

A genetic algorithm (GA)-based method is proposed to solve the nonlinearoptimization problem of minimum zone cylindricity evaluation. First, the background of the problemis introduced. Then the mathematical model and the fitness function are derived from themathematical definition of dimensioning and tolerancing principles. Thirdly with the least squaressolution as the initial values, the whole implementation process of the algorithm is realized inwhich some key techniques, for example, variables representing, population initializing and suchbasic operations as selection, crossover and mutation, are discussed in detail. Finally, examplesare quoted to verify the proposed algorithm. The computation results indicate that the GA-basedoptimization method performs well on cylindricity evaluation. The outstanding advantages concludehigh accuracy, high efficiency and capabilities of solving complicated nonlinear and large spaceproblems.

Enhanced minimum attribute reduction based on quantum-inspired shuffled frog leaping algorithm

Attribute reduction in the rough set theory is an important feature selection method, but finding a minimum attribute reduction has been proven to be a non-deterministic polynomial （NP）-hard problem. Therefore, it is necessary to investigate some fast and effective approximate algorithms. A novel and enhanced quantum-inspired shuffled frog leaping based minimum attribute reduction algorithm （QSFLAR） is proposed. Evolutionary frogs are represented by multi-state quantum bits, and both quantum rotation gate and quantum mutation operators are used to exploit the mechanisms of frog population diversity and convergence to the global optimum. The decomposed attribute subsets are co-evolved by the elitist frogs with a quantum-inspired shuffled frog leaping algorithm. The experimental results validate the better feasibility and effectiveness of QSFLAR, comparing with some representa- tive algorithms. Therefore, QSFLAR can be considered as a more competitive algorithm on the efficiency and accuracy for minimum attribute reduction.

AN ANT COLONY ALGORITHM FOR MINIMUM UNSATISFIABLE CORE EXTRACTION

Explaining the causes of infeasibility of Boolean formulas has many practical applications in electronic design automation and formal verification of hardware.Furthermore,a minimum explanation of infeasibility that excludes all irrelevant information is generally of interest.A smallest-cardinality unsatisfiable subset called a minimum unsatisfiable core can provide a succinct explanation of infea-sibility and is valuable for applications.However,little attention has been concentrated on extraction of minimum unsatisfiable core.In this paper,the relationship between maximal satisfiability and mini-mum unsatisfiability is presented and proved,then an efficient ant colony algorithm is proposed to derive an exact or nearly exact minimum unsatisfiable core based on the relationship.Finally,ex-perimental results on practical benchmarks compared with the best known approach are reported,and the results show that the ant colony algorithm strongly outperforms the best previous algorithm.

High-resolution Remote Sensing Image Segmentation Using Minimum Spanning Tree Tessellation and RHMRF-FCM Algorithm

It is proposed a high resolution remote sensing image segmentation method which combines static minimum spanning tree(MST)tessellation considering shape information and the RHMRF-FCM algorithm.It solves the problems in the traditional pixel-based HMRF-FCM algorithm in which poor noise resistance and low precision segmentation in a complex boundary exist.By using the MST model and shape information,the object boundary and geometrical noise can be expressed and reduced respectively.Firstly,the static MST tessellation is employed for dividing the image domain into some sub-regions corresponding to the components of homogeneous regions needed to be segmented.Secondly,based on the tessellation results,the RHMRF model is built,and regulation terms considering the KL information and the information entropy are introduced into the FCM objective function.Finally,the partial differential method and Lagrange function are employed to calculate the parameters of the fuzzy objective function for obtaining the global optimal segmentation results.To verify the robustness and effectiveness of the proposed algorithm,the experiments are carried out with WorldView-3(WV-3)high resolution image.The results from proposed method with different parameters and comparing methods(multi-resolution method and watershed segmentation method in eCognition software)are analyzed qualitatively and quantitatively.

A Novel Power Optimization Method by Minimum Comparator Number Algorithm for Pipeline ADCs

The effects of stage numbers on power dissipation of pipeline analog-to-digital converter （ADC） are studied and a novel design method aiming for power optimization is presented. In this method, a minimum comparator number algorithm （MCNA） is first introduced, and then the optimum distribution of resolutions through pipeline ADC stages is deduced by MCNA. Based on the optimum stage-resolution distribution, an optimization method is established, which examines the precise function between ADC power and stage resolutions with a parameter of power ratio （Rp）. For 10-bit pipeline ADC with scaling down technology, the simulation results by using MATLAB CAD tools show that an eight-stage topology with 1-bit RSD correction achieves the power optimization indicated by the power reduction ratio.

FAULT DIAGNOSIS FOR ANALOG CIRCUITS WITH TOLERANCE—MINIMUM TOLERANCE ESTIMATION ALGORITHM

Based on the influence of circuit element tolerances to the k-fault diagnosis, a method of fault diagnosis is presented which is called minimum tolerance estimation algorithm and has clear physical meaning. Using this’method, an effective estimation of the equivalent fault sources can be obtained with less computing time. It is especially worthwhile to point out that an adaptive sub-optimum algorithm, which comes from the above method, requires even less computing-labor and is particularly suitable to more complicated circuits as well as real-time fault location.

THE DESIGN AND ANALYSIS OF ALGORITHM OF MINIMUM COST SPANNING TREE

This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves the correctness and the complexity of the algorithm. This algorithm uses the FDG (formula to divide elements into groups) to sort (the FDG sorts a sequence of n elements in expected tir O(n)) and uses the method of path compression to find and to unite. Therefore. n produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)).

Minimum dose path planning for facility inspection based on the discrete Rao-combined ABC algorithm in radioactive environments with obstacles

Workers who conduct regular facility inspections in radioactive environments will inevitably be affected by radiation.Therefore,it is important to optimize the inspection path to ensure that workers are exposed to the least amount of radiation.This study proposes a discrete Rao-combined artificial bee colony(ABC)algorithm for planning inspection paths with minimum exposure doses in radioactive environments with obstacles.In this algorithm,retaining the framework of the traditional ABC algorithm,we applied the directional solution update rules of Rao algorithms at the employed bee stage and onlooker bee stage to increase the exploitation ability of the algorithm and implement discretion using the swap operator and swap sequence.To increase the randomness of solution generation,the chaos algorithm was used at the initialization stage.The K-opt operation technique was introduced at the scout bee stage to increase the exploration ability of the algorithm.For path planning in an environment with complex structural obstacles,an obstacle detour technique using a recursive algorithm was applied.To evaluate the performance of the proposed algorithm,we performed experimental simulations in three hypothetical environments and compared the results with those of improved particle swarm optimization,chaos particle swarm optimization,improved ant colony optimization,and discrete Rao’s algorithms.The experimental results show the high performance of the proposed discrete Rao-combined ABC algorithm and its obstacle detour capability.

The Design of the Minimum Spanning Tree Algorithms

Based on the graphic theory and improved genetic algorithm,an improved genetic algorithm to search the minimum spanning trees is given . The algorithm uses binary code to represent the problem of minimum spanning trees. It designs the corresponding fitness function,operator and few controlling strategies to improve its speed and evolutionary efficiency.Only one solution can be gotten with running traditional al-gorithem atone time.The new algorithm can get a set of the solutions with higher probability in a shorter time.The experiment shows that it has a better performance than traditional methods.

A Novel Binary Firefly Algorithm for the Minimum Labeling Spanning Tree Problem

Given a connected undirected graph G whose edges are labeled,the minimumlabeling spanning tree(MLST)problemis to find a spanning tree of G with the smallest number of different labels.TheMLST is anNP-hard combinatorial optimization problem,which is widely applied in communication networks,multimodal transportation networks,and data compression.Some approximation algorithms and heuristics algorithms have been proposed for the problem.Firefly algorithm is a new meta-heuristic algorithm.Because of its simplicity and easy implementation,it has been successfully applied in various fields.However,the basic firefly algorithm is not suitable for discrete problems.To this end,a novel discrete firefly algorithm for the MLST problem is proposed in this paper.A binary operation method to update firefly positions and a local feasible handling method are introduced,which correct unfeasible solutions,eliminate redundant labels,and make the algorithm more suitable for discrete problems.Computational results show that the algorithm has good performance.The algorithm can be extended to solve other discrete optimization problems.

PCR ALGORITHM FOR PARALLEL COMPUTING MINIMUM-NORM LEAST-SQUARES SOLUTION OF INCONSISTENT LINEAR EQUATIONS

This paper presents a new highly parallel algorithm for computing the minimum-norm least-squares solution of inconsistent linear equations Ax = b(A∈Rm×n,b∈R (A)). By this algorithm the solution x = A + b is obtained in T = n(log2m + log2(n - r + 1) + 5) + log2m + 1 steps with P=mn processors when m × 2(n - 1) and with P = 2n(n - 1) processors otherwise.

Gaussian mixture model clustering with completed likelihood minimum message length criterion

An improved Gaussian mixture model （GMM）- based clustering method is proposed for the difficult case where the true distribution of data is against the assumed GMM. First, an improved model selection criterion, the completed likelihood minimum message length criterion, is derived. It can measure both the goodness-of-fit of the candidate GMM to the data and the goodness-of-partition of the data. Secondly, by utilizing the proposed criterion as the clustering objective function, an improved expectation- maximization （EM） algorithm is developed, which can avoid poor local optimal solutions compared to the standard EM algorithm for estimating the model parameters. The experimental results demonstrate that the proposed method can rectify the over-fitting tendency of representative GMM-based clustering approaches and can robustly provide more accurate clustering results.

最小生成树的prim算法及minimum函数

本文介绍了最小生成树的prim算法,minimum函数的实现过程及该函数对由prim算法所得到的最小生成树的影响。

Two Adaptive Control Algorithms in Semi-Active Suspension System

To reduce the vibration in the suspension, semi active suspension system was employed. And its CARMA model was built. Two adaptive control schemes, the minimum variance self tuning control algorithm and the pole configuration self tuning control algorithm, were proposed. The former can make the variance of the output minimum while the latter can make dynamic behavior satisfying. The stability of the two schemes was analyzed. Simulations of them show that the acceleration in the vertical direction has been reduced greatly. The purpose of reducing vibration is realized. The two schemes can reduce the vibration in the suspension and have some practicability.

基于改进蚁群算法的智能车路径规划研究

该文针对智能车路径规划问题,提出一种改进蚁群算法的路径规划方法。传统蚁群算法虽有良好适应性,但也存在效率低下和易陷入局部最优等问题。为此,该文引入势场启发式函数和信息素奖惩策略,优化启发函数和信息素更新机制,提高算法全局搜索能力和收敛速度。通过最大最小蚂蚁系统保持信息素多样性,有效避免局部最优,并采用路径二次优化策略简化路径,减少长度。实验结果表明,改进算法在复杂环境下有更快的收敛速度和更高的路径质量,为智能车路径规划提供了一种有效的优化策略。

Finding the Minimum Ratio Traveling Salesman Tour by Artificial Ants

Ants of artificial colony are able to generate good solutions to the famous traveling salesman problem (TSP). We propose an artificial ants algorithm for solving the minimum ratio TSP, which is more general than the standard TSP in combinatorial optimization area. In the minimum ratio TSP, another criterion concerning each edge is added, that is, the traveling salesman can have a benefit if he travels from one city to another. The objective is to minimize the ratio between total costs or distances and total benefits. The idea of this type of optimization is in some sense quite similar to that of traditional cost-benefit analysis in management science. Computational results substantiate the solution quality and efficiency of the algorithm.

Research on Algorithm for Generating Min-Area Rectangle Encasing Box for Closed Contour

In many engineering applications, it is necessary to calculate the min-area encasing box of a circumscription. In this paper, an algorithm for generating the min-area rectangle encasing box, based on revolving angle, is investigated and hence put forward. The algorithm computes the areas of the outer rectangular bounds of a closed contour in different revolving angles θ by dispersing approach where 0< θ < π/2 because of the axial symmetry. It is very simple, straight forward and highly efficient. The complexity of its computing time reaches O(n·k ). Practical applications suggest its usefulness and efficiency.

Solving Job-Shop Scheduling Problem Based on Improved Adaptive Particle Swarm Optimization Algorithm

An improved adaptive particle swarm optimization(IAPSO)algorithm is presented for solving the minimum makespan problem of job shop scheduling problem(JSP).Inspired by hormone modulation mechanism,an adaptive hormonal factor(HF),composed of an adaptive local hormonal factor(H l)and an adaptive global hormonal factor(H g),is devised to strengthen the information connection between particles.Using HF,each particle of the swarm can adjust its position self-adaptively to avoid premature phenomena and reach better solution.The computational results validate the effectiveness and stability of the proposed IAPSO,which can not only find optimal or close-to-optimal solutions but also obtain both better and more stability results than the existing particle swarm optimization(PSO)algorithms.

Improved genetic algorithm freely searching for dangerous slip surface of slope

Based on the slice method of the non-circular slip surface for the calculation of integral stability of slope, an improved genetic algorithm was proposed, which can freely search for the most dangerous slip surface of slope and the corresponding minimum safety factor without supposing the geometric shape of the most dangerous slip surface. This improved genetic algorithm can simulate the genetic evolution process of organisms and avoid the local minimum value compared with the classical methods. The results of engineering cases show that it is a global optimal algorithm and has many advantages, such as higher efficiency and shorter time than the simple genetic algorithm.