An identity for multivariate Bernstein polynomials

We prove an identity for multivariate Bernstein polynomials on simplices, which may be considered a pointwise orthogonality relation. Its integrated version provides a new representation for the polynomial dual basis of Bernstein polynomials. An identity for the reproducing kernel is used to define quasi-interpolants of arbitrary order.     

An efficient algorithm for decomposing multivariate polynomials and its applications to cryptography

In this paper, we present an efficient and general algorithm for decomposing multivariate polynomials of the same arbitrary degree. This problem, also known as the Functional Decomposition Problem (FDP), is classical in computer algebra. It is the first general method addressing the decomposition of multivariate polynomials (any degree, any number of polynomials). As a byproduct, our approach can be also used to recover an ideal I from its kth power I^k. The complexity of the algorithm depends on the ratio between the number of variables (n) and the number of polynomials (u). For example, polynomials of degree four can be decomposed in , when this ratio is smaller than . This work was initially motivated by a cryptographic application, namely the cryptanalysis of 2R⁻ schemes. From a cryptographic point of view, the new algorithm is so efficient that the principle of two-round schemes, including 2R⁻ schemes, becomes useless. Besides, we believe that our algorithm is of independent interest.     

A new algorithm for sparse interpolation of multivariate polynomials

To reconstruct a black box multivariate sparse polynomial from its floating point evaluations, the existing algorithms need to know upper bounds for both the number of terms in the polynomial and the partial degree in each of the variables. Here we present a new technique, based on Rutishauser’s qd$qd$-algorithm, in which we overcome both drawbacks.     

An improved exact algorithm for the domatic number problem

The 3-domatic number problem asks whether a given graph can be partitioned into three dominating sets. We prove that this problem can be solved by a deterministic algorithm in time n^2.695 (up to polynomial factors) and in polynomial space. This result improves the previous bound of n^2.8805, which is due to Björklund and Husfeldt. To prove our result, we combine an algorithm by Fomin et al. with Yamamoto's algorithm for the satisfiability problem. In addition, we show that the 3-domatic number problem can be solved for graphs G with bounded maximum degree Δ(G) by a randomized polynomial-space algorithm, whose running time is better than the previous bound due to Riege and Rothe whenever Δ(G)?5. Our new randomized algorithm employs Schöning's approach to constraint satisfaction problems.     

An improved particle swarm optimization algorithm for flowshop scheduling problem

The flowshop scheduling problem has been widely studied and many techniques have been applied to it, but few algorithms based on particle swarm optimization (PSO) have been proposed to solve it. In this paper, an improved PSO algorithm (IPSO) based on the “alldifferent” constraint is proposed to solve the flow shop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnate, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that the proposed IPSO algorithm is more effective and better than the other compared algorithms. It can be used to solve large scale flow shop scheduling problem effectively.     

An improved firefly algorithm for solving dynamic multidimensional knapsack problems

There is a wide range of publications reported in the literature, considering optimization problems where the entire problem related data remains stationary throughout optimization. However, most of the real-life problems have indeed a dynamic nature arising from the uncertainty of future events. Optimization in dynamic environments is a relatively new and hot research area and has attracted notable attention of the researchers in the past decade. Firefly Algorithm (FA), Genetic Algorithm (GA) and Differential Evolution (DE) have been widely used for static optimization problems, but the applications of those algorithms in dynamic environments are relatively lacking. In the present study, an effective FA introducing diversity with partial random restarts and with an adaptive move procedure is developed and proposed for solving dynamic multidimensional knapsack problems. To the best of our knowledge this paper constitutes the first study on the performance of FA on a dynamic combinatorial problem. In order to evaluate the performance of the proposed algorithm the same problem is also modeled and solved by GA, DE and original FA. Based on the computational results and convergence capabilities we concluded that improved FA is a very powerful algorithm for solving the multidimensional knapsack problems for both static and dynamic environments.     

An improved differential evolution algorithm for the task assignment problem

An improved differential evolution algorithm (IDE) is proposed to solve task assignment problem. The IDE is an improved version of differential evolution algorithm (DE), and it modifies two important parameters of DE algorithm: scale factor and crossover rate. Specially, scale factor is adaptively adjusted According to the objective function values of all candidate solutions, and crossover rate is dynamically adjusted with the increasement of iterations. The adaptive scale factor and dynamical crossover rate are combined to increase the diversity of candidate solutions, and to enhance the exploration capacity of solution space of the proposed algorithm. In addition, a usual penalty function method is adopted to trade-off the objective and the constraints. Experimental results demonstrate that the optimal solutions obtained by the IDE algorithm are all better than those obtained by the other two DE algorithms on solving some task assignment problems.     

An improved LNS algorithm for real-time vehicle routing problem with time windows

This paper studies the dynamic vehicle routing problem with hard time windows (DVRPTW). The main study course of this problem was briefly reviewed. The solving strategy and algorithm of the problem are put forward. First of all, DVRPTW problem is decomposed into a series of static VRPTW. When and how to decompose the DVRP is the issue, that must be addressed. An event-trigger mechanism has been proposed and used to decompose the DVRPTW into a series of system delay-snapshots. The trigger event to be adopted is a new request arrival during the stable operation. And each snapshot is regarded as a static VRPTW. Whether each static VRPTW can quickly and efficiently be solved within a given time or a shorter time, i.e. the solving time is another issue for the DVRPTW. In the solving process, how to merge the latest requirement to the current solution is the third issue that must be solved. An improved large neighborhood search (LNS) algorithm is proposed to solve the static problem. Utilizing the remove-reinsert process of the LNS, the latest request nodes are regarded as a part of the removed nodes; these nodes can be inserted into the original or current solution in good time in the reinsertion process; meanwhile, its computing speed is high and effective for it does not need to resolve primal problem each time. Computational results of a large number of test problems, which cited from Solomon's static benchmarks and Lacker’s dynamic data set, show that our method is superior to other methods in most instances.     

An improved model for vehicle routing problem with time constraint based on genetic algorithm

A vehicle routing problem (VRP) with time constraint is one of the important problems in distribution and transportation. Thus the generic VRP and its practical extensions are discussed in great detail in the literatures. In the VRP, the service of a customer must start and finish within a given time interval. The objective of this problem is to minimize the cost of servicing the set of customers without being tardy or exceeding the capacity or travel time of the vehicles. In this research we concentrated on developing a GA–TSP model by improving the genetic algorithm (GA) operators and the initial population. For the computational purpose, we developed a GUI (graphic user interface)-type computer program according to the proposed method. The computational results show that the proposed method is very effective on a set of standard test problems and it can be potentially useful in solving the VRPs.     

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.     

一种图像置乱的改进算法

提出了一种改进的基于混沌的图像置乱算法.该算法在对图像运用抽样技术预处理的基础上,利用Logistic映射产生的伪随机序列,对图像进行灰度值的变换和全局的块置乱.实验仿真表明,该加密算法具有良好的加密效果,能有效地抵御统计攻击和差分攻击.     

An efficient algorithm for computing permanental polynomials of graphs

An efficient numerical method for computing permanental polynomials of graphs is proposed. It adapts multi-entry expansion of FFT, and is parallel in nature. It is applied to fullerene-type graphs, and works for C₅₆, while the largest fullerene computed before is C₄₀. Extensive numerical computations show that the algorithm is fast and stable.     

一种改进的蝙蝠算法

为了增强蝙蝠算法的全局寻优能力,提出一种新的全局"寻优策略",将蝙蝠个体历史最优引入到蝙蝠个体寻优策略中,并引入一种"指引"方向指导蝙蝠个体全局寻优。蝙蝠个体每次迭代后将执行"优胜劣汰"的策略,随机初始化一些蝙蝠个体取代那些适应度值较低的个体,增加种群多样性以防止陷入局部极值。选取UCI中的Iris,Wine,Sonar数据集用来聚类测试,实验结果表明:与原始蝙蝠算法、差分进化算法、粒子群算法相比,改进的蝙蝠算法能够得到更高的聚类准确率,鲁棒性更强。     

一种改进的TLD算法

针对跟踪算法目标遮挡后易出现跟踪漂移的问题,提出了一种跟踪学习检测（TLD）算法与Kalman滤波相结合的手势跟踪方法.在跟踪器跟踪成功后,加入识别窗的方法进行遮挡判定.产生遮挡后目标模型不再更新,学习器不再更新集合分类器.若是部分遮挡,则由TLD学习器处理;若是严重遮挡,则改由Kalman滤波算法预测目标的运动轨迹.该方法在保留TLD算法长期稳定跟踪、适应摄像机快速运动与复杂背景等优点的基础上,改善了目标遮挡后易出现跟踪漂移的问题.实验表明：提出的改进TLD算法比其他常见跟踪方法具有更加优异的性能.     

一种改进的ORB算法

针对目前SLAM算法对特征提取的可靠性和鲁棒性要求越来越高的问题,基于ORB(二进制定向简单描述符)特征提取算法,提出了一种基于模块化区域分割的方法,解决了特征提取过程中提取无效特征点过多和特征点分布不均匀的矛盾。该方法使得ORB算法的特征提取更加均匀和合理,也更有利于图像的特征匹配。实验研究表明,该方法提高了算法的有效性和可靠性。     

An improved SIFT algorithm for infringement retrieval

To achieve powerful infringement retrieval for reference images in digital publications, a new improved Scale Invariant Feature Transformation (SIFT) algorithm has been proposed in this paper. The retrieval process in the improved algorithm is innovatively divided into two stages to achieve coarse retrieval and fine retrieval respectively. In coarse retrieval, Geographical Statistics (GeoStat) is creatively used to describe the global spatial relationship of key-points in different orientations in an image and then generate a 144-dimensional feature vector to represent each image. In fine retrieval, only partial images, which are highly similar to the query image obtained from results of coarse retrieval, need to be considered. And the indexing and matching process in the improved algorithm is improved by adding a judgment process to improve the matching speed and reduce the mistaken matching rate. Experimental results show that the proposed algorithm has more advantages in retrieval speed and higher retrieval accuracy than the original SIFT algorithm. And the proposed algorithm is also more suitable for infringement retrieval of reference images in digital publications than the original one.