A new algorithm for numerical solution of ordinary differential equations

A numerical integration scheme which is particularly well suited to initial value problems having oscillatory or exponential solutions is proposed. The derivation of the algorithm is based on a representation of problems (that is problems having oscillatory or exponential solutions), the complex parameters have the real plane. The interpolating function has two complex parameters whose numerical estimates are obtained by using Newton-like scheme to solve three simultaneous nonlinear equations. For the above class of paoblems (that is problems having oscillatory or exponential solutions), the complex parameters have constant values throughout the interval of integration. Hence, the parameters are obtainable at the first integration step. As the approach is applicable to systems of equations, then for an initial value problem of order m, m sets of simultaneous equations have to be solved for the complex parameters.     

Modified Cuckoo Search Algorithm to Solve Economic Power Dispatch Optimization Problems

A modified cuckoo search (CS) algorithm is proposed to solve economic dispatch (ED) problems that have nonconvex, non-continuous or non-linear solution spaces considering valve-point effects, prohibited operating zones, transmission losses and ramp rate limits. Comparing with the traditional cuckoo search algorithm, we propose a self-adaptive step size and some neighbor-study strategies to enhance search performance. Moreover, an improved lambda iteration strategy is used to generate new solutions. To show the superiority of the proposed algorithm over several classic algorithms, four systems with different benchmarks are tested. The results show its efficiency to solve economic dispatch problems, especially for large-scale systems.      

多Agent自动协商策略和算法

针对传统协商过程周期长、代价高的问题,提出了三类形式化的曲线簇来描述Agent所采取的协商策略以及一种数学化和计算机程序化的多Agent自动协商算法。这三类策略分别为急躁型、节俭型和折中型。通过实验模拟发现采用所提出的协商策略和算法更符合人类思维的直观。该方法可应用于多种电子商务交易（如B2B和B2C）等活动中。     

自适应多普勒补偿与变异选择的蝙蝠算法

为克服蝙蝠算法在高维优化问题上求解精度低和早熟收敛的缺点,提出一种改进的蝙蝠算法。首先根据蝙蝠相对猎物距离的远近程度,对频率引入自适应多普勒补偿策略,并结合速度偏移机制修正飞行方向,产生靠近最优个体的新位置;其次对最优个体构造自适应变异选择策略,先利用柯西变异产生的较大步长摆脱局部极值的束缚,后利用高斯变异产生的较小步长精细搜寻最优区域;最后通过调整响度和脉冲发射率,平衡算法的全局探索和局部开发能力。从理论上分析了算法的收敛性和运算复杂性,对12个标准函数在不同维度下进行仿真实验,并与近年来其他蝙蝠算法进行比较,结果表明改进的算法在求解高维优化问题上具有较优的收敛速度和精度。     

An automatic time-stepping algorithm for dynamic problems

The paper discusses algorithms for automatic computation of time steps in discrete integration of dynamic problems. Objective criteria for performance and guidelines for making an algorithm practically applicable are suggested. A set of parameters for characterizing the dynamic response of a system is proposed, this includes a ‘current frequency’, a ‘current period’, and a ‘dynamic stiffness parameter’. An algorithm for automatic computation of the time step based on the current period is outlined. Aspects of adapting this algorithm to special types of applications are discussed, this involves use of a ‘tuning function’. Several examples of applications are given.     

Harris Hawk Optimization Algorithm Based on Cauchy Distribution Inverse Cumulative Function and Tangent Flight Operator

Harris Hawk Optimization (HHO) algorithm is a new population-based and nature-inspired optimization paradigm, which has strong global search ability, but its diversified local search strategies easily make it fall into local optimum. In order to enhance its search mechanism and speed of convergence, an new improved HHO algorithm based on the inverse cumulative function operator of Cauchy distribution and tangent flight operator was proposed. The proposed two operators are used as scale factors to control the step size. The walk path of Cauchy inverse cumulative integral function shows that its trajectory step length is relative to the average, which can further enhance the search stability of the algorithm. The Tangent flight has the function of balanced exploitation and exploration, and enhances the convergence ability of the algorithm. In order to verify the performance of the proposed algorithm, the 30 benchmark functions of the 2017 Institute of Electrical and Electronic Engineers (IEEE) Conference on Evolutionary Computation (CEC2017) and two practical engineering design problems are adopted to carry out the simulation experiments. On the other hand, the covariance matrix adaptation evolutionary strategies (CMA-ES), arithmetic optimization algorithm (AOA), butterfly optimization algorithm (BOA), bat algorithm (BA), whale optimization algorithm (WOA), sine cosine algorithm (SCA), and the proposed HHO algorithms were used for comparison experiments. Simulation results show that the proposed the Cauchy-distribution and Tangent-Flight Harris Hawk Optimization (CTHHO) Algorithm has strong optimization capability.

     

一种改进的动态多种群并行差分进化算法

针对单种群差分进化算法易出现早熟收敛的问题,提出了一种改进的动态多种群并行差分进化算法。该算法首先利用佳点集方法产生初始种群以增强算法的稳定性和全局搜索能力。基于个体的适应度将种群分为三个子种群,并分别执行采用不同实验向量产生策略和控制参数设置的差分进化算法,既保持了各个子种群算法的独立性和优越性,又不增加算法的复杂性。仿真实验结果表明该算法具有较好的寻优性能。     

Self-adaptive differential evolution algorithm with α-constrained-domination principle for constrained multi-objective optimization

Real-world problems are inherently constrained optimization problems often with multiple conflicting objectives. To solve such constrained multi-objective problems effectively, in this paper, we put forward a new approach which integrates self-adaptive differential evolution algorithm with α-constrained-domination principle, named SADE-αCD. In SADE-αCD, the trial vector generation strategies and the DE parameters are gradually self-adjusted adaptively based on the knowledge learnt from the previous searches in generating improved solutions. Furthermore, by incorporating domination principle into α-constrained method, α-constrained-domination principle is proposed to handle constraints in multi-objective problems. The advantageous performance of SADE-αCD is validated by comparisons with non-dominated sorting genetic algorithm-II, a representative of state-of-the-art in multi-objective evolutionary algorithms, and constrained multi-objective differential evolution, over fourteen test problems and four well-known constrained multi-objective engineering design problems. The performance indicators show that SADE-αCD is an effective approach to solving constrained multi-objective problems, which is basically enabled by the integration of self-adaptive strategies and α-constrained-domination principle.     

一种变步长双链量子遗传算法

为了克服基于实数编码和目标函数梯度信息的双链量子遗传算法存在收敛速度慢和鲁棒性较差的缺点,提出了一种自适应变步长双链量子遗传算法。建立了反映目标适应度函数变化率的数学模型;构造了反映当前搜索点处适应度相对变化率的变步长系数k,通过调整k以改善适应度函数相对变化率从而优化解的搜索过程;提出了在迭代过程中的量子旋转门转角[Δθ]更新策略。针对复杂连续函数的优化问题,设计了算法的具体实施步骤,并对典型复杂函数进行了仿真。结果表明,该算法有效地改善了双链量子遗传算法的鲁棒性,加快了算法收敛速度。     

Distributed cooperative learning algorithms using wavelet neural network

This paper investigates the distributed cooperative learning (DCL) problems over networks, where each node only has access to its own data generated by the unknown pattern (map or function) uniformly, and all nodes cooperatively learn the pattern by exchanging local information with their neighboring nodes. These problems cannot be solved by using traditional centralized algorithms. To solve these problems, two novel DCL algorithms using wavelet neural networks are proposed, including continuous-time DCL (CT-DCL) algorithm and discrete-time DCL (DT-DCL) algorithm. Combining the characteristics of neural networks with the properties of the wavelet approximation, the wavelet series are used to approximate the unknown pattern. The DCL algorithms are used to train the optimal weight coefficient matrix of wavelet series. Moreover, the convergence of the proposed algorithms is guaranteed by using the Lyapunov method. Compared with existing distributed optimization strategies such as distributed average consensus (DAC) and alternating direction method of multipliers (ADMM), our DT-DCL algorithm requires less information communications and training time than ADMM strategy. In addition, it achieves higher accuracy than DAC strategy when the network consists of large amounts of nodes. Moreover, the proposed CT-DCL algorithm using a proper step size is more accurate than the DT-DCL algorithm if the training time is not considered. Several illustrative examples are presented to show the efficiencies and advantages of the proposed algorithms.

     

一种改进的约束优化差分进化算法

提出一种改进的差分进化算法用于求解约束优化问题.该算法在处理约束时不引入惩罚因子,使约束处理问题简单化.利用佳点集方法初始化个体以维持种群的多样性.结合差分进化算法两种不同变异策略的特点,对可行个体与不可行个体分别采用DE/best/1变异策略和DE/rand/1策略,以提高算法的全局收敛性能和收敛速率.用几个标准的Benchmark问题进行了测试,实验结果表明该算法是一种求解约束优化问题的有效方法.     

多策略调和的布谷鸟搜索算法

布谷鸟搜索（CS）算法是一种新型的群智能算法,结构简单且寻优能力较强,但存在勘探与开采不平衡以及易陷入局部极值的问题。提出一种多策略调和的布谷鸟搜索（MSRCS）算法,基于概率规则选择由自适应步长和改进解更新方法组成的调和策略对布谷鸟个体进行更新,其中自适应步长引导布谷鸟在更好的方向上寻优,3种改进的解更新方法分别从自身邻域、当前最优个体和随机位置3个角度对勘探和开采进行调和,从而提升全局搜索和局部搜索在迭代过程中的适应性。在CEC2013测试集的28个基准函数上的实验结果表明,MSRCS算法至少有12个测试函数优于原始CS及其7种改进算法且排名第一,在求解单峰、多峰和组合函数问题时寻优能力更强,同时相比于3种经典群智能优化算法具有更快的收敛速度和更高的解精度。     

求解SAT问题的拟人退火算法

该文利用一个简单的变换，将可满足性（SAT）问题转换为一个求相应目标函数最小值的优化问题，提出了一种用于跳出局部陷阱的拟人策略，基于模拟退火算法和拟人策略，为SAT问题的高效近注解得出了拟人退火算法（PA），该方法不仅具有模拟退火算法的全局收敛性质，而且具有一定的并行性，继承性。数值实验表明，对于本文随机产生的测试问题例，采用拟人策略的模拟退火算法的结果优于局部搜索算法，模拟退火算法以及近来国际上流行的WALKSAT算法，因此拟人退火算法是可行的和有效的。     

Improvement of harmony search algorithm by using statistical analysis

In this article, we suggest a new method to improve the harmony search meta-heuristic algorithm. Several approaches are presented for improving the harmony search algorithm. These approaches consider different values for initial parameters in each optimization problem. Differences between the proposed algorithm and the harmony search algorithm are as follows. First, we add a new step to create a new harmony vector, which increases the accuracy and convergence rate and reduces the impact of the initial parameters in achieving an optimal solution. Second, we set introduce a parameter called bandwidth (bw), which is an important factor with great influence on the convergence rate toward optimal solutions. To prove the efficiency and robustness of the proposed algorithm, we argument about statistical analysis of proposed algorithm and examine it through a variety of optimization problems, including constrained and unconstrained functions, mathematical problems with high dimensions and engineering and reliability problems. In all of these problems, the convergence rate and accuracy of the answer are equal to or better than other methods. In addition, in our proposed method, the effect of initial parameters has been reduced with respect to the optimal solution.     

Evaluation of numerical integration methods in elastodynamics

One-step algorithms are compared for the direct time integration of the spatially discretized equations of linear elastodynamics. Explicit and implicit methods are evaluated for stability and accuracy in terms of the frequency spectrum of the continuum as well as discrete solution. The closed form of the discrete spectrum of a bar and beam are given to illustrate inherent errors of a spatial discretization. Additional errors of a direct time integration scheme are interpreted in terms of the discrete modes. The Newmark family of second-order difference approximations is found superior to either the original or extended Wilson methods, and to that of Houboult. Less than half as many time steps are required for comparable accuracy. If an upper bound on the highest frequency of a system is found, an optimum algorithm for a given time step can be found, rather than the usual selection of a time step for a given algorithm. The algorithmic damping admitted by the Newmark family can be controlled as a “linear artificial viscosity” to smooth shock discontinuities without the excessive damping of the Wilson and Houboult methods. The implications of these algorithms in wave propagation problems are illustrated.     

Integration and Test Sequencing for Complex Systems

The integration and test phase of complex manufacturing machines, like an ASML lithographic manufacturing system, is expensive and time consuming. The tests that can be performed at a certain point in time during the integration phase depend on the modules that are integrated and, therefore, on the preceding integration sequence. In this paper, we introduce a mathematical model to describe an overall integration and test sequencing problem, and we propose an algorithm to solve this problem. The method is a combination of integration sequencing and test sequencing. Furthermore, we introduce several strategies that determine when test phases should start. With a case study within the development of a software release that is used to control an ASML lithographic machine, we show that the described method and strategies can be used to solve real-life problems.      

基于最小概念集的多知识库整合

在语义Web环境下,知识库往往是单一、分散的,阻碍了语义Web的发展。为此,提出一种基于最小概念集的多知识库整合方法。定义知识库系统的最小概念集,给出生成最小概念集的方法,对基于风险最小化的本体映射模型中的映射策略进行改进,并设计基于最小概念集的多知识库整合算法,通过应用实例验证算法的复杂度。     

A new algorithm for numerical solution of dynamic elastic-plastic hardening and softening problems

The objective of this paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems, particularly for the implementation of the gradient dependent model used in solving strain softening problems. The new algorithm for the solution of dynamic elastic-plastic problems is derived based on the parametric variational principle. The gradient dependent model is employed in the numerical model to overcome the mesh-sensitivity difficulty in dynamic strain softening or strain localization analysis. The precise integration method, which has been used for the solution of linear problems, is adopted and improved for the solution of dynamic non-linear equations. The new algorithm is proposed by taking the advantages of the parametric quadratic programming method and the precise integration method. Results of numerical examples demonstrate the validity and the advantages of the proposed algorithm.     

基于进化策略方法求任意函数的数值积分

提出了两种基于进化策略求任意函数数值积分的新方法,其中方法一是基于混合基函数进化策略的数值积分算法;方法二是基于不等距点分割的进化策略数值积分算法.两种算法都采用适用于高维优化问题的单基因突变进化策略,使得该算法不但能计算通常意义下任意函数的定积分,而且能计算奇异函数积分和振荡函数积分.最后给出几个数值积分算例,并与传统数值积分方法作了比较,仿真结果分析表明,两种算法十分有效,能够快速有效地获得任意函数的数值积分值.     

APS 9: an improved adaptive population-based simplex method for real-world engineering optimization problems

The adaptive population-based simplex (APS) algorithm is a recently-proposed optimization method for solving continuous optimization problems. In this paper, a new variant of APS, referred to as APS 9, is proposed to solve engineering optimization problems. APS 9 still follows the main structure of APS where three strategies (i.e., reflection, contraction and local search) can be used to improve the population of solutions. However, the three strategies have been significantly modified and the rules for applying them have been revised. A stagnation detection mechanism and duplicates removal step have been added. The proposed method is compared with the winners of the IEEE CEC 2005 and CEC 2011 competitions on the 22 CEC 2011 problems. The results show the superiority of APS 9 compared to the other two methods. Moreover, APS 9 has been compared with two recent optimization methods on the same test bed. The limitations of the CEC 2011 competition are also discussed and new rules that are more engineering-friendly are proposed.