A Particle Swarm Algorithm Based on a Multi-Stage Search Strategy

Particle swarm optimization (PSO) has the disadvantages of easily getting trapped in local optima and a low search accuracy. Scores of approaches have been used to improve the diversity, search accuracy, and results of PSO, but the balance between exploration and exploitation remains sub-optimal. Many scholars have divided the population into multiple sub-populations with the aim of managing it in space. In this paper, a multi-stage search strategy that is dominated by mutual repulsion among particles and supplemented by attraction was proposed to control the traits of the population. From the angle of iteration time, the algorithm was able to adequately enhance the entropy of the population under the premise of satisfying the convergence, creating a more balanced search process. The study acquired satisfactory results from the CEC2017 test function by improving the standard PSO and improved PSO.     

An Efficient Improved Greedy Harris Hawks Optimizer and Its Application to Feature Selection

To overcome the lack of flexibility of Harris Hawks Optimization (HHO) in switching between exploration and exploitation, and the low efficiency of its exploitation phase, an efficient improved greedy Harris Hawks Optimizer (IGHHO) is proposed and applied to the feature selection (FS) problem. IGHHO uses a new transformation strategy that enables flexible switching between search and development, enabling it to jump out of local optima. We replace the original HHO exploitation process with improved differential perturbation and a greedy strategy to improve its global search capability. We tested it in experiments against seven algorithms using single-peaked, multi-peaked, hybrid, and composite CEC2017 benchmark functions, and IGHHO outperformed them on optimization problems with different feature functions. We propose new objective functions for the problem of data imbalance in FS and apply IGHHO to it. IGHHO outperformed comparison algorithms in terms of classification accuracy and feature subset length. The results show that IGHHO applies not only to global optimization of different feature functions but also to practical optimization problems.     

应用结构摄动策略的有分流换热网络优化

有分流节点非结构模型（NNM-SS）应用于换热网络优化时,因难以生成合适的分流结构而使优化陷入局部极值.根据NNM-SS的优化特点及网络结构中分流次数对费用的影响,提出结构摄动策略,并将其引入强制进化随机游走算法（RWCE-SS）.策略的主要思想为：在优化过程中,以一定的概率随机抽取一个无分流结构的换热器,并在该位置上生成一组新的分流结构以增加网络中的分流次数,通过对结构的摄动实现对算法搜索能力的提升.算例验证表明应用该策略改进的算法可获得更好的优化结果.     

A hybrid membrane evolutionary algorithm for solving constrained optimization problems

Solving constrained optimization problems (COPs) is a central research topic in the field of optimization. Given the complexity of COPs, it is difficult to solve them with traditional optimization techniques. In this paper, a hybrid membrane evolutionary algorithm (HMEA) is proposed. It combines a one-level membrane structure with a particle swarm optimization (PSO) local search algorithm. The simulation results show that the proposed algorithm is valid and outperforms the state-of-the-art algorithms.     

An Enhanced Differential Evolution Algorithm with Bernstein Operator and Refracted Oppositional-Mutual Learning Strategy

Numerical optimization has been a popular research topic within various engineering applications, where differential evolution (DE) is one of the most extensively applied methods. However, it is difficult to choose appropriate control parameters and to avoid falling into local optimum and poor convergence when handling complex numerical optimization problems. To handle these problems, an improved DE (BROMLDE) with the Bernstein operator and refracted oppositional-mutual learning (ROML) is proposed, which can reduce parameter selection, converge faster, and avoid trapping in local optimum. Firstly, a new ROML strategy integrates mutual learning (ML) and refractive oppositional learning (ROL), achieving stochastic switching between ROL and ML during the population initialization and generation jumping period to balance exploration and exploitation. Meanwhile, a dynamic adjustment factor is constructed to improve the ability of the algorithm to jump out of the local optimum. Secondly, a Bernstein operator, which has no parameters setting and intrinsic parameters tuning phase, is introduced to improve convergence performance. Finally, the performance of BROMLDE is evaluated by 10 bound-constrained benchmark functions from CEC 2019 and CEC 2020, respectively. Two engineering optimization problems are utilized simultaneously. The comparative experimental results show that BROMLDE has higher global optimization capability and convergence speed on most functions and engineering problems.     

A Hybrid Rao-NM Algorithm for Image Template Matching

This paper proposes a hybrid Rao-Nelder–Mead (Rao-NM) algorithm for image template matching is proposed. The developed algorithm incorporates the Rao-1 algorithm and NM algorithm serially. Thus, the powerful global search capability of the Rao-1 algorithm and local search capability of NM algorithm is fully exploited. It can quickly and accurately search for the high-quality optimal solution on the basis of ensuring global convergence. The computing time is highly reduced, while the matching accuracy is significantly improved. Four commonly applied optimization problems and three image datasets are employed to assess the performance of the proposed method. Meanwhile, three commonly used algorithms, including generic Rao-1 algorithm, particle swarm optimization (PSO), genetic algorithm (GA), are considered as benchmarking algorithms. The experiment results demonstrate that the proposed method is effective and efficient in solving image matching problems.     

一种采用种群多样性监控和实时更新策略的粒子群优化算法

针对粒子群算法优化后期容易出现早熟收敛问题,建立一种具有种群多样性监测和实时更新策略的改进方法.首先建立种群健康度指标用来评价粒子群进化状态;其次提出随机扰动策略和离心搜索策略用于丰富粒子群的种群多样性,增强算法的全局搜索能力,并提出梯度搜索策略用于精确、高效地搜寻当前邻域内的局部极值点,提高算法的计算效率.最后建立种群健康度反馈机制,使粒子可以实时感知种群的健康程度,并自适应地采用不同的粒子更新策略,保证粒子群处于健康进化水平.将新方法应用于优化实例,并与其它改进方法进行性能比较,结果验证了新方法的有效性.     

Application of the edge of chaos in combinatorial optimization

Many problems in science, engineering and real life are related to the combinatorial optimization. However, many combinatorial optimization problems belong to a class of the NP-hard problems, and their globally optimal solutions are usually difficult to solve. Therefore, great attention has been attracted to the algorithms of searching the globally optimal solution or near-optimal solution for the combinatorial optimization problems. As a typical combinatorial optimization problem, the traveling salesman problem(TSP) often serves as a touchstone for novel approaches. It has been found that natural systems, particularly brain nervous systems, work at the critical region between order and disorder, namely,on the edge of chaos. In this work, an algorithm for the combinatorial optimization problems is proposed based on the neural networks on the edge of chaos(ECNN). The algorithm is then applied to TSPs of 10 cities, 21 cities, 48 cities and 70 cities. The results show that ECNN algorithm has strong ability to drive the networks away from local minimums.Compared with the transiently chaotic neural network(TCNN), the stochastic chaotic neural network(SCNN) algorithms and other optimization algorithms, much higher rates of globally optimal solutions and near-optimal solutions are obtained with ECNN algorithm. To conclude, our algorithm provides an effective way for solving the combinatorial optimization problems.     

EGO方法的训练算法及应用

针对高效全局优化(Efficient Global Optimization,简称EGO)方法的训练问题,选择元启发式(Meta-heuristic)算法、随机取样算法以及低频序列算法,并选用三个无约束、两个带约束解析优化算例以及两个气动优化算例,对这三类训练算法进行详细地比较研究,发现在元启发式算法中差分进化算法最具应用潜力,而低频序列算法可以有效降低EGO方法的随机性,其中Faure序列平均性能最优.     

一种基于多种群对立平行进化策略的DE算法

针对微分进化算法应用于换热网络优化时易陷入局部区域和收敛精度不高的缺点,建立一种多种群对立的平行进化策略的微分进化算法.首先建立原始种群的对立种群;在此基础上,通过原始种群与对立种群的变异操作进行信息共享产生新的试验个体;最后运用多轮对立的思想保持多种群平行进化,使种群在保留当前求解信息的同时又能在求解域内进行更大范围搜索.对换热网络的经典算例计算表明,本文提出的多种群对立平行进化微分进化算法能够有效增强种群多样性,扩大算法的全局搜索能力,跳出局部极值陷阱,得到较好的优化结果.     

应用于换热网络优化的RWCE算法接受差解策略分析与改进

以一定的概率接受差解是强制进化随机游走算法（RWCE）换热网络结构进化、跳出局部最优的关键.首先分析接受差解策略对算法的优化作用,通过设置不同的接受差解概率,对比RWCE算法优化换热网络的结构进化过程,基于分析结论,提出以换热器数目为导向的接受差解概率控制策略,提升算法的计算效率和结构进化能力.通过算例验证,表明引入该策略的RWCE算法具有更强的全局搜索能力,优化质量得到有效提升.     

A New Two-Stage Algorithm for Solving Optimization Problems

Optimization seeks to find inputs for an objective function that result in a maximum or minimum. Optimization methods are divided into exact and approximate (algorithms). Several optimization algorithms imitate natural phenomena, laws of physics, and behavior of living organisms. Optimization based on algorithms is the challenge that underlies machine learning, from logistic regression to training neural networks for artificial intelligence. In this paper, a new algorithm called two-stage optimization (TSO) is proposed. The TSO algorithm updates population members in two steps at each iteration. For this purpose, a group of good population members is selected and then two members of this group are randomly used to update the position of each of them. This update is based on the first selected good member at the first stage, and on the second selected good member at the second stage. We describe the stages of the TSO algorithm and model them mathematically. Performance of the TSO algorithm is evaluated for twenty-three standard objective functions. In order to compare the optimization results of the TSO algorithm, eight other competing algorithms are considered, including genetic, gravitational search, grey wolf, marine predators, particle swarm, teaching-learning-based, tunicate swarm, and whale approaches. The numerical results show that the new algorithm is superior and more competitive in solving optimization problems when compared with other algorithms.     

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy).     

Optimal Performance and Application for Seagull Optimization Algorithm Using a Hybrid Strategy

This paper aims to present a novel hybrid algorithm named SPSOA to address problems of low search capability and easy to fall into local optimization of seagull optimization algorithm. Firstly, the Sobol sequence in the low-discrepancy sequences is used to initialize the seagull population to enhance the population’s diversity and ergodicity. Then, inspired by the sigmoid function, a new parameter is designed to strengthen the ability of the algorithm to coordinate early exploration and late development. Finally, the particle swarm optimization learning strategy is introduced into the seagull position updating method to improve the ability of the algorithm to jump out of local optimization. Through the simulation comparison with other algorithms on 12 benchmark test functions from different angles, the experimental results show that SPSOA is superior to other algorithms in stability, convergence accuracy, and speed. In engineering applications, SPSOA is applied to blind source separation of mixed images. The experimental results show that SPSOA can successfully realize the blind source separation of noisy mixed images and achieve higher separation performance than the compared algorithms.     

Mutated and converged damping factors in lens system optimization to find new local minima

In this paper, we proposed a strategy to find new local minima based on mutated damping factors and converged damping factor (conventional damping factor). In this proposed strategy, the converged damping factor is used to make the algorithm converge to a certain local minimum, and the mutated damping factors are used to make the trapped solution jump out of present convergence area. We study the behavior of the two kinds of factors in lens system optimization. The proposed strategy is successfully applied in lens system optimization. The result shows that the proposed strategy is reliable to make a further improvement especially when the solution is approaching target design.     

An Opposition-Based Learning CRO Algorithm for Solving the Shortest Common Supersequence Problem

As a non-deterministic polynomial hard (NP-hard) problem, the shortest common supersequence (SCS) problem is normally solved by heuristic or metaheuristic algorithms. One type of metaheuristic algorithms that has relatively good performance for solving SCS problems is the chemical reaction optimization (CRO) algorithm. Several CRO-based proposals exist; however, they face such problems as unstable molecular population quality, uneven distribution, and local optimum (premature) solutions. To overcome these problems, we propose a new approach for the search mechanism of CRO-based algorithms. It combines the opposition-based learning (OBL) mechanism with the previously studied improved chemical reaction optimization (IMCRO) algorithm. This upgraded version is dubbed OBLIMCRO. In its initialization phase, the opposite population is constructed from a random population based on OBL; then, the initial population is generated by selecting molecules with the lowest potential energy from the random and opposite populations. In the iterative phase, reaction operators create new molecules, where the final population update is performed. Experiments show that the average running time of OBLIMCRO is more than 50% less than the average running time of CRO_SCS and its baseline algorithm, IMCRO, for the desoxyribonucleic acid (DNA) and protein datasets.     

A Local Optima Network View of Real Function Fitness Landscapes

The local optima network model has proved useful in the past in connection with combinatorial optimization problems. Here we examine its extension to the real continuous function domain. Through a sampling process, the model builds a weighted directed graph which captures the function’s minima basin structure and its interconnection and which can be easily manipulated with the help of complex networks metrics. We show that the model provides a complementary view of function spaces that is easier to analyze and visualize, especially at higher dimensions. In particular, we show that function hardness as represented by algorithm performance is strongly related to several graph properties of the corresponding local optima network, opening the way for a classification of problem difficulty according to the corresponding graph structure and with possible extensions in the design of better metaheuristic approaches.     

粒子群优化算法在自适应偏振模色散补偿中的性能研究

反馈控制算法是偏振模色散的自适应补偿器的关键组成部分,将粒子群优化算法(PSO)引入到偏振模色散自适应补偿系统中。该算法的优点是具有快速收敛到全局最佳值的能力、避免搜索陷入局部极值的能力、抗噪声能力和多自由度控制能力。理论上分析了粒子群优化算法的两个分类———全局邻居结构粒子群优化(GPSO)和局部邻居结构粒子群优化(LPSO)在搜索全局最佳值方面的能力优劣,给出了局部邻居结构粒子群优化算法成功率达100%的三种邻居拓扑结构。实验表明:在补偿一阶偏振模色散时,全局邻居结构和局部邻居结构搜索全局最佳的成功率都能满足要求,全局邻居结构算法收敛速度快。而在补偿二阶偏振模色散时,全局邻居结构成功率降低,而局部邻居结构仍可以满足要求。     

换热网络中温度交叉结构的分析与处理

在以换热量作为待优化连续变量的换热网络优化问题中,流股匹配可能出现温度交叉,常以惩罚函数法处理存在温度交叉的不可行结构.然而,当采用强制进化随机游走算法时,由于其接受差解的变异操作,温度交叉结构可能以差解的形式被接受,对优化进程产生负面影响而降低优化效率.因此,首先分析换热网络中温度交叉结构的成因,接着分析该不可行结构对算法优化进程的消极作用,然后提出一种处理方法,当种群中个体随机游走到不可行域时,强制使其回到可行域内的原位重新优化,从而提升算法优化效率.     

连续面型高效率光栅分束器件的设计

阐述了用虚源法设计连续面型光栅分束器件的原理 ,提出了一种局部搜索遗传算法 ,并将其用于优化器件的性能。局部搜索遗传算法结合了局部搜索算法和遗传算法的优点 ,可以有效地克服遗传算法的“早熟收敛”现象 ,具有更强的全局收敛能力。用文中给出的方法可以得到具有较好均匀性的、高衍射效率的连续面型光栅分束器件。