A hybrid memory-based dragonfly algorithm with differential evolution for engineering application

The dragonfly algorithm (DA) is a swarm-based stochastic algorithm which possesses static and dynamic behavior of swarm and is gaining meaningful popularity due to its low computational cost and fast convergence in solving complex optimization problems. However, it lacks internal memory and is thereby not able to keep track of its best solutions in previous generations. Furthermore, the solution also lacks in diversity and thereby has a propensity of getting trapped in the local optimal solution. In this paper, an iterative-level hybridization of dragonfly algorithm (DA) with differential evolution (DE) is proposed and named as hybrid memory-based dragonfly algorithm with differential evolution (DADE). The reason behind selecting DE is for its computational ability, fast convergence and capability in exploring the solution space through the use of crossover and mutation techniques. Unlike DA, in DADE the best solution in a particular iteration is stored in memory and proceeded with DE which enhances population diversity with improved mutation and accordingly increases the probability of reaching global optima efficiently. The efficiency of the proposed algorithm is measured based on its response to standard set of 74 benchmark functions including 23 standard mathematical benchmark functions, 6 composite benchmark function of CEC2005, 15 benchmark functions of CEC2015 and 30 benchmark function of CEC2017. The DADE algorithm is applied to engineering design problems such as welded beam deign, pressure vessel design, and tension/compression spring design. The algorithm is also applied to the emerging problem of secondary user throughput maximization in an energy-harvesting cognitive radio network. A comparative performance analysis between DADE and other most popular state-of-the-art optimization algorithms is carried out and significance of the results is deliberated. The result demonstrates significant improvement and prominent advantages of DADE compared to conventional DE, PSO and DA in terms of various performance measuring parameters. The results of the DADE algorithm applied on some important engineering design problems are encouraging and validate its appropriateness in the context of solving interesting practical engineering challenges. Lastly, the statistical analysis of the algorithm is also performed and is compared with other powerful optimization algorithms to establish its superiority.

     

一种基于教与学的混合灰狼优化算法

针对灰狼优化算法(GWO)存在收敛精度不高、易陷入局部最优的不足,提出一种基于教与学的混合灰狼优化算法(HGWO).首先,采用佳点集理论进行种群初始化,提高初始种群的遍历性;其次,提出一种非线性控制参数策略,在迭代前期增加全局搜索能力,避免算法陷入局部最优,在迭代后期增加局部开发能力,提高收敛精度;最后,结合教与学算法(TLBO)和粒子群优化算法,修改原位置更新公式以优化算法搜索方式,从而提升算法的收敛性能.为验证HGWO算法的有效性,选取9种标准测试函数,将HGWO算法、GWO算法以及其他群体智能优化算法和其他改进GWO算法进行仿真实验.实验结果表明,所提出的HGWO算法性能优于GWO算法和其他群体智能优化算法,且在改进算法中具有一定优势.     

A parallel boundary search particle swarm optimization algorithm for constrained optimization problems

During the past decade, considerable research has been conducted on constrained optimization problems (COPs) which are frequently encountered in practical engineering applications. By introducing resource limitations as constraints, the optimal solutions in COPs are generally located on boundaries of feasible design space, which leads to search difficulties when applying conventional optimization algorithms, especially for complex constraint problems. Even though penalty function method has been frequently used for handling the constraints, the adjustment of control parameters is often complicated and involves a trial-and-error approach. To overcome these difficulties, a modified particle swarm optimization (PSO) algorithm named parallel boundary search particle swarm optimization (PBSPSO) algorithm is proposed in this paper. Modified constrained PSO algorithm is adopted to conduct global search in one branch while Subset Constrained Boundary Narrower (SCBN) function and sequential quadratic programming (SQP) are applied to perform local boundary search in another branch. A cooperative mechanism of the two branches has been built in which locations of the particles near boundaries of constraints are selected as initial positions of local boundary search and the solutions of local boundary search will lead the global search direction to boundaries of active constraints. The cooperation behavior of the two branches effectively reinforces the optimization capability of the PSO algorithm. The optimization performance of PBSPSO algorithm is illustrated through 13 CEC06 test functions and 5 common engineering problems. The results are compared with other state-of-the-art algorithms and it is shown that the proposed algorithm possesses a competitive global search capability and is effective for constrained optimization problems in engineering applications.     

A comparative study of the improvement of performance using a PSO modified by ACO applied to TSP

Swarm-inspired optimization has become very popular in recent years. Particle swarm optimization (PSO) and Ant colony optimization (ACO) algorithms have attracted the interest of researchers due to their simplicity, effectiveness and efficiency in solving complex optimization problems. Both ACO and PSO were successfully applied for solving the traveling salesman problem (TSP). Performance of the conventional PSO algorithm for small problems with moderate dimensions and search space is very satisfactory. As the search, space gets more complex, conventional approaches tend to offer poor solutions. This paper presents a novel approach by introducing a PSO, which is modified by the ACO algorithm to improve the performance. The new hybrid method (PSO–ACO) is validated using the TSP benchmarks and the empirical results considering the completion time and the best length, illustrate that the proposed method is efficient.     

Nonlinear continuous multi-response problems: a novel two-phase hybrid genetic based metaheuristic

Generally the most real world production systems are tackling several different responses and the problem is optimizing these responses concurrently. This study strives to present a new two-phase hybrid genetic based metaheuristic for optimizing nonlinear continuous multi-response problems. Premature convergence and getting stuck in local optima, which makes the algorithm time consuming, are common problems dealing with genetic algorithms (GAs). So we hybridize GA with a clustering approach and particle swarm optimization algorithm (PSO) to make a balanced relationship between time consuming and premature termination. The proposed algorithm also tries to find Ideal Points (IPs) for response functions. IPs are considered as improvement measures that determine when PSO should start. PSO based local search exploit Pareto archive solutions to enhance performance of the algorithm by expanding the search space. Since there is no standard benchmark in this field, we use two case studies from distinguished paper in multi-response optimization and compare the results with some of the mentioned algorithms in the literature. Results show the outperformance of the proposed algorithm than all of them.     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

求解优化问题的混合PSO-Solver算法

融合了粒子群算法(PSO) 和Solver 加载宏,形成混合PSO-Solver算法进行优化问题的求解。PSO作为全局搜索算法首先给出问题的全局可行解,Solver则是基于梯度信息的局部搜索工具,对粒子群算法得出的解再进行改进,二者互相结合,既加快了全局搜索的速度,又有效地避免了陷入局部最优。算法用VBA语言进行编程,简单且易于实现。通过对无约束优化问题和约束优化问题的求解,以及和标准PSO、其他一些混合算法的比较表明,PSO-Solver算法能够有效地提高求解过程的收敛速度和解的精确性。     

一种催化粒子群算法及其性能分析

针对粒子群算法（PSO）在解决高维、多模复杂问题时容易陷入局部最优的问题,提出了一种新颖的混合算法—催化粒子群算法（CPSO）。在CPSO优化过程中,种群中的粒子始终保持其个体历史最优值pbests。CPSO种群更新由改造PSO、横向交叉以及垂直交叉三个搜索算子交替进行,其中,每个算子产生的中庸解均通过贪婪思想产生占优解pbests,并作为下一个算子的父代种群。在CPSO中,纵横交叉算法（CSO）作为PSO的加速催化剂,一方面通过横向交叉改善PSO的全局收敛性能,另一方面通过纵向交叉维持种群的多样性。对6个典型benchmark函数的仿真结果表明,相比其它主流PSO变体,CPSO在全局收敛能力和收敛速率方面具有明显优势。     

引入人工蜂群搜索算子的粒子群算法

针对标准粒子群算法易出现早熟现象和收敛速度慢等问题,提出一种引入人工蜂群搜索算子的粒子群算法.首先利用人工蜂群搜索算子很强的探索能力,对粒子搜索到的历史最优位置进行搜索以帮助算法快速跳出局部最优点;然后,为了提高算法的全局收敛速度,提出一种基于混沌和反学习的初始化方法.通过12个标准测试函数的仿真实验并与其他算法相比较,所得结果表明所提出的算法具有较快的收敛速度和很强的跳出局部最优的能力.     

独立自适应调整参数的粒子群优化算法

针对传统粒子群优化算法在求解复杂优化问题时易陷入局部最优和依赖参数的取值等问题,提出了一种独立自适应参数调整的粒子群优化算法。算法重新定义了粒子进化能力、种群进化能力以及进化率,在此基础上给出了粒子群惯性权重及学习因子的独立调整策略,更好地平衡了算法局部搜索与全局搜索的能力。为保持种群多样性,提高粒子向全局最优位置的收敛速度,在算法迭代过程中,采用粒子重构策略使种群中进化能力较弱的粒子向进化能力较强的粒子进行学习,重新构造生成新粒子。最后通过CEC2013中的10个基准测试函数与4种改进粒子群算法在不同维度下进行测试对比,实验结果验证了该算法在求解复杂函数时具有高效性,通过收敛性分析说明了算法的有效性。     

若干新型群智能优化算法的对比研究

随着计算机技术的发展,算法技术也在不断交替更新。近年来,群体智能算法受到了广泛的关注和研究,并在诸如机器学习、过程控制、工程预测等领域取得了进展。群智能优化算法属于生物启发式方法,广泛应用在解决最优化问题上,传统的群智能算法为解决一些实际问题提供了新思路,但是也在一些实验中暴露出不足。近年来,许多学者相继提出了很多新型群智能优化算法,选取了最近几年国内外提出的比较典型的群智能算法,蝙蝠算法（Bat Algorithm,BA）、灰狼优化算法（Grey Wolf Optimization,GWO）、蜻蜓算法（Dragonfly Algorithm,DA）、鲸鱼优化算法（Whale Optimization Algorithm,WOA）、蝗虫优化算法（Grasshopper Optimization Algorithm,GOA）和麻雀搜索算法（Sparrow Search Algorithm,SSA）,并进一步通过22个标准的CEC测试函数从收敛速度、精度和稳定性等方面对比了这些算法的实验性能,并对比分析了其相关的改进方法。最后总结了群智能优化算法的特点,探讨了其今后的发展潜力。     

A hybrid Improved Quantum-behaved Particle Swarm Optimization–Simplex method (IQPSOS) to solve power system load flow problems

This study proposes a new approach, based on a hybrid algorithm combining of Improved Quantum-behaved Particle Swarm Optimization (IQPSO) and simplex algorithms. The Quantum-behaved Particle Swarm Optimization (QPSO) algorithm is the main optimizer of algorithm, which can give a good direction to the optimal global region and Nelder Mead Simplex method (NM) which is used as a local search to fine tune the obtained solution from QPSO. The proposed improved hybrid QPSO algorithm is tested on several benchmark functions and performed better than particle swarm optimization (PSO), QPSO and weighted QPSO (WQPSO). To assess the effectiveness and feasibility of the proposed method on real problems, it is used for solving the power system load flow problems and demonstrated by different standard and ill-conditioned test systems including IEEE 14, 30 and 57 buses test systems, and compared with the conventional Newton–Raphson (NR) method, PSO and some versions of QPSO algorithms. Furthermore, the proposed hybrid algorithm is proposed for solving load flow problems with considering the reactive limits at generation buses. Simulation results prove the robustness and better convergence of IQPSOS under normal and critical conditions, when conventional load flow methods fail.     

基于局部搜索的反向学习竞争粒子群优化算法

为提升粒子群优化算法在复杂优化问题,特别是高维优化问题上的优化性能,提出一种基于Solis&Wets局部搜索的反向学习竞争粒子群优化算法(solis and wets-opposition based learning competitive particle swarm optimizer with local se...     

Particle Swarm Optimization inspired by starling flock behavior

Swarm intelligence is a meta-heuristic algorithm which is widely used nowadays for efficient solution of optimization problems. Particle Swarm Optimization (PSO) is one of the most popular types of swarm intelligence algorithm. This paper proposes a new Particle Swarm Optimization algorithm called Starling PSO based on the collective response of starlings. Although PSO performs well in many problems, algorithms in this category lack mechanisms which add diversity to exploration in the search process. Our proposed algorithm introduces a new mechanism into PSO to add diversity, a mechanism which is inspired by the collective response behavior of starlings. This mechanism consists of three major steps: initialization, which prepares alternative populations for the next steps; identifying seven nearest neighbors; and orientation change which adjusts velocity and position of particles based on those neighbors and selects the best alternative. Because of this collective response mechanism, the Starling PSO explores a wider area of the search space and thus avoids suboptimal solutions. We tested the algorithm with commonly used numerical benchmarking functions as well as applying it to a real world application involving data clustering. In these evaluations, we compared Starling PSO with a variety of state of the art algorithms. The results show that Starling PSO improves the performance of the original PSO and yields the optimal solution in many numerical benchmarking experiments. It also gives the best results in almost all clustering experiments.     

Modified firefly algorithm for multidimensional optimization in structural design problems

An enhanced nature-inspired metaheuristic optimization algorithm, called the modified firefly algorithm (MFA) is proposed for multidimensional structural design optimization. The MFA incorporates metaheuristic components, namely logistic and Gauss/mouse chaotic maps, adaptive inertia weight, and Lévy flight with a conventional firefly algorithm (FA) to improve its optimization capability. The proposed MFA has several advantages over its traditional FA counterpart. Logistic chaotic maps provide a diverse initial population. Gauss/mouse maps allow the tuning of the FA attractiveness parameter. The adaptive inertia weight controls the local exploitation and the global exploration of the search process. Lévy flight is used in the exploitation of the MFA. The proposed MFA was evaluated by comparing its performance in solving a series of benchmark functions with those of the FA and other well-known optimization algorithms. The efficacy of the MFA was then proven by its solutions to three multidimensional structural design optimization problems; MFA yielded the best solutions among the observed algorithms. Experimental results revealed that the proposed MFA is more efficient and effective than the compared algorithms. Therefore, the MFA serves as an alternative algorithm for solving multidimensional structural design optimization problems.     

一种求解高维约束优化问题的γ-PSO算法

PSO算法是一种随机搜索的群体智能算法,在求解高维约束优化问题,尤其是在约束条件较多时,PSO算法易陷入局部极值且收敛速度慢。针对上述问题,对PSO算法进行了改进,提出了γ-PSO算法,把PSO算法的随机数由(0,1)扩展到(-1,1),这样加大了粒子飞行速度和飞行方向的多样性,从而使PSO算法具有摆脱局部极值的能力。对γ-PSO算法进行了求解高维约束优化问题的实验,实验结果表明γ-PSO算法能收敛到全局最优值,收敛性能明显优于其他改进的PSO算法和其他优化算法。     

A hybrid particle swarm optimization algorithm for high-dimensional problems

In recent years, particle swarm optimization (PSO) emerges as a new optimization scheme that has attracted substantial research interest due to its simplicity and efficiency. However, when applied to high-dimensional problems, PSO suffers from premature convergence problem which results in a low optimization precision or even failure. To remedy this fault, this paper proposes a novel memetic PSO (CGPSO) algorithm which combines the canonical PSO with a Chaotic and Gaussian local search procedure. In the initial evolution phase, CGPSO explores a wide search space that helps avoid premature convergence through Chaotic local search. Then in the following run phase, CGPSO refines the solutions through Gaussian optimization. To evaluate the effectiveness and efficiency of the CGPSO algorithm, thirteen high dimensional non-linear scalable benchmark functions were examined. Results show that, compared to the standard PSO, CGPSO is more effective, faster to converge, and less sensitive to the function dimensions. The CGPSO was also compared with two PSO variants, CPSO-H, DMS-L-PSO, and two memetic optimizers, DEachSPX and MA-S2. CGPSO is able to generate a better, or at least comparable, performance in terms of optimization accuracy. So it can be safely concluded that the proposed CGPSO is an efficient optimization scheme for solving high-dimensional problems.     

基于粒子滤波重采样与变异操作的改进粒子群算法

针对标准粒子群优化(PSO)算法在求解过程中存在求解精度低、搜索后期收敛速度慢等问题,提出一种基于粒子滤波重采样步骤与变异操作相结合的改进PSO算法——RSPSO。该算法充分利用重采样中具有较大权值的粒子被保留和复制、较小权值的粒子被舍弃的特点,并利用已有的变异操作方法克服粒子匮乏的缺点,大大增强了PSO算法中后期搜索阶段的局部搜索能力。在不同基准函数下对RSPSO算法和标准PSO算法以及文献中其他改进算法进行对比。实验结果表明, RSPSO算法的收敛速度较快,同时其搜索精度和解的稳定性均有所提高,且能够全局地解决多峰问题。     

基于群体爬山策略的混合粒子群优化算法

针对粒子群优化算法（PSO）在求解高维复杂优化问题时存在搜索精度不高和易陷入局部最优解的缺陷,借鉴混合蛙跳算法（SFLA）的群体爬山思想,提出一种基于群体爬山策略的混合粒子群优化算法（CMCPSO）,并证明了CMCPSO算法的全局收敛性。对四个典型高维连续优化函数的求解表明,该算法不仅保持了PSO算法的快速收敛能力,而且吸收了SFLA算法局部精细搜索和保持种群多样性的优点,具有良好的全局收敛性。     

Feedback controlled particle swarm optimization and its application in time-series prediction

Particle swarm optimization (PSO) algorithm is an algorithmic technique for optimization by solving a wide range of optimization problems. This paper presents a new approach of extending PSO to solve optimization problems by using the feedback control mechanism (FCPSO). The proposed FCPSO consists of two major steps. First, by evaluating the fitness value of each particle, a simple particle evolutionary fitness function is designed to control parameters involving acceleration coefficient, refreshing gap, learning probabilities and number of the potential exemplars automatically. By such a simple particle evolutionary fitness function, each particle has its own search parameters in a search environment. Secondly, a local learning method using a competitive penalized method is developed to refine the solution. The FCPSO has been comprehensively evaluated on 18 unimodal, multimodal and composite benchmark functions with or without rotation. Compared with various state-of-the-art algorithms, including traditional PSO algorithms and representative variants of PSO algorithms, the performance of FCPSO is promising. The effects of parameter adaptation, parameter sensitivity and local search method are studied. Lastly, the proposed FCPSO is applied to constructing a radial basis neural network, together with the K-means method for time-series prediction.