多目标快速群搜索优化算法及在模型修正中的应用

为解决群搜索算法在求解多目标优化问题时易陷于局部最优或过早收敛,限制其在复杂结构模型修正中的应用问题,提出改进的群搜索优化算法-多目标快速群搜索优化算法(MQGSO)。采用LPS搜索方法对发现者进行迭代更新,能使发现者更快到达最优位置,提升寻优效率;对追随者增加速度更新机制,考虑其自身历史最优信息以保证收敛精度,并在算法后期采用交叉变异策略增加追随者个体多样性,避免陷入局部最优;在游荡者迭代更新中引入分量变异控制策略,增加其搜索的随机性,提高算法的全局寻优性能。通过7个典型多目标优化测试函数及某发射台有限元模型修正实例,对算法性能进行验证分析。结果表明,与已有MPSO(Multi-objective Particle Swarm Optimization)及MBFO(Multi-objective Bacterial Foraging Optimization)两种算法相比,所提MQGSO算法搜索性能更强、收敛速度更快、计算精度更高,不失为求解复杂多目标优化问题的有效方法。     

一种改进的广义遗传算法及其在鲁棒优化问题中的应用

提出一种改进的广义遗传算法,算法中引入了异种机制以提高种群的多样性,在保证收敛速度的同时防止了早熟收敛。将该方法应用于复杂载荷作用下结构的鲁棒优化问题,并采用Taguchi望目特性的SN比构造了遗传算法的目标函数。数值算例表明,异种机制能够有效地提高广义遗传算法收敛于全局最优解的概率,加快收敛速度;结合了Taguchi鲁棒设计方法的广义遗传算法能够有效地求解复杂载荷作用下带有不确定参数的结构鲁棒优化问题。     

基于AHP-TOPSIS的可持续包装设计最优方案的筛选

目的 针对基本灰狼算法在函数优化过程中精度低、收敛速度慢、局部搜索能力差等问题,提出一种基于收敛因子和权重动态变化的自适应灰狼优化算法。方法 为了平衡算法的全局和局部搜索能力,引入聚焦距离变化率来动态调整收敛因子;使用自适应权重因子来改变算法的位置更新公式,以提高算法的收敛速度和精度。结果 仿真实验结果表明,改进后的算法在收敛精度和速度上都有了显著的提升,并且克服了灰狼算法在处理多峰函数时易陷入局部最优的缺点;对于纸浆浓度控制系统,控制效果更加理想。结论 通过改进的灰狼算法对PID控制器参数进行整定,可以显著提高系统的控制精度和其他性能指标,能更好地满足实际应用的要求。     

基于Kriging代理模型的改进EGO算法研究

 代理模型是复杂工程优化设计问题的关键技术之一．基于Kriging代理模型的EGO算法作为一种贝叶斯全局优化算法引入了EI函数来确定校正点,保证了算法的全局收敛性．首先针对原始EGO算法的不足之处,提出改进EGO算法．然后采用改进EGO算法对4个经典函数和1个工程算例进行测试,最后从算法的收敛速度和精度两方面将不同的算法进行比较．结果表明改进后的EGO算法达到原始EGO算法精度时所需迭代步数更少,与基于响应面的优化算法相比在收敛速度和精度方面更具有优势．说明该方法适应性强,具有很高的工程实用价值．     

带回溯线搜索步的双子问题信赖域算法

无约束非线性优化问题广泛存在于工程、科学计算等实际应用领域。本文在信赖域算法的框架下提出无约束子问题,将它与信赖子问题相结合,构造了求解无约束优化问题的双子问题信赖域算法。同时利用信赖域子问题得到的试探步一定是目标函数充分下降方向的性质使得每次求解信赖域子问题之后均能得到使目标函数下降的步。在标准假设下证明了该算法具有全局收敛性和局部二次收敛速度。数值结果表明该算法比传统的信赖域算法速度更快更有效。     

一种改进的模糊神经网络控制器学习算法

提出了一种改进的模糊神经网络混合学习算法,运用遗传算法优化构成隶属函数的网络结构,运用最小二乘法进行解模糊,具有更高的学习精度和更快的收敛速度,解决了在多变量系统中采用模糊神经网络时学习收敛慢且易陷入局部极小点的问题。     

约束自适应桁架优化设计方法

为求解多峰值、高度非线性桁架尺寸及形状优化问题,减少算法参数设置的盲目性,将Oracle罚函数与启发式算法相结合,提出可自适应处理约束列式的优化算法Ω-CMA-ES。该算法在处理各类复杂桁架优化问题时仅需设置一个参数Ω。测试算例表明,该算法对参数Ω具有良好的鲁棒性,可有效处理各类动态约束;且在探索全局最优解时体现出较高潜力,优化质量及收敛速度优于既有结果。     

基于膜计算与粒子群算法的盲源分离方法

为了解决盲源分离方法收敛速度慢、分离性能不高的问题,提出一种基于膜计算(Membrane Computing,MC)和粒子群算法(Particle Swarm Optimization,PSO)的盲源分离方法。算法以分离信号负熵作为粒子群的适应值函数,将粒子均匀分布到各基本膜中,将各基本膜内最优位置输出到表层膜并选择适应值最小的最优位置作为群体最优位置,通过粒子自身最优位置和群体最优位置对种群粒子进行速度和位置的更新。粒子群最优解调整盲源分离的步长函数,进行信号的分离。提出的算法简化了惯性权重取值问题,保证了PSO算法局部搜索的精度,满足了全局搜索的多样性。仿真实验和实例应用表明,提出的算法可以很好地分离混合信号,并且能避免PSO算法的早熟收敛问题,具有更快的收敛速度和更优异的分离性能。     

求解结构型优化问题的随机步长ADMM下降算法

本文考虑求解带有两块变量的结构型凸优化问题．ADMM算法是求解该问题的一种经典算法,主要思想是在増广拉格朗日乘子算法的基础上,利用目标函数关于两块变量的可分性,降低了子问题的计算难度．ADMM下降算法是ADMM算法的一种改进,对部分变量利用最优步长外加一个固定的延长因子进行延长,以加快ADMM算法的收敛速度．数值实验结果表明,ADMM下降算法比ADMM算法收敛速度更快．根据徐海文提出的随机步长收缩算法的思想,我们在ADMM下降算法的基础上,将延长因子改为利用随机数生成,提出了带随机步长的ADMM下降算法,并证明了新算法的收敛性．初步数值实验结果,表明新算法的计算效率优于经典ADMM算法和ADMM下降算法,且新算法的计算效率对问题规模的增长有更好的尺度适应性．     

带爆炸算子的粒子群优化算法

粒子群优化算法(PSO)在应用中极易陷入局部最优并且后期收敛速度较慢。针对这两个问题,分析标准粒子群优化算法的收敛特性,利用粒子群算法的惯性权重来保证算法的全局寻优能力,提出的局部搜索策略是在两次迭代过程中粒子位置突变较大时融合爆炸算子提高粒子的局部开采能力,极大的改善算法后期的收敛速度。通过典型的函数优化实验验证,改进算法在寻优能力、寻优精度、收敛速度等方面都有较好性能。是平衡粒子探索和开采能力的高效算法。     

Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization

This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, standard deviation, and CPU time were compared with those of both the other PSO algorithms. The experimental results reveal that the proposed momentum-type PSO algorithm can efficiently solve unconstrained and constrained engineering optimization problems.     

Modification of DIRECT for high-dimensional design problems

DIviding RECTangles (DIRECT), as a well-known derivative-free global optimization method, has been found to be effective and efficient for low-dimensional problems. When facing high-dimensional black-box problems, however, DIRECT's performance deteriorates. This work proposes a series of modifications to DIRECT for high-dimensional problems (dimensionality d>10). The principal idea is to increase the convergence speed by breaking its single initialization-to-convergence approach into several more intricate steps. Specifically, starting with the entire feasible area, the search domain will shrink gradually and adaptively to the region enclosing the potential optimum. Several stopping criteria have been introduced to avoid premature convergence. A diversification subroutine has also been developed to prevent the algorithm from being trapped in local minima. The proposed approach is benchmarked using nine standard high-dimensional test functions and one black-box engineering problem. All these tests show a significant efficiency improvement over the original DIRECT for high-dimensional design problems.     

Topology and sizing optimization of discrete structures using a cooperative coevolutionary genetic algorithm with independent ground structures

This article proposes a method called the cooperative coevolutionary genetic algorithm with independent ground structures (CCGA-IGS) for the simultaneous topology and sizing optimization of discrete structures. An IGS strategy is proposed to enhance the flexibility of the optimization by offering two separate design spaces and to improve the efficiency of the algorithm by reducing the search space. The CCGA is introduced to divide a complex problem into two smaller subspaces: the topological and sizing variables are assigned into two subpopulations which evolve in isolation but collaborate in fitness evaluations. Five different methods were implemented on 2D and 3D numeric examples to test the performance of the algorithms. The results demonstrate that the performance of the algorithms is improved in terms of accuracy and convergence speed with the IGS strategy, and the CCGA converges faster than the traditional GA without loss of accuracy.     

Two-timescale algorithms for simulation optimization of hidden Markov models

We propose two finite difference two-timescale Simultaneous Perturbation Stochastic Approximation (SPSA) algorithms for simulation optimization of hidden Markov models. Stability and convergence of both the algorithms is proved. Numerical experiments on a queueing model with high-dimensional parameter vectors demonstrate orders of magnitude faster convergence using these algorithms over related (N = l)-Simulation finite difference analogues and another Two-Simulation finite difference algorithm that updates in cycles.     

A decreasing inertia weight particle swarm optimizer

It has been over ten years since the pioneering work of particle swarm optimization (PSO) espoused by Kennedy and Eberhart. Since then, various modifications, well suited to particular application areas, have been reported widely in the literature. The evolutionary concept of PSO is clear-cut in nature, easy to implement in practice, and computationally efficient in comparison to other evolutionary algorithms. The above-mentioned merits are primarily the motivation of this article to investigate PSO when applied to continuous optimization problems. The performance of conventional PSO on the solution quality and convergence speed deteriorates when the function to be optimized is multimodal or with a large problem size. Toward that end, it is of great practical value to develop a modified particle swarm optimizer suitable for solving high-dimensional, multimodal optimization problems. In the first part of the article, the design of experiments (DOE) has been conducted comprehensively to examine the influences of each parameter in PSO. Based upon the DOE results, a modified PSO algorithm, termed Decreasing-Weight Particle Swarm Optimization (DW-PSO), is addressed. Two performance measures, the success rate and number of function evaluations, are used to evaluate the proposed method. The computational comparisons with the existing PSO algorithms show that DW-PSO exhibits a noticeable advantage, especially when it is performed to solve high-dimensional problems.     

求解约束优化问题的改进布谷鸟搜索算法

为了提高约束优化问题的求解精度和收敛速度,提出求解约束优化问题的改进布谷鸟搜索算法。首先分析了基本布谷鸟搜索算法全局搜索和局部搜索过程中的不足,对其中全局搜索和局部搜索迭代公式进行重新定义,然后以一定概率在最优解附近进行搜索。对12个标准约束优化问题和4个工程约束优化问题进行测试并与多种算法进行对比,实验结果和统计分析表明所提算法在求解约束优化问题上具有较强的优越性。     

A global optimization algorithm for simulation-based problems via the extended DIRECT scheme

This article presents a global optimization algorithm via the extension of the DIviding RECTangles (DIRECT) scheme to handle problems with computationally expensive simulations efficiently. The new optimization strategy improves the regular partition scheme of DIRECT to a flexible irregular partition scheme in order to utilize information from irregular points. The metamodelling technique is introduced to work with the flexible partition scheme to speed up the convergence, which is meaningful for simulation-based problems. Comparative results on eight representative benchmark problems and an engineering application with some existing global optimization algorithms indicate that the proposed global optimization strategy is promising for simulation-based problems in terms of efficiency and accuracy.     

Comparison of the Luus–Jaakola optimization procedure and the genetic algorithm

The success of both genetic algorithms (GA) and the Luus–Jaakola (LJ) optimization procedure in engineering optimization and the desire for efficient optimization methods arising from practical experience make the comparison of these two methods necessary. The GA and the LJ optimization procedure are compared in terms of convergence speed and reliability in obtaining the global optimum. Instead of using the number of function evaluations, this study uses computation time for comparison of convergence speed, which is more precise. Although for some problems, such as parameter estimation for the catalytic cracking process of gas oil, both GA and LJ converge to the optimum rapidly and show high reliability; in most cases, the LJ optimization procedure was found to be faster than GA and exhibited higher reliability in obtaining the global optimum. Furthermore, the LJ optimization procedure is easier to program.     

Structural reliability assessment by salp swarm algorithm–based FORM

The first-order reliability method (FORM) is well recognized as an efficient approach for reliability analysis. Rooted in considering the reliability problem as a constrained optimization of a function, the traditional FORM makes use of gradient-based optimization techniques to solve it. However, the gradient-based optimization techniques may result in local convergence or even divergence for the highly nonlinear or high-dimensional performance function. In this paper, a hybrid method combining the Salp Swarm Algorithm (SSA) and FORM is presented. In the proposed method, a Lagrangian objective function is constructed by the exterior penalty function method to facilitate meta-heuristic optimization strategies. Then, SSA with strong global optimization ability for highly nonlinear and high-dimensional problems is utilized to solve the Lagrangian objective function. In this regard, the proposed SSA-FORM is able to overcome the limitations of FORM including local convergence and divergence. Finally, the accuracy and efficiency of the proposed SSA-FORM are compared with two gradient-based FORMs and several heuristic-based FORMs through eight numerical examples. The results show that the proposed SSA-FORM can be generally applied for reliability analysis involving low-dimensional, high-dimensional, and implicit performance functions.