Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.     

A hybrid global–local approach for optimization of injection gate locations in liquid composite molding process simulations

The optimization of injection gate locations in liquid composite molding processes by trial and error based methods is time consuming and requires an elevated level of intuition, even when high fidelity physics-based numerical models are available. Optimization based on continuous sensitivity equations (CSE) and gradient search algorithms focused towards minimizing the mold infusion time gives a robust approach that will converge to local optima based on the initial solution. Optimization via genetic algorithms (GA) utilizes natural selection as a means of finding the optimal solution in the global domain; the computed solution is at best, close to the global optimum with further refinement still possible. In this paper, we present a hybrid global–local search approach that combines evolutionary GAs with gradient-based searches via the CSE. The hybrid approach provides a global search with the GA for a predetermined amount of time and is subsequently further refined with a gradient-based search via the CSE. In our hybrid method, we utilize the efficiency of gradient searches combined with the robustness of the GA. The resulting combination has been demonstrated to provide better and more physically correct results than either method alone. The hybrid method provides optimal solutions more quickly than GA alone and more robustly than CSE based searches alone. A resin infusion quality parameter that measures the deviation from a near uniform mold volume infusion rate is defined. The effectiveness of the hybrid method with a modified objective function that includes both the infusion time and the defined mold infusion quality parameter is demonstrated.     

A hybrid multi-objective evolutionary algorithm for wind-turbine blade optimization

A concurrent-hybrid non-dominated sorting genetic algorithm (hybrid NSGA-II) has been developed and applied to the simultaneous optimization of the annual energy production, flapwise root-bending moment and mass of the NREL 5 MW wind-turbine blade. By hybridizing a multi-objective evolutionary algorithm (MOEA) with gradient-based local search, it is believed that the optimal set of blade designs could be achieved in lower computational cost than for a conventional MOEA. To measure the convergence between the hybrid and non-hybrid NSGA-II on a wind-turbine blade optimization problem, a computationally intensive case was performed using the non-hybrid NSGA-II. From this particular case, a three-dimensional surface representing the optimal trade-off between the annual energy production, flapwise root-bending moment and blade mass was achieved. The inclusion of local gradients in the blade optimization, however, shows no improvement in the convergence for this three-objective problem.     

SoftFEM: The Soft Finite Element Method

While the finite element method (FEM) has now reached full maturity both in academy and industry, its use in optimization pipelines remains either computationally intensive or cumbersome. In particular, currently used optimization schemes leveraging FEM still require the choice of dedicated optimization algorithms for a specific design problem, and a “black box” approach to FEM-based optimization remains elusive. To this end, we propose here an integrated finite element-soft computing method, ie, the soft FEM (SoftFEM), which integrates a finite element solver within a metaheuristic search wrapper. To illustrate this general method, we focus here on solid mechanics problems. For these problems, SoftFEM is able to optimize geometry changes and mechanistic measures based on geometry constraints and material properties inputs. From the optimization perspective, the use of a fitness function based on finite element calculation imposes a series of challenges. To bypass the limitations in search capabilities of the usual optimization techniques (local search and gradient-based methods), we propose, instead a hybrid self adaptive search technique, the multiple offspring sampling (MOS), combining two metaheuristics methods: one population-based differential evolution method and a local search optimizer. The formulation coupling FEM to the optimization wrapper is presented in detail and its flexibility is illustrated with three representative solid mechanics problems. More particularly, we propose here the MOS as the most versatile search algorithm for SoftFEM. A new method for the identification of nonfully determined parameters is also proposed.     

An Improved Whale Optimization Algorithm for Feature Selection

Whale optimization algorithm (WOA) is a new population-based metaheuristic algorithm. WOA uses shrinking encircling mechanism, spiral rise, and random learning strategies to update whale’s positions. WOA has merit in terms of simple calculation and high computational accuracy, but its convergence speed is slow and it is easy to fall into the local optimal solution. In order to overcome the shortcomings, this paper integrates adaptive neighborhood and hybrid mutation strategies into whale optimization algorithms, designs the average distance from itself to other whales as an adaptive neighborhood radius, and chooses to learn from the optimal solution in the neighborhood instead of random learning strategies. The hybrid mutation strategy is used to enhance the ability of algorithm to jump out of the local optimal solution. A new whale optimization algorithm (HMNWOA) is proposed. The proposed algorithm inherits the global search capability of the original algorithm, enhances the exploitation ability, improves the quality of the population, and thus improves the convergence speed of the algorithm. A feature selection algorithm based on binary HMNWOA is proposed. Twelve standard datasets from UCI repository test the validity of the proposed algorithm for feature selection. The experimental results show that HMNWOA is very competitive compared to the other six popular feature selection methods in improving the classification accuracy and reducing the number of features, and ensures that HMNWOA has strong search ability in the search feature space.     

A hybrid genetic based optimization procedure for aircraft conceptual analysis

The problem to define a methodology for the analysis of aircraft performances, in the phase of conceptual design, is addressed. The proposed approach is based on a numerical optimization procedure where a scalar objective function, the take-off weight, is minimized. Deterministic and stochastic approaches as well as hybridizations between these two search techniques are considered. More precisely, we consider two-stage strategies where the optimum localization is performed by a genetic algorithm, while a gradient-based method is used to terminate the optimization process. Also, another type of hybridization strategy is investigated where a partially converged gradient-based method is incorporated in the genetic algorithm as a new operator. A detailed discussion is made and various different solutions are critically compared. The proposed methodology is consistent and capable of giving fundamental information to the designer for further investigating towards the directions identified by the procedure. A basic example is described, and the use of the methodology to establish the effects of different geometrical and technological parameters is discussed.     

Studies of multi‐start clustering for global optimization

Global/multi‐modal optimization problems arise in many engineering applications. Owing to the existence of multiple minima, it is a challenge to solve the multi‐modal optimization problem and to identify the global minimum especially if efficiency is a concern. In this paper, variants of the multi‐start with clustering strategy are developed and studied for identifying multiple local minima in nonlinear global optimization problems. The study considers the sampling procedure, the use of Hessian information in forming clusters, the technique for cluster analysis and the local search procedure. Variations of multi‐start with clustering are applied to 15 multi‐modal problems. A comparative study focuses on the overall search effectiveness in terms of the number of local searches performed, local minima found and required function evaluations. The performance of these multi‐start clustering algorithms ranges from very efficient to very robust. Copyright © 2002 John Wiley & Sons, Ltd.     

An efficient and practical approach to obtain a better optimum solution for structural optimization

For many structural optimization problems, it is hard or even impossible to find the global optimum solution owing to unaffordable computational cost. An alternative and practical way of thinking is thus proposed in this research to obtain an optimum design which may not be global but is better than most local optimum solutions that can be found by gradient-based search methods. The way to reach this goal is to find a smaller search space for gradient-based search methods. It is found in this research that data mining can accomplish this goal easily. The activities of classification, association and clustering in data mining are employed to reduce the original design space. For unconstrained optimization problems, the data mining activities are used to find a smaller search region which contains the global or better local solutions. For constrained optimization problems, it is used to find the feasible region or the feasible region with better objective values. Numerical examples show that the optimum solutions found in the reduced design space by sequential quadratic programming (SQP) are indeed much better than those found by SQP in the original design space. The optimum solutions found in a reduced space by SQP sometimes are even better than the solution found using a hybrid global search method with approximate structural analyses.     

混合遗传算法在结构动力反演中的应用研究

研究了输入荷载未知条件下的结构参数识别及荷载反演问题,该问题最终归结为一个非线性的优化问题求解,根据目标函数、约束条件的具体特性,采用BFGS算法作为局部搜索算子,构造了基于浮点编码的混合遗传算法。针对系统输入未知的激励特性,采用分解反演的计算策略,从而提高了动力反演中混合遗传算法的稳健性和收敛速度。数值算例表明,这种方法具有很好的参数识别精度及荷载反演效果,对测试噪声有较强的适应能力。     

基于IHHO算法的光伏电池工程模型的参数辨识

针对HHO算法存在搜索过程调整不够灵活,不能针对性地进行阶段性搜索,有时会陷入局部最优使算法搜索精度相对较差等问题,提出了一种基于改进哈里斯鹰优化(IHHO)算法的参数辨识方法。对HHO算法进行了两项改进:引入柔性递减策略,在迭代初期扩大全局搜索范围,在迭代后期延长局部搜索时间,从而加强了初期的全局搜索能力和后期的局部搜索能力;引入黄金正弦法,不但增加了种群的多样性,减少算法陷入局部最优的可能性,并且缩小了搜索空间,提高了寻优效率。应用于光伏电池工程模型的参数辨识中,IHHO算法比其他算法得到的辨识结果更为精确,辨识结果与实测数据拟合度更高,IHHO算法能够在不同环境下对光伏电池的工程模型进行准确的参数辨识。     

基于速度交流的多种群多目标粒子群算法研究

为提高多目标优化算法的收敛精度和搜索性能,提出一种基于速度交流的多种群多目标粒子群算法。算法引入速度交流机制,将种群划分为多个子种群以实现速度信息共享,改善粒子单一搜索模式,提高算法的全局搜索能力。采用混沌映射优化惯性权重,提高粒子搜索遍历性和全局性,为降低算法在运行后期陷入局部最优Pareto前沿的可能性,对各个子种群执行不同的变异操作。将算法与NSGA-Ⅱ、SPEA2、AbYSS、MOPSO、SMPSO和GWASF-GA先进多目标优化算法进行对比,实验结果表明:该算法得到的解集具有更好的收敛性和分布性。     

Dynamic multi-swarm particle swarm optimizer using parallel PC cluster systems for global optimization of large-scale multimodal functions

This article presents a novel parallel multi-swarm optimization (PMSO) algorithm with the aim of enhancing the search ability of standard single-swarm PSOs for global optimization of very large-scale multimodal functions. Different from the existing multi-swarm structures, the multiple swarms work in parallel, and the search space is partitioned evenly and dynamically assigned in a weighted manner via the roulette wheel selection (RWS) mechanism. This parallel, distributed framework of the PMSO algorithm is developed based on a master–slave paradigm, which is implemented on a cluster of PCs using message passing interface (MPI) for information interchange among swarms. The PMSO algorithm handles multiple swarms simultaneously and each swarm performs PSO operations of its own independently. In particular, one swarm is designated for global search and the others are for local search. The first part of the experimental comparison is made among the PMSO, standard PSO, and two state-of-the-art algorithms (CTSS and CLPSO) in terms of various un-rotated and rotated benchmark functions taken from the literature. In the second part, the proposed multi-swarm algorithm is tested on large-scale multimodal benchmark functions up to 300 dimensions. The results of the PMSO algorithm show great promise in solving high-dimensional problems.     

A simulated weed colony system with subregional differential evolution for multimodal optimization

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.     

An improved hybrid self-inertia weight adaptive particle swarm optimization algorithm with local search

As an evolutionary computing technique, particle swarm optimization (PSO) has good global search ability, but the swarm can easily lose its diversity, leading to premature convergence. To solve this problem, an improved self-inertia weight adaptive particle swarm optimization algorithm with a gradient-based local search strategy (SIW-APSO-LS) is proposed. This new algorithm balances the exploration capabilities of the improved inertia weight adaptive particle swarm optimization and the exploitation of the gradient-based local search strategy. The self-inertia weight adaptive particle swarm optimization (SIW-APSO) is used to search the solution. The SIW-APSO is updated with an evolutionary process in such a way that each particle iteratively improves its velocities and positions. The gradient-based local search focuses on the exploitation ability because it performs an accurate search following SIW-APSO. Experimental results verified that the proposed algorithm performed well compared with other PSO variants on a suite of benchmark optimization functions.     

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.     

基于改进遗传算法的水轮发电机振动荷载参数识别

根据水轮发电机现场振动测试实验数据,采用改进的遗传算法研究了水轮发电机运行过程中振动荷载反演问题。与传统的参数反演方法相比,遗传算法并不是基于对目标函数梯度方向搜索,而是在解的整个区域随机搜索.将遗传算法与模拟退火算法相结合,提高了种群在进化过程中个体多样性,可以有效地防止简单遗传算法早熟问题。同时,将遗传算法与梯度优化方法相结合,使得混合型遗传算法有效地解决了梯度算法局部极小问题和简单遗传算法的收敛速度慢问题。工程实际应用表明,采用本文所建立改进遗传算法所反演的水轮发电机振动荷载参数,预报其它振动观测点的位移具有较高的预报精度。     

几种优化算法在浅海匹配场反演中的性能比较

在分析模拟退火算法、遗传算法、差异进化算法、下山单纯形差异进化算法的优化机理的基础上,定量比较了上述算法在浅海匹配场反演中的效率差异。模拟退火算法与遗传算法只使用目标函数值信息在参数空间搜索全局最优值,效率低且易受参数间耦合的影响。差异进化算法使用种群中个体间的距离与方位信息在参数空间中搜索全局最优值,优化效率随着优化过程的进行而下降。下山单纯形差异进化算法将下山单纯形算法融入差异进化算法,增强了差异进化算法的寻优能力,混合算法对目标函数梯度信息敏感的特性使得这一算法具有较强的解耦能力。浅海匹配场反演仿真算例从最优参数反演结果、最终目标函数值、反演时间等方面检验了上述算法的反演效率。     

Multiobjective design of actively controlled structures using a hybrid optimization method

A multiobjective approach to the combined structure and control optimization problem for flexible space structures is presented. The proposed formulation addresses robustness considerations for controller design, as well as a simultaneous determination of optimum actuator locations. The structural weight, controlled system energy, stability robustness index and damping augmentation provided by the active controller are considered as objective functions of the multiobjective problem which is solved using a cooperative game-theoretic approach. The actuator locations and the cross-sectional areas of structural members are treated as design variables. Since the actuator locations are spatially discrete, whereas the cross-sectional areas are continuous, the optimization problem has mixed discrete-continuous design variables. A solution approach to this problem based on a hybrid optimization scheme is presented. The hybrid optimizer is a synergetic blend of artificial genetic search and gradient-based search techniques. The computational procedure is demonstrated through the design of an ACOSS-FOUR space structure. The optimum solutions obtained using the hybrid optimizer are shown to outperform the optimum results obtained using gradient-based search techniques.     

A multi-objective metamodel-assisted memetic algorithm with strength-based local refinement

Metamodel-assisted evolutionary algorithms are low-cost optimization methods for CPU-demanding problems. Memetic algorithms combine global and local search methods, aiming at improving the quality of promising solutions. This article proposes a metamodel-assisted memetic algorithm which combines and extends the capabilities of the aforementioned techniques. Herein, metamodels undertake a dual role: they perform a low-cost pre-evaluation of population members during the global search and the gradient-based refinement of promising solutions. This reduces significantly the number of calls to the evaluation tool and overcomes the need for computing the objective function gradients. In multi-objective problems, the selection of individuals for refinement is based on domination and distance criteria. During refinement, a scalar strength function is maximized and this proves to be beneficial in constrained optimization. The proposed metamodel-assisted memetic algorithm employs principles of Lamarckian learning and is demonstrated on mathematical and engineering applications.     

A hybrid cellular automaton–bi-directional evolutionary optimization algorithm for topological optimization of crashworthiness

This article proposes a new algorithm for topological optimization under dynamic loading which combines cellular automata with bi-directional evolutionary structural optimization (BESO). The local rules of cellular automata are used to update the design variables, which avoids the difficulty of obtaining gradient information under nonlinear collision conditions. The intermediate-density design problem of hybrid cellular automata is solved using the BESO concept of 0–1 binary discrete variables. Some improvement strategies are also proposed for the hybrid algorithm to solve certain problems in nonlinear topological optimization, e.g. numerical oscillation. Some typical examples of crashworthiness problems are provided to illustrate the efficiency of the proposed method and its ability to find the final optimal solution. Finally, numerical results obtained using the proposed algorithms are compared with reference examples taken from the literature. The results show that the hybrid method is computationally efficient and stable.