Strength design of composite beam using gradient and particle swarm optimization

This work addresses the optimum design of a composite box-beam structure subject to strength constraints. Such box-beams are used as the main load carrying members of helicopter rotor blades. A computationally efficient analytical model for box-beam is used. Optimal ply orientation angles are sought which maximize the failure margins with respect to the applied loading. The Tsai–Wu–Hahn failure criterion is used to calculate the reserve factor for each wall and ply and the minimum reserve factor is maximized. Ply angles are used as design variables and various cases of initial starting design and loadings are investigated. Both gradient-based and particle swarm optimization (PSO) methods are used. It is found that the optimization approach leads to the design of a box-beam with greatly improved reserve factors which can be useful for helicopter rotor structures. While the PSO yields globally best designs, the gradient-based method can also be used with appropriate starting designs to obtain useful designs efficiently.     

An efficient particle swarm approach for mixed-integer programming in reliability-redundancy optimization applications

The reliability-redundancy optimization problems can involve the selection of components with multiple choices and redundancy levels that produce maximum benefits, and are subject to the cost, weight, and volume constraints. Many classical mathematical methods have failed in handling nonconvexities and nonsmoothness in reliability-redundancy optimization problems. As an alternative to the classical optimization approaches, the meta-heuristics have been given much attention by many researchers due to their ability to find an almost global optimal solutions. One of these meta-heuristics is the particle swarm optimization (PSO). PSO is a population-based heuristic optimization technique inspired by social behavior of bird flocking and fish schooling. This paper presents an efficient PSO algorithm based on Gaussian distribution and chaotic sequence (PSO-GC) to solve the reliability-redundancy optimization problems. In this context, two examples in reliability-redundancy design problems are evaluated. Simulation results demonstrate that the proposed PSO-GC is a promising optimization technique. PSO-GC performs well for the two examples of mixed-integer programming in reliability-redundancy applications considered in this paper. The solutions obtained by the PSO-GC are better than the previously best-known solutions available in the recent literature.     

Multi-objective design optimization of reconfigurable machine tools: a modified fuzzy-Chebyshev programming approach

A reconfigurable manufacturing system (RMS) is designed for rapid adjustment of functionalities in response to market changes. A RMS consists of a number of reconfigurable machine tools (RMTs) for processing different jobs using different processing modules. The potential benefits of a RMS may not be materialized if not properly designed. This paper focuses on RMT design optimization considering three important yet conflicting factors: configurability, cost and process accuracy. The problem is formulated as a multi-objective model. A mechanism is developed to generate and evaluate alternative designs. A modified fuzzy-Chebyshev programming (MFCP) method is proposed to achieve a preferred compromise of the design objectives. Unlike the original fuzzy-Chebyshev programming (FCP) method which imposes an identical satisfaction level for all objectives regardless of their relative importance, the MFCP respects their priority order. This method also features an adaptive satisfaction-level-dependent process to dynamically adjust objective weights in the search process. A particle swarm optimization algorithm (PSOA) is developed to provide quick solutions. The application of the proposed approach is demonstrated using a reconfigurable boring machine. Our computational results have shown that the combined MFCP and PSOA algorithm is efficient and robust. The advantages of the MFCP over the original FCP are also illustrated based on the results.     

A hybrid multi-objective particle swarm algorithm for a mixed-model assembly line sequencing problem

Mixed-model assembly line sequencing is one of the most important strategic problems in the field of production management where diversified customers' demands exist. In this article, three major goals are considered: (i) total utility work, (ii) total production rate variation and (iii) total setup cost. Due to the complexity of the problem, a hybrid multi-objective algorithm based on particle swarm optimization (PSO) and tabu search (TS) is devised to obtain the locally Pareto-optimal frontier where simultaneous minimization of the above-mentioned objectives is desired. In order to validate the performance of the proposed algorithm in terms of solution quality and diversity level, the algorithm is applied to various test problems and its reliability, based on different comparison metrics, is compared with three prominent multi-objective genetic algorithms, PS-NC GA, NSGA-II and SPEA-II. The computational results show that the proposed hybrid algorithm significantly outperforms existing genetic algorithms in large-sized problems.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

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.     

结构主动控制的一体化多目标优化研究

基于Pareto多目标遗传算法提出了结构主动控制系统的一体化多目标优化设计方法,对作动器位置与主动控制器进行同步优化设计.外界激励采用平稳过滤白噪声来模拟,在状态空间下通过求解Lyapunov方程,得到结构响应和主动控制力的均方值.主动控制器采用LQG控制算法来进行设计.以结构位移和加速度均方值最大值与相应无控响应均方值的最大值之比,以及所需控制力均方值之和作为多目标同步优化的目标函数.优化过程还考虑了结构与激励参数对优化结果的影响.最后以某6层平面框架有限元模型为例进行了计算机仿真分析,结果表明所提出的主动控制系统多目标一体化优化方法简单,高效,实用,具有较好的普适性.     

A parallel particle swarm optimization algorithm for multi-objective optimization problems

In this article, a new proposal of using particle swarm optimization algorithms to solve multi-objective optimization problems is presented. The algorithm is constructed based on the concept of Pareto dominance, as well as a state-of-the-art ‘parallel’ computing technique that intends to improve algorithmic effectiveness and efficiency simultaneously. The proposed parallel particle swarm multi-objective evolutionary algorithm (PPS-MOEA) is tested through a variety of standard test functions taken from the literature; its performance is compared with six noted multi-objective algorithms. The computational experience gained from the first two experiments indicates that the algorithm proposed in this article is extremely competitive when compared with other MOEAs, being able to accurately, reliably and robustly approximate the true Pareto front in almost every tested case. To justify the motivation behind the research of the parallel swarm structure, the computational results of the third experiment confirm the PPS-MOEA's merit in solving really high-dimensional multi-objective optimization problems.     

Drilling path optimization by the particle swarm optimization algorithm with global convergence characteristics

Drilling path optimization is one of the key problems in holes-machining. This paper presents a new approach to solve the drilling path optimization problem belonging to discrete space, based on the particle swarm optimization (PSO) algorithm. Since the standard PSO algorithm is not guaranteed to be global convergent or local convergent, based on the mathematical model, the algorithm is improved by adopting the method to generate the stop evolution particle once again to obtain the ability of convergence on the global optimization solution. Also, the operators are proposed by establishing the Order Exchange Unit (OEU) and the Order Exchange List (OEL) to satisfy the need of integer coding in drilling path optimization. The experimentations indicate that the improved algorithm has the characteristics of easy realization, fast convergence speed, and better global convergence capability. Hence the new PSO can play a role in solving the problem of drilling path optimization.     

Optimum design of composite laminates for frequency constraints

A method for minimum thickness multilayer rectangular composite laminates is presented which is based on a layerwise optimization procedure under natural frequency limitations. In this method, all types of boundary conditions and their combinations can be taken into account. Analysis is based on the Ritz approximations, and no limitations exist on the number of layers that can be considered or the plate’s aspect ratio. Coupling of flexural and torsional stiffness terms need not be zero in any of the cases. Optimization constraints can be either limits on the fundamental frequency or separation between two natural frequencies. Hybrid combination of layers is also made possible in order to enhance the laminate economy, and a short cut procedure is recommended to save total computational efforts.

Examples are offered that illustrate the method’s capabilities, and the results are verified by comparison to some published ones.     

A multi-objective approach for multi-material topology and shape optimization

An automated multi-material approach that integrates multi-objective Topology Optimization (TO) and multi-objective shape optimization is presented. A new ant colony optimization algorithm is presented and applied to solving the TO problem, estimating a trade-off set of initial topologies or distributions of material. The solutions found usually present irregular boundaries, which are not desirable in applications. Thus, shape parameterization of the internal boundaries of the design region, and subsequent shape optimization, is performed to improve the quality of the estimated Pareto-optimal solutions. The selection of solutions for shape optimization is done by using the PROMETHEE II decision-making method. The parameterization process involves identifying the boundaries of different materials and describing these boundaries by non-uniform rational B-spline curves. The proposed approach is applied to the optimization of a C-core magnetic actuator, with two objectives: the maximization of the attractive force on the armature and the minimization of the volume of permanent magnet material.     

基于多目标优化策略的扭杆可靠性稳健优化设计

为提高机械零部件的安全性和稳健性,应用可靠性稳健优化设计理论和多目标决策方法,建立了适合结构可靠性稳健优化设计的多目标优化模型.为能迅速准确地对具有约束条件的多目标优化模型进行求解,提出一种利用模糊理论对约束条件进行处理的方法,然后应用灰色粒子群算法对多目标优化模型进行求解.通过对正态分布参数和任意分布参数的扭杆可靠性稳健优化设计,表明该方法行之有效.     

Enhanced particle swarm optimization for size and shape optimization of truss structures

This article presents an enhanced particle swarm optimization (EPSO) algorithm for size and shape optimization of truss structures. The proposed EPSO introduces a particle categorization mechanism into the particle swarm optimization (PSO) to eliminate unnecessary structural analyses during the optimization process and improve the computational efficiency of the PSO-based structural optimization. The numerical investigation, including three benchmark truss optimization problems, examines the efficiency of the EPSO. The results demonstrate that the particle categorization mechanism greatly reduces the computational requirements of the PSO-based approaches while maintaining the original search capability of the algorithms in solving optimization problems with computationally cheap objective function and expensive constraints.     

Multi-objective robust design optimization of fatigue life for a welded box girder

To reduce the scatter of fatigue life for welded structures, a robust optimization method is presented in this study based on a dual surrogate modelling and multi-objective particle swam optimization algorithm. Considering the perturbations of material parameters and environment variables, the mean and standard deviation of fatigue life are fitted using dual surrogate modelling and selected as the objective function to be minimized. As an example, a welded box girder is presented to reduce the standard deviation of fatigue life. A set of non-dominated solutions is produced through a multi-objective particle swam optimization algorithm. A cognitive approach is used to select the optimum solution from the Pareto sets. As a comparative study, traditional single objective optimizations are also presented in this study. The results reduced the standard deviation of the fatigue life by about 16.5%, which indicated that the procedure improved the robustness of the fatigue life.     

Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.     

Function-transformation methods for multi-objective optimization

It is useful with multi-objective optimization (MOO) to transform the objective functions such that they all have similar units and orders of magnitude. This article evaluates various transformation methods using simple example problems. Viewing these methods as different means to restrict function values sheds light on how the methods perform. The weighted sum approach for MOO is used to study how well different methods aid in depicting the Pareto optimal set. Whereas using unrestricted weights is well suited for providing a single solution that reflects preferences, it is found that using a convex combination of functions is desirable when generating the Pareto set. In addition, it is shown that some transformation methods are detrimental to the process of generating a diverse spread of points, and criteria are proposed for determining when the methods fail to generate an accurate representation of the Pareto set. Advantages of using a simple normalization–modification are demonstrated.     

Particle swarm optimization for problems with variable number of dimensions

Some real-life optimization problems, apart from dependence on the combination of state variables, also show dependence on the complexity of the model describing the problem. Changing model complexity implies changing the number of decision space dimensions.

A new method called Particle Swarm Optimization for Variable Number of Dimensions is developed here. The well-known particle swarm optimization procedure is modified to handle spaces with a variable number of dimensions within a single run. Some well-known benchmark problems are modified to depend on the number of dimensions. Novel performance metrics are defined in the article to evaluate convergence properties of the method. Some recommendations for setting the optimization are made according to results of the method on the proposed benchmark test suite. The method is compared with conventional swarm strategies able to solve problems with variable number of dimensions.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

Multi-objective optimization design using amended particle swarm optimization and Taguchi method for a six-phase copper rotor induction motor

A multi-objective optimization design technique for a six-phase copper rotor induction motor is proposed. The amended particle swarm optimization (PSO) and Taguchi methods combined with finite element analysis are used in this design technique. The objectives in the first-stage optimization are the minimization of manufacturing cost and starting current. In the second-stage optimization, the objectives are the maximization of efficiency, power factor and output torque. The Taguchi method can optimize the machine parameters of performance characteristics in electrical discharge machining. The experimental results are further transformed into the signal-to-noise ratios and amended PSO coefficients based on amended PSO analysis with regard to multiple performance characteristics index values. The results of the optimizations showed significant reduction in terms of the use of magnets as well as improvement in the machine performance. Finally, the experimental results confirm the validity of the proposed optimization design approach.     

Decomposition-based multi-objective differential evolution particle swarm optimization for the design of a tubular permanent magnet linear synchronous motor

This article proposes a decomposition-based multi-objective differential evolution particle swarm optimization (DMDEPSO) algorithm for the design of a tubular permanent magnet linear synchronous motor (TPMLSM) which takes into account multiple conflicting objectives. In the optimization process, the objectives are evaluated by an artificial neural network response surface (ANNRS), which is trained by the samples of the TPMSLM whose performances are calculated by finite element analysis (FEA). DMDEPSO which hybridizes differential evolution (DE) and particle swarm optimization (PSO) together, first decomposes the multi-objective optimization problem into a number of single-objective optimization subproblems, each of which is associated with a Pareto optimal solution, and then optimizes these subproblems simultaneously. PSO updates the position of each particle (solution) according to the best information about itself and its neighbourhood. If any particle stagnates continuously, DE relocates its position by using two different particles randomly selected from the whole swarm. Finally, based on the DMDEPSO, optimization is gradually carried out to maximize the thrust of TPMLSM and minimize the ripple, permanent magnet volume, and winding volume simultaneously. The result shows that the optimized TPMLSM meets or exceeds the performance requirements. In addition, comparisons with chosen algorithms illustrate the effectiveness of DMDEPSO to find the Pareto optimal solutions for the TPMLSM optimization problem.