Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

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 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.     

Multiple sequence alignment using modified dynamic programming and particle swarm optimization

Abstract

Dynamic Programming (DP) is widely used in Multiple Sequence Alignment (MSA) problems. However, when the number of the considered sequences is more than two, multiple dimensional DP may suffer from large storage and computational complexities. Often, progressive pairwise DP is employed for MSA. However, such an approach also suffers from local optimum problems. In this paper, we present a hybrid algorithm for MSA. The algorithm combines the pairwise DP and the particle swarm optimization (PSO) techniques to overcome the above drawbacks. In the algorithm, pairwise DP is used to align sequences progressively and PSO is employed to avoid the result of alignment being trapped into local optima. Several existing MSA tools are employed for comparison. The experimental results show excellent performance of the proposed algorithm.     

基于物理规划的 Stewart 平台多目标优化

应用物理规划方法对500米口径球面射电望远镜(FAST)精调 Stewart 平台进行了多目标优化设计.根据 Stewart 平台的设计准则,将 Stewart 平台的运动精度、重量和工作效率作为目标函数,构造了相应的以目标函数为变量的偏好函数,建立了基于物理规划的多目标优化模型,采用遗传算法对该优化问题进行求解.结果表明,物理规划避免了基于权重的多目标优化方法中权系数难以确定的问题,有效地给出了优化问题的 Pareto 解.     

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.     

Multi-objective robust optimization design of a front-end underframe structure for a high-speed train

A multi-objective robust design optimization of a front-end underframe structure for application in high-speed trains is proposed and the structural parameter uncertainty is considered. A finite element model of the structure is developed and verified by dynamic impact experiments. The sensitivity analysis demonstrates that the thicknesses of the centre sill have significant influences on structural crushing behaviours. The specific energy absorption and the initial peak crushing force (F_p) are taken as optimization objectives. Compared with the baseline structure, the 6-sigma robust design shows that the F_p and the structural mass are reduced by 54.86% and 13.06%, respectively, and the robust optimum is more reliable. The 6-sigma robust optimal solution has an efficient energy-absorbing capacity while satisfying the design constraint. Thus, 6-sigma robust optimization can be applied for high-speed trains.     

Decoupled approach to multidisciplinary design optimization under uncertainty

We propose solution methods for multidisciplinary design optimization (MDO) under uncertainty. This is a class of stochastic optimization problems that engineers are often faced with in a realistic design process of complex systems. Our approach integrates solution methods for reliability-based design optimization (RBDO) with solution methods for deterministic MDO problems. The integration is enabled by the use of a deterministic equivalent formulation and the first order Taylor’s approximation in these RBDO methods. We discuss three specific combinations: the RBDO methods with the multidisciplinary feasibility method, the all-at-once method, and the individual disciplinary feasibility method. Numerical examples are provided to demonstrate the procedure. Anukal Chiralaksanakul is currently a full-time lecturer in the Graduate School of Business Administration at National Institute of Development Administration (NIDA), Bangkok, Thailand.     

Multi-objective optimization of generalized reliability design problems using feature models—A concept for early design stages

Reliability optimization problems such as the redundancy allocation problem (RAP) have been of considerable interest in the past. However, due to the restrictions of the design space formulation, they may not be applicable in all practical design problems. A method with high modelling freedom for rapid design screening is desirable, especially in early design stages. This work presents a novel approach to reliability optimization. Feature modelling, a specification method originating from software engineering, is applied for the fast specification and enumeration of complex design spaces. It is shown how feature models can not only describe arbitrary RAPs but also much more complex design problems. The design screening is accomplished by a multi-objective evolutionary algorithm for probabilistic objectives. Comparing averages or medians may hide the true characteristics of this distributions. Therefore the algorithm uses solely the probability of a system dominating another to achieve the Pareto optimal set. We illustrate the approach by specifying a RAP and a more complex design space and screening them with the evolutionary algorithm.     

基于GA-NLP的剪刀式折叠桥梁展桥机构多目标优化设计

针对新型剪刀式折叠桥梁展桥机构的优化设计问题,首先建立了展桥机构的运动学和静力学模型,然后以展桥机构关键铰点位置和岸桥节与竖直方向所成夹角为优化设计变量,以展桥机构的空间位置为主要约束条件,以展桥油缸、连杆、关键铰点受力峰值最小为优化目标,通过正规化和加权处理构造了展桥机构多目标优化分析模型,并采用遗传算法（genetic algorithm, GA）和非线性规划(nonlinear programming, NLP)混合算法对该优化分析模型进行求解。最后,利用ADAMS（automatic dynamic analysis of mechanical systems,机械系统动力学自动分析）软件验证了展桥机构多目标优化分析模型的正确性。结果表明,优化后展桥油缸承载的拉力与推力峰值分别减小了57.9%和25.3%,连杆承载的拉力与压力峰值分别减小了26.1%和55.2%,展桥机构2个关键铰点受力峰值分别减小了23.5%和26.8%。研究结果可为展桥机构的改进设计提供理论依据。     

Multi-objective optimization of space station logistics strategies using physical programming

This study extends a previously proposed single-objective optimization formulation of space station logistics strategies to multi-objective optimization. The four-objective model seeks to maximize the mean utilization capacity index, total utilization capacity index, logistics robustness index and flight independency index, aiming to improve both the utilization benefit and the operational robustness of a space station operational scenario. Physical programming is employed to convert the four-objective optimization problem into a single-objective problem. A genetic algorithm is proposed to solve the resulting physical programming-based optimization problem. Moreover, the non-dominated sorting genetic algorithm-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the physical programming-based solution. The proposed approach is demonstrated with a notional one-year scenario of China's future space station. It is shown that the designer-preferred compromise solution improving both the utilization benefit and the operational robustness is successfully obtained.     

Multi-objective optimization of a flexible slider-crank mechanism synthesis,based on dynamic responses

This work deals with a multi-body system synthesis. A flexible slider crank mechanism has been investigated as an illustrative application. The main interest is focused on the mechanism design variables’ identification based on its dynamic responses. Three responses have been involved such as the slider velocity, the slider acceleration and the mid-point transversal deflection of the flexible connecting rod. Each of these responses has been embroiled separately in a mono-objective optimization. Subsequently, the multi-objective optimization subsuming these responses has been established. Two different optimization methods have been studied namely the genetic algorithm (GA) and the particle swarm optimization (PSO) technique. It has been proved that the multi-objective optimization presents more accurate results beside the mono-objective optimization. Compared to the GA, the PSO is more powerful and is able to identify the mechanism design variable with better accuracy, in spite of the affordable computational time allowed with the GA optimization.     

Multi-objective optimization of combined Brayton and inverse Brayton cycles using advanced optimization algorithms

This study explores the use of teaching-learning-based optimization (TLBO) and artificial bee colony (ABC) algorithms for determining the optimum operating conditions of combined Brayton and inverse Brayton cycles. Maximization of thermal efficiency and specific work of the system are considered as the objective functions and are treated simultaneously for multi-objective optimization. Upper cycle pressure ratio and bottom cycle expansion pressure of the system are considered as design variables for the multi-objective optimization. An application example is presented to demonstrate the effectiveness and accuracy of the proposed algorithms. The results of optimization using the proposed algorithms are validated by comparing with those obtained by using the genetic algorithm (GA) and particle swarm optimization (PSO) on the same example. Improvement in the results is obtained by the proposed algorithms. The results of effect of variation of the algorithm parameters on the convergence and fitness values of the objective functions are reported.     

The MINLP optimization approach to structural synthesis. Part I: A general view on simultaneous topology and parameter optimization

This paper presents the Mixed-Integer Non-linear Programming (MINLP) optimization approach to structural synthesis. Non-linear continuous/discrete non-convex problems of structural synthesis are proposed to be solved by means of simultaneous topology, parameter and standard dimension optimization. Part I of this three-part series of papers contains a general view of the MINLP approach to simultaneous topology and continuous parameter optimization. The MINLP optimization approach is performed through three steps. The first one includes the generation of a mechanical superstructure of different topology alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the formulated MINLP problem. Some MINLP methods are also presented. A Modified OA/ER algorithm is applied to solve the MINLP problem and a simple example of a multiple cantilever beam is given to demonstrate the steps of the proposed MINLP optimization approach. As simultaneous optimization, extended to include also standard dimensions, requires additional effort, the development of suitable strategies to carry out the optimization is further discussed in Part II. The modelling of MINLP superstructures and the topology and parameter optimization of roller and sliding hydraulic steel gate structures are shown in Part III of the paper. An example of the synthesis of an already erected roller gate, i.e. the Intake Gate of Aswan II in Egypt, is presented as a comparative design research work. © 1998 John Wiley & Sons, Ltd.     

Multi-objective design optimization of functionally graded material for the femoral component of a total knee replacement

The optimal design of complex systems in engineering requires pursuing rigorous mathematical modeling of the system’s behavior as a function of a set of design variables to achieve goal-oriented design. Despite the success of current knee implants, the limited life span remains the main concern of this complex system. The mismatch between the properties of engineered biomaterials and those of biological materials leads to insufficient bonding with bone, stress shielding effects and wear problems (i.e. aseptic loosening). The use of a functionally graded material (FGM) for the femoral component of knee implants is attractive because the properties can be designed to vary in a certain pattern to meet the desired requirements at different regions in the knee joint system, thereby decreasing loosening problem. However, matching the properties does not necessarily guarantee the best functionality of the knee implant and there is a need for developing the optimal design of an FGM femoral component that is longer lasting. In this study, therefore, a multi-objective design optimization of a FGM femoral component is carried out using finite element analysis (FEA) and response surface methodology (RSM). The results of using optimized FGM are then compared with the use of standard Co–Cr alloy in a femoral component knee implant to demonstrate relative performance.     

Sequential linear programming and particle swarm optimization for the optimization of energy districts

This article deals with the optimization of energy resource management of industrial districts, with the aim of minimizing customer energy expenses. A model of the district is employed, whose optimization gives rise to a nonlinear constrained optimization problem. Here the focus is on its numerical solution. Two different methods are considered: a sequential linear programming method and a particle swarm optimization method. Efficient implementations of both approaches are devised and the results of the tests performed on several energetic districts are reported, including a real case study.     

基于粒子群算法多目标优化液压支架四连杆

针对煤矿液压支架四连杆受力计算较为复杂,简化计算时易出现较大误差且稳定性较差的问题,提出从四连杆机构的空间受力出发并结合支架的运动轨迹,采用粒子群优化算法对四连杆机构展开优化研究。首先建立了四连杆优化模型,在优化模型中选取对结果影响较大的参数作为优化变量,以轨迹偏差、连杆长、连杆力之和作为目标函数,根据液压支架设计规范确定约束条件。然后使用粒子群算法对目标函数进行迭代求解并在求解过程中采用惩罚函数法解决优化模型中不等式约束问题。对比优化前后连杆的杆长、受力和稳定性数据,发现优化后的四连杆实现了轻量化,且受力较小,稳定性提高。研究结果对四连杆的设计有实际参考价值。     

Evaluation of the influence of dominance rules for the assembly line design problem under consideration of product design alternatives

The current competitive situation increases the importance of realistically estimating product costs during the early phases of product and assembly line planning projects. In this article, several multi-objective algorithms using difference dominance rules are proposed to solve the problem associated with the selection of the most effective combination of product and assembly lines. The list of developed algorithms includes variants of ant colony algorithms, evolutionary algorithms and imperialist competitive algorithms. The performance of each algorithm and dominance rule is analysed by five multi-objective quality indicators and fifty problem instances. The algorithms and dominance rules are ranked using a non-parametric statistical test.     

Multi-objective scheduling problems: Determination of pruned Pareto sets

There are often multiple competing objectives for industrial scheduling and production planning problems. Two practical methods are presented to efficiently identify promising solutions from among a Pareto optimal set for multi-objective scheduling problems. Generally, multi-objective optimization problems can be solved by combining the objectives into a single objective using equivalent cost conversions, utility theory, etc., or by determination of a Pareto optimal set. Pareto optimal sets or representative subsets can be found by using a multi-objective genetic algorithm or by other means. Then, in practice, the decision maker ultimately has to select one solution from this set for system implementation. However, the Pareto optimal set is often large and cumbersome, making the post-Pareto analysis phase potentially difficult, especially as the number of objectives increase. Our research involves the post Pareto analysis phase, and two methods are presented to filter the Pareto optimal set to determine a subset of promising or desirable solutions. The first method is pruning using non-numerical objective function ranking preferences. The second approach involves pruning by using data clustering. The k-means algorithm is used to find clusters of similar solutions in the Pareto optimal set. The clustered data allows the decision maker to have just k general solutions from which to choose. These methods are general, and they are demonstrated using two multi-objective problems involving the scheduling of the bottleneck operation of a printed wiring board manufacturing line and a more general scheduling problem.     

Offshore manufacturing contract design based on transfer price considering green tax: a bilevel programming approach

The problem of designing offshore manufacturing contract resulting in optimal transfer price is troubling multinational companies over the past few years. This paper proposes designing offshore manufacturing contracts based on the transfer price in the form of bilevel programming problems after considering green tax. In these contract designs, a firm in a developed country sells a single product in its market. The same product is simultaneously being manufactured by another firm in a developing country with lower manufacturing cost. After anticipating the consumer demand, the seller places an order, based on which the manufacturer manufactures the ordered quantity, and offers a transfer price which in turn maximises its net profit after paying green tax to its government. While setting the transfer price, the manufacturer considers the manufacturing cost, the export duty payable to its government and the cost of shipping the product to the developed country. After buying the product from the manufacturer at the transfer price, the seller then sets the retail price which maximises its net profit after paying the import duty to its government; the retail price, however, must not be more than the maximum retail price applicable to the market. Thus, offshore manufacturing contract results in optimal after-tax profits for both the firms. An experimental study has been carried out to discuss the practical aspects of the results developed, where a US firm is offshoring its manufacturing activity to a Chinese firm in order to draw maximum profit.