刚架与板组合结构动力学形状优化研究

针对刚架与板组合结构动力学形状优化问题,提出一套联合运用序列二次规划 法、ＢＦＧＳ变尺度法及二次插值技术（一维搜索）,将约束优化问题转化为无约束序 列优化问题,得到了满意的结果。算例表明本文所述方法对刚架与板组合结构的有 效性,显示了算法的工程实用性,并能够推广到其它复杂结构的动力学形状优化问 题中去。     

三种无约束优化算法的比较分析

机械产品优化设计的问题大多数属于有约束条件的优化设计问题,在优化求解的过程中常常要把有约束的最优化问题转换为无约束的最优化问题。本文从数值试验的角度,通过对两个测试问题的求解,对最速下降法、共轭梯度法和鲍威尔法三种无约束优化算法进行研究,根据试验数据结果对上述三种算法进行比较分析,以供进一步的有约束条件的优化设计问题使用。     

基于能量法的曲线曲面优化设计方法研究

利用能量法及最小二乘法建立曲线优化数学模型,同时应用罚函数法将有约束多目标优化问题转变为无约束优化问题,并采用遗传算法进行曲线优化.通过实例验证了算法的有效性,并将此法应用到曲面优化设计中,得到了较好结果.     

改进粒子群优化算法在工程优化问题中的应用研究

粒子群优化（PSO）算法是一种群集智能方法，它通过粒子之间的合作与竞争以实现对多维复杂空间的高效搜索。在对于粒子群群体构造和粒子多样性对收敛速度和精度影响的研究基础上提出了一种改进型粒子群优化算法。针对工程中的有约束的优化问题，将改进粒子群算法与函数法相结合进行求解。计算实例表明改进型粒子群优化算法大大改善了传统PSO算法的全局收敛性能，解的精度提高了很多。     

桁架优化遗传算法的若干改进

针对桁架优化问题研究二进制编码遗传算法，采用凝聚函数将约束优化问题转化为无约束优化问题，提出一种综合考虑约束值和适应度值的选择方法，保证了有潜力的设计被优先选择。并利用子代和父代之间的竞争使进化过程充分考虑以前最优值的遗传基因。算例表明，本文提出的方法是可行的，而且适应性更广。     

基于改进粒子群算法的隐式广义预测控制

针对大多数工业系统的控制输入输出都存在约束的情况,提出一种基于改进粒子群算法的隐式广义预测控制算法(IGPC)。粒子群算法(PSO)是一种基于群体的智能优化算法,解决受约束的优化问题具有精度高、收敛速度快等优点;为了避免粒子群算法陷入早熟,提高精度,引入细菌觅食算法中的自适应迁徙机制。在隐式广义预测控制的滚动优化环节引入改进粒子群算法,弥补了传统GPC在处理受约束控制问题上的缺陷。仿真结果表明了该方法的有效性和良好的控制性能。     

Novel Discrete Particle Swarm Optimization Based on Huge Value Penalty for Solving Engineering Problem

For the purpose of solving the engineering constrained discrete optimization problem, a novel discrete particle swarm optimization(DPSO) is proposed. The proposed novel DPSO is based on the idea of normal particle swarm optimization(PSO), but deals with the variables as discrete type, the discrete optimum solution is found through updating the location of discrete variable. To avoid long calculation time and improve the efficiency of algorithm, scheme of constraint level and huge value penalty are proposed to deal with the constraints, the stratagem of reproducing the new particles and best keeping model of particle are employed to increase the diversity of particles. The validity of the proposed DPSO is examined by benchmark numerical examples, the results show that the novel DPSO has great advantages over current algorithm. The optimum designs of the 100-1 500 mm bellows under 0.25 MPa are fulfilled by DPSO. Comparing the optimization results with the bellows in-service, optimization results by discrete penalty particle swarm optimization(DPPSO) and theory solution, the comparison result shows that the global discrete optima of bellows are obtained by proposed DPSO, and confirms that the proposed novel DPSO and schemes can be used to solve the engineering constrained discrete problem successfully.     

扩展拉格朗日乘子粒子群算法解决工程优化问题

工程上很多优化问题,如容器设计、波纹管、板翅式换热器的结构优化设计等,皆为非线性约束优化设计问题,常采用惩罚函数法处理约束条件;为获得问题最优解,该方法需要合理确定初始惩罚因子,且需要动态惩罚因子无穷大。扩展拉格朗日乘子法是一种改进的惩罚函数法,可以克服惩罚函数法的不足,获得全局最优解,但目前对其研究和应用有限。对拉格朗日乘子法与粒子群算法相结合处理非线性约束问题进行研究,提出惩罚因子更新策略,确定扩展拉格朗日乘子粒子群算法合理的操作过程。标准测试函数结果显示：提出的方法及策略实现了扩展拉格朗日乘子粒子群算法解决非线性约束问题,并得到了问题的全局最优解;其在容器及波纹管系列优化设计中的应用进一步显示,提出的方法在处理非线性约束工程实际问题时,运行稳定可靠,可快捷获得问题的全局最优解或近似最优解。     

Solutions of nonlinear constrained optimal control problems using quasilinearization and variational pseudospectral methods

An alternative method for nonlinear constrained optimal control problems is developed in this paper. The proposed method converts the nonlinear optimal control problem into a sequence of constrained linear quadratic (LQ) optimal control problems using quasilinearization methods. And then we present a variational pseudospectral method based on dual variational principles and pseudospectral approximations in order to transform the constrained LQ problem into standard linear complementary problems (LCPs) which can be solved easily. The proposed method is highly efficient due to the benefits of qualsilineaization techniques and the sparse and symmetric properties of coefficient matrixes obtained by variational principles. And solutions of high precisions can be obtained with few time nodes and boundary conditions can be prescribed because of pseudospectral approximations. Besides, extra costate estimations are not required simply because this method is constructed by dual variational principles. Several numerical examples are simulated and comparisons between different methods are offered to demonstrate effectiveness and advantages of the proposed method.     

Preference adjustable multi-objective NMPC: An unreachable prioritized point tracking method

This paper proposes a new preference adjustable multi-objective model predictive control (PA-MOMPC) law for constrained nonlinear systems. With this control law, a reasonable prioritized optimal solution can be directly derived without constructing the Pareto front by solving a minimal optimization problem, which is a novel development of recently proposed utopia tracking approaches by additionally considering objective preferences with more flexible terminal and stability constraints. The tracking point of the proposed PA-MOMPC law is represented by a parametric vector with the parameters adjustable on the basis of objective preferences. The main result of this paper is that the solution obtained through the proposed PA-MOMPC law is demonstrated to have two important properties. One is the inherent Pareto optimality, and the other is the priority consistency between the solution and the tuning parametric vector. This combination makes the objective priorities tuning process transparent and efficient. The proposed PA-MOMPC law is supported by feasibility analyses, proof of nominal stability, and a numerical case study.