A combinatorial algorithm for the discrete optimization of structures

The definition of local optimum solution of the discrete optimization is first given, and then a comprehensive combinatorial algorithm is proposed in this paper. Two-level optimum method is used in the algorithm. In the first level optimization, an approximate local optimum solution is found by using the heuristic algorithm, relative difference quotient algorithm, with high computational efficiency and high performance demonstrated by the performance test of random samples. In the second level, a mathematical model of (-1, 0, 1) programming is established first, and then it is changed into (0, 1) programming model. The local optimum solution X^* will be from the (0, 1) programming by using the delimitative and combinatorial algorithm or the relative difference quotient algorithm. By this algorithm, the local optimum solution can be obtained certainly, and a method is provided to judge whether or not the approximate optimum solution obtained by heuristic algorithm is an optimum solution. The above comprehensive combinatorial algorithm has higher computational efficiency.Project supported by Natural Science Foundation of Shandong Province     

包含两类变量的离散变量桁架结构拓扑优化设计

建立了包含截面和拓扑两类变量的离散变量结构拓扑优化设计的数学模型,该模型考虑了截面变量与拓扑变量间的耦合关系,反映了拓扑优化问题的组合优化本质,可以较好地解决"极限应力"、"最优解的奇异性"等困扰结构拓外优化设计的问题．同时采用相对差商法进行离散变量桁架结构拓扑优化,直接求解包含两类变量的离散变量结构拓扑优化设计数学模型,收到了比较满意的效果．     

离散变量结构优化设计的相对差商-遗传算法

将相对差商法(RDQA)和遗传算法(GA)结合起来,提出一个离散变量结构优化设计的有效解法———相对差商-遗传算法。3个算例结果显示出其优于相对差商法与遗传算法:(1)大大提高了遗传算法搜索全局最优解的能力及计算效率;(2)间接证明了相对差商法具有足够的逼近全局最优解的能力。     

离散变量框架结构的可靠性优化

以框架结构系统的可靠性分析为基础,给出离散变量框架结构可靠性优化的相对差商方法及迭代格式,并用算例证明了该法的有效性及实用性。     

面向工程全局优化的混沌优化算法研究进展Research advances of chaos optimization algorithms for engineering global optimization

近年来,基于混沌的初值敏感性、伪随机性、遍历性以及自相似分形等非线性动力学特性所发展的混沌优化方法,是一种有潜力的工程全局优化新工具,已广泛应用于科学与工程技术的各学科领域。根据混沌优化方法的发展历程,以算法基本思想和工程应用研究状况为重点,评述了混沌神经网络优化方法、第一类混合混沌优化算法（基于混沌搜索）、第二类混合混沌优化算法（混沌序列代替随机序列）以及混沌分形优化四种主要混沌优化算法。混沌映射最早被引入神经网络,发展了混沌神经网络优化方法,可解决复杂的组合优化等全局优化问题。遗传算法及粒子群等启发式随机算法虽具全局搜索能力,但易出现早熟并陷入局部最优。然后,出现了混沌搜索的概念,研究者将其嵌入启发式算法建立了第一类混合混沌优化算法,可有效克服原启发式算法早熟收敛的缺点。随后,利用混沌映射产生的混沌序列代替启发式算法中的随机参数形成了第二类混合混沌优化算法。混合混沌优化算法有益于实现快速全局收敛和提高计算精度。最后,利用混沌分形特性,从分形理论出发提出一类新颖的混沌分形优化算法,可搜索到优化问题的所有全局最优解。此外,对混沌优化算法研究的几个发展方向进行了展望,诸如加强混沌优化算法的参数设计、处理大规模优化、多目标优化问题以及使用代理模型等。     

相对差商算法性能的统计研究

本文通过服从一致分布随机算例的均匀抽样方式，对离散变量优化问题的相对差商算法进行了数值实验，按启发式算法的性能评价指标对数值实验结果进行了统计分析，为评价相对差商算法的实际性能提供了统计依据     

框架结构的可靠性优化

以框架结构系统的可靠性分析为基础,给出离散变量框架结构可靠性优化的相对差商方法及迭代格式,并用算例证明了该法的有效性及实用性。     

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.     

采用小生境技术的混合蛙跳算法

混合蛙跳算法是一种新兴的启发式全局优化算法。本文研究了其寻优机制,提出了一种采用小生境技术的混合蛙跳算法：运用RCS小生境技术,使各子种群动态形成了互相独立的搜索空间;在解的更新公式中,设计了一种自适应因子来调节移动步长;采用种群淘汰机制,随机初始化已陷入局部最优的子种群。实验结果表明：本文给出的算法有效提高了寻优精度和收敛速度。     

离散变量结构拓扑优化设计研究

研究了离散变量结构拓扑优化设计的若干问题，讨论了离散型优化模型的合理性，提出截面设计变量的离散程度和全局约束影响最优拓扑，是优化中不可忽视的因素，文中还提出了一种解离散变量桁架，刚架结构拓扑优化的启发式算法。     

具有动应力和动位移约束的离散变量结构形状优化设计方法

讨论了动应力、动位移约束下离散变量状优化设计问题。首先用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,然后将考虑动应力约束和动作移约束的离散变量结构优化设计问题化为静应力和静位移约束的优化问题。在求解过程中,将单元内力作了一阶近似,并将多约束问题转化为单约束问题,然后利用两类变量统一考虑的离散变量结构形状优化设计的综合算法进行求解。     

Numerical performance of two formulations of truss topology optimization

The present paper studies topology optimization of truss structures in multiple loading cases and with stress constraints. It is pointed out in the paper that the special difficulty of adding bars and/or deleting bars from structure in the numerical algorithm of truss topology optimization is caused by the discontinuity of stress functions at the zero cross sectional area in the conventional formulation. In a new formulation, we replace the stress constraints by new constraints. The new constraints retain the same feasibility of the stress constraints, but are continuous in the closed interval up to zero cross sectional area. The new formulation enables us to solve topology optimization problem in the frame of the existing FEM software and mathematical programming techniques. Powell constrained variable metric method is applied to a number of examples of truss topology optimization. Numerical performances of the two formulations are compared. It is shown that in the conventional formulation the iteration of numerical algorithm may be blocked by discontinuity of the stress constraint and often stops at a nonoptimum solution. And in the new formulation the bar adding and bar deleting is done rationally and a local optimum, even the global optimum can be obtained by iteration. The project supported by the National Natural Science Foundation of China     

两类变量综合处理的结构形状优化设计方法

本文针对截面变量为离散变量为连续变量的结构优化问题提出了一种优化设计的方法,首先将单元内力作一阶近似,利用凝聚函数多约束问题转化了单约束问题。在解过程中,把定义在连续区间上的形状变量看成是在一些离散以值的离工用变量,然后将两类变量统一考虑并利用相对差商法求解。将该算法应用于几个经典的结构优化算例,运算结果显示了该方法是可行的,优化结果也比较满意。     

基于层次分解方法的桁架结构形状优化

对于桁架结构形状优化,应用层次分解优化方法,将设计变量分成杆件截面积和节点位置两类变量。求解时分为两层,第一层在给定节点位置下对杆件截面进行优化,同时考虑了应力、局部稳定约束和位移约束的重量最轻;第二层假定截面层的有效位移约束作用不变,求解一个使桁架刚度增强的二次规划问题,获得既不违反约束,又使目标函数不上升的新的节点位置,再返回第一层。两层交替进行直至收敛。     

非光滑优化的双层规划模型及内点算法

对于包含接触约束的非光滑结构优化问题,其非光滑性体现在状态函数并不是处处可微的,针对含有应力约束及接触约束的非光滑结构优化问题,建立了一种双层规划模型,避免了求解时非光滑性所带来的问题,同时提出了一种迭代算法,用对偶内点二次规划进行分析,线性规划进行优化,算例表明这种方法十分有效。     

Studies on optimal topology design of structures with discrete variables

Some problems in the optimal topology design of structures with discrete variables are studied in this paper. The problem of a model of discrete optimization is discussed and a neglected fact that discrete optimum design may be controlled by the discreteness of sizing variables and global constraints is pointed out. A heuristic algorithm for solving discrete topology optimization problems of trusses and frames is proposed.     

A Method for Topological Optimization of Structures with Discrete Variables under Dynamic Stress and Displacement Constraints

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自适应Kriging近似模型及其在二维扩压器优化设计中的应用

将均匀设计方法、CFD技术、Kriging近似模型及小生境微种群遗传算法相结合发展了一种自适应全局优化设计方法.优化过程中综合考虑Kriging模型的预测值与预测标准差,引入了EI(Expected Improvement)函数得到校正点,解决了采用近似模型最优策略得到校正点带来的局部收敛问题.分别采用该方法和小生境微...     

油井套管结构的最小成本设计

油井套管的最小成本设计是工程中关心的问题,本文提出了Fibonacci搜索法与相对差商法相结合的套管截面尺寸参数和扶正器布局问题的混合整数-离散变量优化方法,解决了多工况、多约束下套管结构的优化问题,已应用于工程实际。     

正交异性钢桥面系的多目标离散优化设计

将大跨径钢桥的正交异性钢桥面板和其上的铺装层作为钢桥面铺装体系整体进行多目标优化设计.取钢桥面铺装体系结构总重量最轻及铺装层使用年限最长两类指标构造目标函数,在此基础上采用功效函数法确定了目标函数的权重系数.应用正交异性钢桥面系力学性能控制指标和疲劳寿命预测公式,建立多目标优化设计的数学模型.引入蚂蚁算法,开发了钢桥面铺装体系结构多目标离散优化设计程序.以国内某大跨径钢桥为对象, 采用多目标优化设计方法, 给出钢桥面铺装体系中各参数的优化值.结果表明, 应用多目标优化设计方法对大跨径钢桥面铺装体系设计是可行的.研究成果可为大跨径钢桥面铺装体系结构的设计提供理论依据.