遗传算法及其在复合材料层合板设计中应用的研究
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摘要
遗传算法是近年来飞速发展的一种通用性强，稳定性好，具有全局收敛性的优化方法。本文的主要目的是研究遗传算法的优化机理并将遗传算法应用到复合材料层合板的优化设计中，致力于发展一种无需依赖梯度信息和初始条件的新型的复合材料层合板优化设计方法。
本文在基本遗传算法的基础上首先研究了浮点编码遗传算法在数值优化中的应用，通过引进“移民策略”和自适应算子相结合的方法，改进了基本遗传算法在后期进化缓慢的问题，极大地减少了早熟性收敛的现象。其次，本文根据层合板优化设计的具体问题提出了一种符号编码方式，虽然优化参数的基因编码表达方式并不能改变优化问题的本质，但是不同的编码表达方式对于遗传算法搜索的效率和最终的优化结果有着重要的影响，因此优化参数的基因编码表达是遗传算法应用于工程问题中非常关键的一步。本文中的编码方式的思想简单直观，使用方便，易于进行遗传算法的交叉、变异操作，取得了令人满意的效果。
本文阐述了层合板强度分析的方法，通过和遗传算法相结合提出了一种不依赖于初始条件和梯度信息的新型的优化设计方法。同时针对强度优化的具体问题构造合适的适应度函数，并且通过采用“局部退化算子”和“自适应算子”相结合的方法较好地解决了基本遗传算法中常见的早熟性收敛问题。
泊松比是反映物体体积变化的性能参数，大部分材料的泊松比为正值且集中在0.3附近。本文通过对层合板泊松比和铺层角度关系的研究后指出，经过设计的层合板不仅可以具有超过1.0以上的正泊松比，还可以有负的泊松比，这种现象对于普通材料无法想象的。层合板这种特殊的性能在很多方面都可以有广泛的应用。应用遗传算法对层合板的泊松比进行优化设计的结果进一步证明了层合板具有特殊泊松比这一特殊的性能和设计的可操作性。
层合板的热膨胀系数是判断层合板热稳定性的重要指标，由于航空领域材料的特殊要求，零膨胀系数的材料是最为理想的。本文通过对层合板热膨胀系数的研究和设计，指出了过去常用的零膨胀系数的工程设计方法在精度上的不足，应用遗传算法进行优化设计的层合板更加接近真正意义上的零膨胀。另外应用遗传算法对由多种材料组成的层合板进行了零膨胀系数的设计，弥补了工程设计方法只能对由单一材料构成的层合板进行设计的不足。
复合材料层合板设计是一个涉及因素较多的多目标优化问题，由于多目标设计问题本身的特点——各个优化目标之间经常是相互制约的，在绝大多数情况下无法找到
遗传算法及其在复合材料层合板设计中的应用研究
满足所有优化目标的最优解，因此本文在常用的线性加权法的基础上，针对定系数加
权法的不足，把权系数作为优化变量参与优化过程，提出了变系数的线性加权法。另
外根据层合板的特点提出了构造了一种多目标优化函数的方法，利用遗传算法对层合
板进行了优化设计，设计的结果表明，由于遗传算法特有的群体搜索的性质决定了遗
传算法在多目标优化问题中具有特别的优势。
Genetic Algorithms as a good optimization method, which has been rapid developed in the last decades, have feature of robustness and global convergence. The goal of this dissertation is to study the theory of Genetic Algorithm(GA) and to apply it on optimization of composite laminate, then to develop a new gradient free optimization design method.
At first, based on the simple Genetic Algorithm, an improved GA which adopts a combination of emigration policy and adaptive operator is presented. Results of numerical optimization show that the improved GA is effective on preventing premature problem. Second, by combining theories of strength of laminate with GA, a new gradient free optimization method with new code strategy is discussed. The representation itself does not change the nature of the problem, but effects the searching efficiency of the algorithm. So the representation of the parameters to be optimized is a very important factor and the new code strategy is also easy used with crossover operator and variation operator in GA applications. In order to solve the premature problem in strength optimization design of laminate, to combine the part-degenerate operator and adaptive operator is a good idea.
Poisson's ratio is a parameter which measures the volume-changed of objects. Generally, the value of Poisson's ratio is around 0.3, but elaborate laminates can have especial Poisson's ratio more than 1.0, moreover the negative. For sake of using this property, GA is used to design the Poisson's ration of laminate, and some optimization samples are given to show that laminates with this especial performance are available.
Thermal expansion coefficient is an important property of composite laminate. In order to satisfy the special request in aero field, zero expansion coefficient is perfect. On the basis of analyzing the behavior of the thermal expansion coefficient of laminate, a new method used GA has been developed. Compared with results of two methods, GA method is much better than the 'isotropy' method . Furthermore, GA method also overcomes the shortcoming of the ' isotropy' method that can be only used for laminate composed with one kind of material.
Design of composite laminate is a multi-objective optimization problem. The targets of each optimization are not consistent and it is very difficult to find the best solution to satisfy all the targets, which is the nature of multi-objective problem. In order to solve this question, an improved linear weighting method is presented of which the weight factors are changeable. In this method, the weight factors are used for optimize variables during the
algorithm. Based on the method, combined with GA, a multiobjective optimum design of composite laminates is discussed. The results indicate that GA is an efficient method in solving multi-objective problems.
本文在基本遗传算法的基础上首先研究了浮点编码遗传算法在数值优化中的应用，通过引进“移民策略”和自适应算子相结合的方法，改进了基本遗传算法在后期进化缓慢的问题，极大地减少了早熟性收敛的现象。其次，本文根据层合板优化设计的具体问题提出了一种符号编码方式，虽然优化参数的基因编码表达方式并不能改变优化问题的本质，但是不同的编码表达方式对于遗传算法搜索的效率和最终的优化结果有着重要的影响，因此优化参数的基因编码表达是遗传算法应用于工程问题中非常关键的一步。本文中的编码方式的思想简单直观，使用方便，易于进行遗传算法的交叉、变异操作，取得了令人满意的效果。
本文阐述了层合板强度分析的方法，通过和遗传算法相结合提出了一种不依赖于初始条件和梯度信息的新型的优化设计方法。同时针对强度优化的具体问题构造合适的适应度函数，并且通过采用“局部退化算子”和“自适应算子”相结合的方法较好地解决了基本遗传算法中常见的早熟性收敛问题。
泊松比是反映物体体积变化的性能参数，大部分材料的泊松比为正值且集中在0.3附近。本文通过对层合板泊松比和铺层角度关系的研究后指出，经过设计的层合板不仅可以具有超过1.0以上的正泊松比，还可以有负的泊松比，这种现象对于普通材料无法想象的。层合板这种特殊的性能在很多方面都可以有广泛的应用。应用遗传算法对层合板的泊松比进行优化设计的结果进一步证明了层合板具有特殊泊松比这一特殊的性能和设计的可操作性。
层合板的热膨胀系数是判断层合板热稳定性的重要指标，由于航空领域材料的特殊要求，零膨胀系数的材料是最为理想的。本文通过对层合板热膨胀系数的研究和设计，指出了过去常用的零膨胀系数的工程设计方法在精度上的不足，应用遗传算法进行优化设计的层合板更加接近真正意义上的零膨胀。另外应用遗传算法对由多种材料组成的层合板进行了零膨胀系数的设计，弥补了工程设计方法只能对由单一材料构成的层合板进行设计的不足。
复合材料层合板设计是一个涉及因素较多的多目标优化问题，由于多目标设计问题本身的特点——各个优化目标之间经常是相互制约的，在绝大多数情况下无法找到
遗传算法及其在复合材料层合板设计中的应用研究
满足所有优化目标的最优解，因此本文在常用的线性加权法的基础上，针对定系数加
权法的不足，把权系数作为优化变量参与优化过程，提出了变系数的线性加权法。另
外根据层合板的特点提出了构造了一种多目标优化函数的方法，利用遗传算法对层合
板进行了优化设计，设计的结果表明，由于遗传算法特有的群体搜索的性质决定了遗
传算法在多目标优化问题中具有特别的优势。
Genetic Algorithms as a good optimization method, which has been rapid developed in the last decades, have feature of robustness and global convergence. The goal of this dissertation is to study the theory of Genetic Algorithm(GA) and to apply it on optimization of composite laminate, then to develop a new gradient free optimization design method.
At first, based on the simple Genetic Algorithm, an improved GA which adopts a combination of emigration policy and adaptive operator is presented. Results of numerical optimization show that the improved GA is effective on preventing premature problem. Second, by combining theories of strength of laminate with GA, a new gradient free optimization method with new code strategy is discussed. The representation itself does not change the nature of the problem, but effects the searching efficiency of the algorithm. So the representation of the parameters to be optimized is a very important factor and the new code strategy is also easy used with crossover operator and variation operator in GA applications. In order to solve the premature problem in strength optimization design of laminate, to combine the part-degenerate operator and adaptive operator is a good idea.
Poisson's ratio is a parameter which measures the volume-changed of objects. Generally, the value of Poisson's ratio is around 0.3, but elaborate laminates can have especial Poisson's ratio more than 1.0, moreover the negative. For sake of using this property, GA is used to design the Poisson's ration of laminate, and some optimization samples are given to show that laminates with this especial performance are available.
Thermal expansion coefficient is an important property of composite laminate. In order to satisfy the special request in aero field, zero expansion coefficient is perfect. On the basis of analyzing the behavior of the thermal expansion coefficient of laminate, a new method used GA has been developed. Compared with results of two methods, GA method is much better than the 'isotropy' method . Furthermore, GA method also overcomes the shortcoming of the ' isotropy' method that can be only used for laminate composed with one kind of material.
Design of composite laminate is a multi-objective optimization problem. The targets of each optimization are not consistent and it is very difficult to find the best solution to satisfy all the targets, which is the nature of multi-objective problem. In order to solve this question, an improved linear weighting method is presented of which the weight factors are changeable. In this method, the weight factors are used for optimize variables during the
algorithm. Based on the method, combined with GA, a multiobjective optimum design of composite laminates is discussed. The results indicate that GA is an efficient method in solving multi-objective problems.
引文
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