NSGA-Ⅱ多目标优化算法的改进及应用研究
发布时间：2019-01-05 19:12
【摘要】：实际生活中,常会遇到关于多个目标同时优化的各种问题。比如大众消费时都想以便宜的价格买到优质的商品,这个“矛盾”就是一个关于多目标优化的典型事例。在生活中众多领域,多目标优化问题皆扮演着重要角色,包括制造业、运输业、服务业、电信业等行业,多目标优化问题无处不在。为了解决此类多个目标间相互“矛盾”的问题,常常需要将与这些问题相关的多个子目标转化为与之对应的函数表达式,然后再对其进行优化求解,这就是多目标问题的优化。遗传算法(GA)在多目标优化方法中具有独特的优势,特别是近年来广泛研究和应用的多目标优化遗传算法(MOGA)及其相关的衍生算法,以非支配排序遗传算法-Ⅱ(NSGA-Ⅱ)为代表。然而,传统的NSGA-Ⅱ受限于模拟二进制交叉算子(SBX)和多项式变异算子,使非支配个体的全局搜索能力较弱,种群的多样性较差等。针对传统NSGA-Ⅱ中存在的诸多问题,本文提出了一种改进的NSGA-Ⅱ多目标优化算法,经过仿真实验得到满意的Pareto最优解集,并通过实际应用验证了改进的理论成果,解决了多目标优化问题。本文提出改进的NSGA-Ⅱ多目标优化算法,具体研究内容主要体现在以下几个方面:(1)针对不同的多目标优化问题建立数学模型,并结合正交实验法获取实验样本,确定最佳优化参数,提升算法效率,节省运算时间。(2)在进化过程中引入正态分布交叉算子(NDX),有效解决了传统的NSGA-Ⅱ算法中利用模拟二进制交叉算子(SBX)引起的搜索空间狭窄、容易陷入局部最优等问题,增强了算法的空间搜索能力。(3)提出改进的自适应调整变异方式,提高了种群取优速度。对于复杂的非线性优化问题,传统的NSGA-Ⅱ算法采用Deb提出的多项式变异方式,由于这种变异算子中含有随机参数和主观参数,使其随机性较大,收敛速度较慢。改进的自适应调整变异方式能够通过其作用机理得到更好的收敛效果,不仅加快了种群的收敛速度,还维持了种群个体的多样性,使得Pareto边界分布更优。(4)通过改进的NSGA-Ⅱ算法优化聚硅氧烷的合成过程中反应温度、反应时间、催化剂及其助剂的量,得到单分子转化率的最大值和粘度分子量的期望值。实验中定义了解集覆盖度和空间分布量来衡量Pareto解的性能,并采用正交实验法确定最优进化参数。仿真测试结果用量化标准对比证明了改进的NSGA-Ⅱ算法取优特性高于传统的MOGA及其衍生算法,Pareto最优前沿进一步显示改进算法的解集分布更加均匀、连续,验证了本文提出改进的NSGA-Ⅱ多目标优化算法理论在聚合优化中应用的正确性及合理性。
[Abstract]:In real life, there are often problems with multiple goals being optimized at the same time. For example, when people consume, they want to buy quality goods at a low price. This contradiction is a typical example of multi-objective optimization. In many fields of life, multi-objective optimization problems play an important role, including manufacturing, transportation, service, telecommunications and other industries, multi-objective optimization problems everywhere. In order to solve this kind of "contradiction" between multiple objectives, it is often necessary to transform multiple sub-objectives related to these problems into corresponding functional expressions, and then optimize them. This is the optimization of multi-objective problems. Genetic algorithm (GA) has unique advantages in multi-objective optimization, especially (MOGA) and its related derivative algorithms, which have been widely studied and applied in recent years. Undominated sorting genetic algorithm-鈪，
本文编号：2402187
[Abstract]:In real life, there are often problems with multiple goals being optimized at the same time. For example, when people consume, they want to buy quality goods at a low price. This contradiction is a typical example of multi-objective optimization. In many fields of life, multi-objective optimization problems play an important role, including manufacturing, transportation, service, telecommunications and other industries, multi-objective optimization problems everywhere. In order to solve this kind of "contradiction" between multiple objectives, it is often necessary to transform multiple sub-objectives related to these problems into corresponding functional expressions, and then optimize them. This is the optimization of multi-objective problems. Genetic algorithm (GA) has unique advantages in multi-objective optimization, especially (MOGA) and its related derivative algorithms, which have been widely studied and applied in recent years. Undominated sorting genetic algorithm-鈪，
本文编号：2402187
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