高维最优化问题的有效遗传算法的活动子空间监督学习方法
A supervised learning approach involving active subspaces for an efficient genetic algorithm in high-dimensional optimization problems
摘要：
在这项工作中，我们提出了一个扩展的遗传算法（GA），它利用监督学习技术称为主动子空间（AS）进化的个人在一个较低的维度空间。在许多情况下，遗传算法实际上需要比其他最优化方法更多的函数求值来收敛到全局最优值。因此，复杂和高维函数可能导致非常苛刻的（从计算的角度来看），以优化与标准算法。为了解决这个问题，我们提出了线性映射的输入参数空间的原始功能到其AS的进化之前，执行变异和交配过程中的一个较低的维空间。在这方面的贡献，我们描述了新的方法称为ASGA，提出与标准GA方法的差异和相似之处。我们在n维基准函数上测试了所提出的方法- Rosenbrock，Ackley，Bohachevsky，Rastrigin，Schaffer N。7，和Zakharov --最后我们将其应用于一个航空外形最优化问题。
英文摘要：
In this work, we present an extension of the genetic algorithm (GA) which exploits the supervised learning technique called active subspaces (AS) to evolve the individuals on a lower dimensional space. In many cases, GA requires in fact more function evaluations than others optimization method to converge to the global optimum. Thus, complex and high-dimensional functions may result extremely demanding (from computational viewpoint) to optimize with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over n-dimensional benchmark functions -- Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov -- and finally we apply it to an aeronautical shape optimization problem.
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