Latent variable crossover for k-tablet structures and its application to lens design problems
Latent variable crossover for k-tablet structures and its application to lens design problems
复制标题
k-片结构的潜变量交叉及其在镜片设计问题中的应用
DOI：
10.1145/1068009.1068226
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
S. Kobayashi
中科院分区：
文献类型：
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作者：
J. Sakuma;S. Kobayashi
本文提出了一种求解高维病态结构的实数编码遗传算法，即k-平板结构。k片结构是指适应度函数的尺度在k维子空间和正交（n-k）维子空间之间是不同的。当适应度函数的景观中包含高维k片结构时，传统GAs的搜索速度会下降。在这种结构中，杂交产生的后代可能比亲本种群所覆盖的区域分布得更广，这导致了搜索的停滞。为了解决这个问题，我们提出了一个新的交叉LUNDX-m，只使用m维潜在变量。通过若干基准函数（包括k片结构）测试了该方法的有效性，结果表明，当维数n大于100时，该方法的性能优于传统的交叉算法。作为一个k片结构在实际应用中的例子，我们证明了透镜设计问题具有一种k片结构，并且我们提出的方法在这个问题上也比传统的交叉算法表现得更好。
This paper presents the Real-coded Genetic Algorithms for high-dimensional ill-scaled structures, what is called, the k-tablet structure. The k-tablet structure is the landscape that the scale of the fitness function is different between a k-dimensional subspace and the orthogonal (n-k)-dimensional subspace. The search speed of traditional GAs degrades when a high dimensional k-tablet structure is included in the landscape of the fitness function.In this structure, offspring generated by crossovers are likely to spread wider region than the region where the parental population covers and this causes the stagnation of the search. To resolve this problem, we propose a new crossover LUNDX-m using only m-dimensional latent variables. The effectiveness of the proposal method is tested with several benchmark functions including k-tablet structures and we show that our proposed method performs better than traditional crossovers especially when the dimensionality n is higher than 100.As an example of a k-tablet structure in real world applications, we show that the lens design problem has a kind of k-tablet structures and that our proposed method also performs better than conventional crossovers in this problem.