Hafner Christian, Xudong Cui, Smajic Jasmin, Vahldieck Ruediger
Laboratory for Electromagnetic Fields and Microwave Electronics, ETH Zurich, 8092, Zurich, Switzerland.
J Opt Soc Am A Opt Image Sci Vis. 2007 Apr;24(4):1177-88. doi: 10.1364/josaa.24.001177.
Seven different stochastic binary optimizers--based on the concepts of genetic algorithms and evolutionary strategies--are developed, applied to determine defect locations in several photonic crystal structures that serve as test cases, and compared by extensive statistical analysis. In addition to the stochastic optimizers, a quasi-deterministic optimizer based on an algorithm inspired by hill-climbing algorithms was implemented. The test cases include the prominent 90 degrees photonic crystal waveguide bend and a photonic crystal power divider. The analysis of the results shows that many different photonic crystal structures with high transmission may be found for any operating frequency. All of the eight optimizers outperform standard codes-because they maintain an incomplete fitness table-and find the global optima with a high probability even when the number of fitness evaluations is much smaller than the number of potential solutions contained in the discrete search space. Based on the incomplete fitness table, an algorithm to estimate bit-fitness values is presented. The bit-fitness values are then used to improve the performance of some algorithms. The four best algorithms-an extended microgenetic algorithm, two mutation-based algorithms, and the quasi-deterministic algorithm inspired by hill-climbing algorithms-are considered to be of high value for the optimization of defects in photonic crystals and for similar binary optimization problems.
基于遗传算法和进化策略的概念，开发了七种不同的随机二元优化器，将其应用于确定用作测试案例的几种光子晶体结构中的缺陷位置，并通过广泛的统计分析进行比较。除了随机优化器之外，还实现了一种基于受爬山算法启发的算法的准确定性优化器。测试案例包括著名的90度光子晶体波导弯曲和一个光子晶体功率分配器。结果分析表明，对于任何工作频率，都可以找到许多具有高传输率的不同光子晶体结构。所有这八种优化器都优于标准代码，因为它们维护一个不完整的适应度表，并且即使适应度评估的次数远小于离散搜索空间中包含的潜在解的数量，也能以高概率找到全局最优解。基于不完整的适应度表，提出了一种估计位适应度值的算法。然后使用位适应度值来提高一些算法的性能。四种最佳算法——一种扩展的微遗传算法、两种基于变异的算法以及受爬山算法启发的准确定性算法——被认为对于光子晶体中的缺陷优化以及类似的二元优化问题具有很高的价值。
