Constrained optimization problems can be difficult because their search spaces have properties not conducive to search, e.g., multimodality, discontinuities, or deception. To address such difficulties, considerable research has been performed on creating novel evolutionary algorithms or specialized genetic operators. However, if the representation that defined the search space could be altered such that it only permitted valid solutions that satisfied the constraints, the task of finding the optimal would be made more feasible without any need for specialized optimization algorithms. We propose the use of a Variational Autoencoder to learn such representations. We present Constrained Optimization in Latent Space (COIL), which uses a VAE to generate a learned latent representation from a dataset comprising samples from the valid region of the search space according to a constraint, thus enabling the optimizer to find the objective in the new space defined by the learned representation. We investigate the value of this approach on different constraint types and for different numbers of variables. We show that, compared to an identical GA using a standard representation, COIL with its learned latent representation can satisfy constraints and find solutions with distance to objective up to two orders of magnitude closer.
翻译:由于搜索空间的特性不利于搜索,例如多式联运、不连续或欺骗等,因此限制优化问题可能比较困难。为了解决这些困难,已经对创建新的进化算法或专门的遗传操作者进行了大量研究。然而,如果能够改变确定搜索空间的表述,使之只允许有效的解决办法满足这些制约因素,那么寻找最佳方法的任务将变得更加可行,而不需要专门的优化算法。我们建议使用一个变式自动编码器来学习这种表达方式。我们介绍了在远程空间的控制优化(COIL),我们利用VAE从由来自有效搜索空间区域的样本组成的数据集中产生一个学习到的潜在代表方式,从而使得优化者能够在所了解的代表所定义的新空间中找到目标。我们对不同制约类型和不同数量变量的这一方法的价值进行了调查。我们表明,与使用标准表达方式的相同GA相比,COIL及其所学到的潜在代表方式可以满足各种限制,并找到距离目标距离近至两级的解决方案。