In this paper, we scale evolutionary algorithms to high-dimensional optimization problems that deceptively possess a low effective dimensionality (certain dimensions do not significantly affect the objective function). To this end, an instantiation of the multiform optimization paradigm is presented, where multiple low-dimensional counterparts of a target high-dimensional task are generated via random embeddings. Since the exact relationship between the auxiliary (low-dimensional) tasks and the target is a priori unknown, a multiform evolutionary algorithm is developed for unifying all formulations into a single multi-task setting. The resultant joint optimization enables the target task to efficiently reuse solutions evolved across various low-dimensional searches via cross-form genetic transfers, hence speeding up overall convergence characteristics. To validate the overall efficacy of our proposed algorithmic framework, comprehensive experimental studies are carried out on well-known continuous benchmark functions as well as a set of practical problems in the hyper-parameter tuning of machine learning models and deep learning models in classification tasks and Predator-Prey games, respectively.

翻译：本文针对一类具有欺骗性的高维优化问题——其真实有效维度较低（即某些维度对目标函数影响甚微）——提出了适用于此类问题的进化算法扩展方案。为此，我们构建了多形态优化范式的具体实例：通过随机嵌入技术生成目标高维任务的多个低维对应问题。由于辅助（低维）任务与目标任务之间的确切关系先验不可知，我们开发了一种多形态进化算法，将所有问题形式统一整合至单一多任务学习框架中。这种联合优化机制使目标任务能够通过跨形态遗传传递，高效复用各低维搜索过程中已求解的优质解，从而显著加速整体收敛特性。为全面验证所提算法框架的有效性，我们在经典连续基准函数以及两类实际问题上开展了系统性实验研究：其一为机器学习模型超参数调优任务，其二为深度学习模型在分类任务与捕食者-猎物博弈中的超参数优化。