Multiform Evolution for High-Dimensional Problems with Low Effective Dimensionality

• URL: http://arxiv.org/abs/2401.00168v1
• Date: Sat, 30 Dec 2023 08:13:47 GMT
• Title: Multiform Evolution for High-Dimensional Problems with Low Effective Dimensionality
• Authors: Yaqing Hou, Mingyang Sun, Abhishek Gupta, Yaochu Jin, Haiyin Piao, Hongwei Ge, Qiang Zhang
• Abstract summary: We scale evolutionary algorithms to high-dimensional optimization problems that deceptively possess a low effective dimensionality. 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.
• Score: 36.44425198302701
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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