Learnable Evolutionary Search Across Heterogeneous Problems via Kernelized Autoencoding

The design of the evolutionary algorithm with learning capability from past search experiences has attracted growing research interests in recent years. It has been demonstrated that the knowledge embedded in the past search experience can greatly speed up the evolutionary process if properly harnessed. Autoencoding evolutionary search (AEES) is a recently proposed search paradigm, which employs a single-layer denoising autoencoder to build the mapping between two problems by configuring the solutions of each problem as the input and output for the autoencoder, respectively. The learned mapping makes it possible to perform knowledge transfer across heterogeneous problem domains with diverse properties. It has shown a promising performance of learning and transferring the knowledge from past search experiences to facilitate the evolutionary search on a variety of optimization problems. However, despite the success enjoyed by AEES, the linear autoencoding model cannot capture the nonlinear relationship between the solution sets used in the mapping construction. Taking this cue, in this article, we devise a kernelized autoencoder to construct the mapping in a reproducing kernel Hilbert space (RKHS), where the nonlinearity among problem solutions can be captured easily. Importantly, the proposed kernelized autoencoding method also holds a closed-form solution which will not bring much computational burden in the evolutionary search. Furthermore, a kernelized autoencoding evolutionary-search (KAES) paradigm is proposed that adaptively selects the linear and kernelized autoencoding along the search process in pursuit of effective knowledge transfer across problem domains. To validate the efficacy of the proposed KAES, comprehensive empirical studies on both benchmark multiobjective optimization problems as well as real-world vehicle crashworthiness design problem are presented.