Surrogate-assisted evolutionary algorithms (EAs) have been intensively used to solve computationally expensive problems with some success. However, traditional EAs are not suitable to deal with high-dimensional expensive problems (HEPs) with high-dimensional search space even if their fitness evaluations are assisted by surrogate models. The recently proposed autoencoder-embedded evolutionary optimization (AEO) framework is highly appropriate to deal with high-dimensional problems. This work aims to incorporate surrogate models into it to further boost its performance, thus resulting in surrogate-assisted AEO (SAEO). It proposes a novel model management strategy that can guarantee reasonable amounts of re-evaluations; hence, the accuracy of surrogate models can be enhanced via being updated with new evaluated samples. Moreover, to ensure enough data samples before constructing surrogates, a problem-dimensionality-dependent activation condition is developed for incorporating surrogates into the SAEO framework. SAEO is tested on seven commonly used benchmark functions and compared with state-of-the-art algorithms for HEPs. The experimental results show that SAEO can further enhance the performance of AEO on most cases and SAEO performs significantly better than other algorithms. Therefore, SAEO has great potential to deal with HEPs.

Evolutionary computation is a rapidly evolving field and the related algorithms have been successfully used to solve various real-world optimization problems. The past decade has also witnessed their fast progress to solve a class of challenging optimization problems called high-dimensional expensive problems (HEPs). The evaluation of their objective fitness requires expensive resource due to their use of time-consuming physical experiments or computer simulations. Moreover, it is hard to traverse the huge search space within reasonable resource as problem dimension increases. Traditional evolutionary algorithms (EAs) tend to fail to solve HEPs competently because they need to conduct many such expensive evaluations before achieving satisfactory results. To reduce such evaluations, many novel surrogate-assisted algorithms emerge to cope with HEPs in recent years. Yet there lacks a thorough review of the state of the art in this specific and important area. This paper provides a comprehensive survey of these evolutionary algorithms for HEPs. We start with a brief introduction to the research status and the basic concepts of HEPs. Then, we present surrogate-assisted evolutionary algorithms for HEPs from four main aspects. We also give comparative results of some representative algorithms and application examples. Finally, we indicate open challenges and several promising directions to advance the progress in evolutionary optimization algorithms for HEPs.

Biogeography-based optimization (BBO), a recent proposed metaheuristic algorithm, has been successfully applied to many optimization problems due to its simplicity and efficiency. However, BBO is sensitive to the curse of dimensionality; its performance degrades rapidly as the dimensionality of the search space increases. In this paper, a selective migration operator is proposed to scale up the performance of BBO and we name it selective BBO (SBBO). The differential migration operator is selected heuristically to explore the global area as far as possible whist the normal distributed migration operator is chosen to exploit the local area. By the means of heuristic selection, an appropriate migration operator can be used to search the global optimum efficiently. Moreover, the strategy of cooperative coevolution (CC) is adopted to solve large-scale global optimization problems (LSOPs). To deal with subgroup imbalance contribution to the whole solution in the context of CC, a more efficient computing resource allocation is proposed. Extensive experiments are conducted on the CEC 2010 benchmark suite for large-scale global optimization, and the results show the effectiveness and efficiency of SBBO compared with BBO variants and other representative algorithms for LSOPs. Also, the results confirm that the proposed computing resource allocation is vital to the large-scale optimization within the limited computation budget.

Cancer subtyping (or cancer subtypes identification) based on multi-omics data has played an important role in advancing diagnosis, prognosis and treatment, which triggers the development of advanced multi-view clustering algorithms. However, the high-dimension and heterogeneity of multi-omics data make great effects on the performance of these methods. In this paper, we propose to learn the informative latent representation based on autoencoder (AE) to naturally capture nonlinear omic features in lower dimensions, which is helpful for identifying the similarity of patients. Moreover, to take advantage of survival information or clinical information, a multi-omic survival analysis approach is embedded when integrating the similarity graph of heterogeneous data at the multi-omics level. Then, the clustering method is performed on the integrated similarity to generate subtype groups. In the experimental part, the effectiveness of the proposed framework is confirmed by evaluating five different multi-omics datasets, taken from The Cancer Genome Atlas. The results show that AE-assisted multi-omics clustering method can identify clinically significant cancer subtypes.