Evolutionary Optimization Methods for High-Dimensional Expensive Problems:A Survey

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.

A Bi-population Cooperative Optimization Algorithm Assisted by an Autoencoder for Medium-scale Expensive Problems

This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.