The expected improvement (EI) algorithm is a very popular method for expensive optimization problems. In the past twenty years, the EI criterion has been extended to deal with a wide range of expensive optimization problems. This paper gives a comprehensive review of the EI extensions designed for parallel optimization, multiobjective optimization, constrained optimization, noisy optimization, multi-fidelity optimization and high-dimensional optimization. The main challenges of extending the EI approach to solve these complex optimization problems are pointed out, and the ideas proposed in literature to tackle these challenges are highlighted. For each reviewed algorithm, the surrogate modeling method, the computation of the infill criterion and the internal optimization of the infill criterion are carefully studied and compared. In addition, the monotonicity properties of the multiobjective EI criteria and constrained EI criteria are analyzed in detail. Through this review, we give an organized summary about the EI developments in the past twenty years and show a clear picture about how the EI approach has advanced. In the end of this paper, several interesting problems and future research topics about the EI developments are given.

预期改进（EI）算法是解决昂贵的优化问题的一种非常流行的方法。在过去的二十年中，EI标准已得到扩展，以处理各种昂贵的优化问题。本文对为并行优化，多目标优化，约束优化，噪声优化，多保真度优化和高维优化而设计的EI扩展进行了全面回顾。指出了扩展EI方法以解决这些复杂的优化问题的主要挑战，并着重指出了文献中提出的解决这些挑战的想法。对于每种审查算法，都仔细研究和比较了替代建模方法，填充标准的计算和填充标准的内部优化。此外，详细分析了多目标EI准则和约束EI准则的单调性。通过这次回顾，我们对过去20年的EI发展进行了有组织的总结，并清晰地展示了EI方法的发展情况。在本文的最后，给出了一些有关EI发展的有趣问题和未来的研究主题。