An enhanced surrogate assisted framework, based on Probability of Improvement (PI) method, is proposed in this paper. We made some modifications to the original PI approach to enhance the performance of the modeling and optimization framework, leading to fewer rigorous simulations to find the optimal solution without loss of accuracy. We also extended the algorithm for handling general constraints using a fully probabilistic approach. The behavior of the proposed framework was investigated through a set of 9 Unconstrained Test Functions (UTF), 7 Constrained Optimization Problems (COP) and 3 Chemical Engineering Problems (CEP). The numerical results indicate that a lower number of rigorous model simulations were needed for optimizing UTF compared to the classic PI method and that the proposed framework was capable of achieving sustained near optimal solutions for COP and CEP. These results indicate that the proposed framework is suitable for solving computationally expensive constrained black-box optimization problems.

本文提出了一种基于改进概率（PI）方法的增强型代理辅助框架。我们对原始的PI方法进行了一些修改，以增强建模和优化框架的性能，从而减少了进行精确模拟的次数，以找到最佳解决方案而又不损失准确性。我们还扩展了使用完全概率方法来处理一般约束的算法。通过一组9个无约束测试函数（UTF），7个约束优化问题（COP）和3个化学工程问题（CEP）来研究所提出框架的行为。数值结果表明，与传统的PI方法相比，优化UTF所需的精确模型仿真次数更少，并且所提出的框架能够为COP和CEP实现持续的接近最优的解决方案。这些结果表明，提出的框架适用于解决计算量大的受限黑盒优化问题。