International Journal of Naval Architecture and Ocean Engineering

The Society of Naval Architects of Korea (대한조선학회)
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A cross-entropy algorithm based on Quasi-Monte Carlo estimation and its application in hull form optimization

  • Liu, Xin (Weihai Institute of Marine Information Science and Technology, Shandong Jiaotong University) ;
  • Zhang, Heng (Wuchang Shipbuilding Industry Group Co., Ltd.) ;
  • Liu, Qiang (Wuchang Shipbuilding Industry Group Co., Ltd.) ;
  • Dong, Suzhen (SOYOTEC LIMITED) ;
  • Xiao, Changshi (Hubei Key Laboratory of Inland Shipping Technology)
  • Received : 2020.05.23
  • Accepted : 2021.01.05
  • Published : 2021.11.30
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Abstract

Simulation-based hull form optimization is a typical HEB (high-dimensional, expensive computationally, black-box) problem. Conventional optimization algorithms easily fall into the "curse of dimensionality" when dealing with HEB problems. A recently proposed Cross-Entropy (CE) optimization algorithm is an advanced stochastic optimization algorithm based on a probability model, which has the potential to deal with high-dimensional optimization problems. Currently, the CE algorithm is still in the theoretical research stage and rarely applied to actual engineering optimization. One reason is that the Monte Carlo (MC) method is used to estimate the high-dimensional integrals in parameter update, leading to a large sample size. This paper proposes an improved CE algorithm based on quasi-Monte Carlo (QMC) estimation using high-dimensional truncated Sobol subsequence, referred to as the QMC-CE algorithm. The optimization performance of the proposed algorithm is better than that of the original CE algorithm. With a set of identical control parameters, the tests on six standard test functions and a hull form optimization problem show that the proposed algorithm not only has faster convergence but can also apply to complex simulation optimization problems.

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Acknowledgement

This research was supported by the National Natural Science Foundation of China (Grant No: 51709213, No: 551720105011, No: 51979211). The authors thank the editors and reviewers for suggesting valuable improvements to the paper.

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