Study of a hull form optimization system based on a Gaussian process regression algorithm and an adaptive sampling strategy, Part I: Single-objective optimization

Abstract

Simulation-based design (SBD) is recognized as a hull form optimization method with great advantages, but its development process has exposed two obvious shortcomings: difficulty in uncertainty quantification (UQ) of the surrogate model and inefficiencies when solving large-scale optimization problems. To mitigate these deficiencies, this paper first proposes a UQ method for the surrogate model based on a Gaussian process regression (GPR) algorithm. Mathematical optimization results show that when the number of samples is insufficient, coupling this UQ method into the deterministic optimization process can, to some extent, reduce the uncertainty of the optimization results. The drawback of the SBD over-reliance on the surrogate model for global prediction accuracy is addressed by designing a hull form optimization system that performs the sequential sampling specifically for the region of interest. This method is referred to as sequential sampling-based optimization (SBO). It was combined with the basic properties of a GPR surrogate model, and a variety of adaptive sampling strategies suitable for the SBO optimization system were designed. Mathematical optimization results show that a hybrid optimization system, SBO-MSE + LCB, which uses the adaptive sampling strategy with the maximum squared error (MSE) and the minimum lower confidence bound (LCB) of the GPR surrogate model has the best efficiency when solving single-objective optimization problems. This method was also used for optimization design of the total resistance coefficient of a 130,000-ton deep-sea aquaculture vessel. The results show that the optimization efficiency of the SBO-MSE + LCB optimization system was improved by 46.67% with respect to that of a conventional SBD optimization system when the optimization solutions were similar, hence demonstrating the efficiency advantage of this system in practical applications.