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

Abstract

Ships have a wide variety of performance specifications and experience complex navigation conditions. Thus, an efficient numerical optimization system for general hull forms must be able to deal with multi-objective optimization problems. Based on a Gaussian process regression (GPR) algorithm and an adaptive sampling strategy, the authors have developed a single-objective optimization system, SBO-MSE + LCB, which is more efficient than the conventional simulation-based design (SBD) optimization system. However, the application of this system to hull form multi-objective optimization problems presents problems such as excessive new samplings, insufficient exploration of new sample points, and unsuitable convergence criteria. To solve the above problems, we first propose an adaptive sampling strategy based on the idea of spatial clustering. The strategy not only effectively controls the number of sampling numbers at each iteration in the SBO-MSE + LCB optimization system but also enables new sample points to achieve the multi-objective efficient exploration of optimal solution sets for optimization. Then, from the perspective of the convergence and diversity of Pareto optimal solution sets, we design adaptive sampling convergence criteria suitable for multi-objective optimization problems. Based on this, we enable the SBO-MSE + LCB optimization system to solve multi-objective optimization problems and verify its applicability with several cases for which the multi-objective mathematical optimization is performed. Finally, we use the SBO-MSE + LCB multi-objective optimization system and the SBD optimization system to optimize the total resistance coefficient of a deep-sea aquaculture vessel at the scantling and ballast drafts. The results show that the optimization efficiency of the SBO-MSE + LCB multi-objective optimization system is improved by 33.33% from the SBD optimization system for similar optimization performance, proving its advantage in efficiency in practical applications.