A multi-objective DIRECT algorithm for ship hull optimization

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of "hard" nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.