Derivative-free global ship design optimization using global/local hybridization of the DIRECT algorithm

Abstract

The application of global/local hybrid DIRECT algorithms to the sim- ulation-based hull form optimization of a military vessel is presented, aimed at the reduction of the resistance in calm water. The specific features of the black-box-type objective function make the problem suitable for the application of DIRECT-type algorithms. The objective function is given by numerical iterative procedures, which could lead to inaccurate derivative calculations. In addition, the presence of local minima cannot be excluded a priori. The algorithms proposed (namely DIRMIN and DIRMIN-2) are hybridizations of the classic DIRECT algorithm, with deterministic derivative-free local searches. The algorithms’ performances are first assessed on a set of test problems, and then applied to the ship optimization application. The numerical results show that the local hybridization of the DIRECT algorithm has beneficial effects on the overall computational cost and on the efficiency of the simulation-based optimization procedure

Parameter selection in synchronous and asynchronous deterministic particle swarm optimization for ship hydrodynamics problems

“…f is the associated normalized distance in the image space, where f min is the minimum found by the algorithm, f min is the analytical minimum, and f max is the analytical maximum of the function f(x) in the domain L. t is a combination of x and f and is used for an overall assessment. Additionally, the relative variability 2 r,k [29] for each metric…”

“…The approach includes a preliminary parametric analysis on 100 analytical test functions [26][27][28][29] characterized by different degrees of non-linearities and number of local minima, with fullfactorial combination of: (a) number of particles (using a power of two times the number of design variables); (b) initialization of the particle position and velocity (using Hammersley sequence sampling (HSS) [30]); (c) set of coefficients, chosen from literature [12,16,17,31,32]; (d) inelastic and semi-elastic wall-type approach for box constraints [22]. In order to handle the box constraints, wall-type approaches are preferred instead of penalty approaches or Lagrangian functions, which might introduce additional bias in the analysis.…”

Ship hydrodynamic optimization by local hybridization of deterministic derivative-free global algorithms

“…DIRMIN-2 is a global/local hybridization of the DIRECT algorithm and a variant of DIRMIN [28,14]. Differently from DIRMIN, that performs as many local searches as the number of identified potentially optimal hyper-rectangles, DIRMIN-2 performs a single derivativefree local minimization per iteration, starting from the best point produced by dividing the potentially-optimized hyper-rectangles.…”

“…The local search is not allowed to violate the box constraints. The performance of the algorithm varying the tolerance ˇ and the activation trigger has been studied in [14], where DIRMIN-2 is applied to a ship optimization problem. Herein the following set up are used: = 0.25, ˇ = 10 −3 for problem I, and = 0, ˇ = 10 −2 for problem II.…”

“…The other two algorithms are hybrid global/local techniques integrated in (a) and (b), respectively, enhancing the global methods with proved stationarity of the final solution. A hybrid DIRECT method coupled with line search-based derivative-free optimization, namely DIRMIN-2 [14], and a hybrid DPSO coupled with line search-based derivative-free optimization, namely LS-DF PSO [15] are presented and applied.…”