The hybrid use of exact and heuristic derivative-free methods for global unconstrained optimization problems is presented. Many real-world problems are modeled by computationally expensive functions, such as problems in simulationbased design of complex engineering systems. Objective-function values are often provided by systems of partial differential equations, solved by computationally expensive black-box tools. The objective-function is likely noisy and its derivatives are often not available. On the one hand, the use of exact optimization methods might be computationally too expensive, especially if asymptotic convergence properties are sought. On the other hand, heuristic methods do not guarantee the stationarity of their final solutions. Nevertheless, heuristic methods are usually able to provide an approximate solution at a reasonable computational cost, and have been widely applied to real-world simulation-based design optimization problems. Herein, an overall hybrid algorithm combining the appealing properties of both exact and heuristic methods is discussed, with focus on Particle Swarm Optimization (PSO) and line search-based derivative-free algorithms. The theoretical properties of the hybrid algorithm are detailed, in terms of limit points stationarity. Numerical results are presented for a specific test function and for two real-world optimization problems in ship hydrodynamics.

A proposal for particles' initialization in PSO is presented and discussed, with focus on costly global unconstrained optimization problems. The standard PSO iteration is reformulated such that the trajectories of the particles are studied in an extended space, combining particles' position and speed. To the aim of exploring effectively and efficiently the optimization search space since the early iterations, the particles are initialized using sets of orthogonal vectors in the extended space (orthogonal initialization, ORTHOinit). Theoretical derivation and application to a simulation-based optimization problem in ship design are presented, showing the potential benefits of the current approach.

. A guideline for an effective and efficient use of a deterministic variant of the Particle Swarm Optimization (PSO) algorithm is presented and discussed, assuming limited computational resources. PSO was introduced in Kennedy and Eberhart (1995) and successfully applied in many fields of engineering optimization for its ease of use. Its performance depends on three main characteristics: the number of swarm particles used, their initialization in terms of initial location and speed, and the set of coefficients defining the behavior of the swarm. Original PSO makes use of random coefficients to sustain the variety of the swarm dynamics, and requires extensive numerical campaigns to achieve statistically convergent results. Such an approach can be too expensive in industrial applications, especially when CFD simulations are used, and for this reason, efficient deterministic approaches have been developed (Campana et al. 2009). Additionally, the availability of parallel architectures has offered the opportunity to develop and compare synchronous and asynchronous implementation of PSO. The objective of present work is the identification of the most promising implementation for deterministic PSO. A parametric analysis is conducted using 60 analytical test functions and three different performance criteria, varying the number of particles, the initialization of the swarm, and the set of coeffi- cients. The most promising PSO setup is applied to a ship design optimization problem, namely the high-speed Delft catamaran advancing in calm water at fixed speed, using a potential-flow code.

The paper presents a two-stage approach for ship design optimisation under uncertainties related to stochastic parameters that cannot be controlled by the designer. The designer decision is partitioned into two sets: the first contains variables that have to be decided before the onset of any uncertain condition, while the second Involves variables that may be decided once the random events have occurred. The first-stage variables are selected so that the sum of the first-stage cost and the expectation of the second-stage cost is minimised. The problem is solved as a two-nested-loop minimisation problem, which combines robustness of the first-stage decision with flexibility of the second-stage decision. The approach is applied to the conceptual optimisation of a bulk carrier. © 2010 Institute of Ship Technology and Ocean Engineering.