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.