Cecilia Leotardi

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

Graphical abstractDisplay Omitted HighlightsParametric study of deterministic PSO setting under limited computational resources.Comparison of synchronous and asynchronous implementations.Identification of most significant parameter based on more than 40k optimizations.Identification of most promising and robust setup for simulation-based problems.Hydrodynamic hull-form optimization of a high speed catamaran. Deterministic optimization algorithms are very attractive when the objective function is computationally expensive and therefore the statistical analysis of the optimization outcomes becomes too expensive. Among deterministic methods, deterministic particle swarm optimization (DPSO) has several attractive characteristics such as the simplicity of the heuristics, the ease of implementation, and its often fairly remarkable effectiveness. The performances of DPSO depend on four main setting parameters: the number of swarm particles, their initialization, the set of coefficients defining the swarm behavior, and (for box-constrained optimization) the method to handle the box constraints. Here, a parametric study of DPSO is presented, with application to simulation-based design in ship hydrodynamics. The objective is the identification of the most promising setup for both synchronous and asynchronous implementations of DPSO. The analysis is performed under the assumption of limited computational resources and large computational burden of the objective function evaluation. The analysis is conducted using 100 analytical test functions (with dimensionality from two to fifty) and three performance criteria, varying the swarm size, initialization, coefficients, and the method for the box constraints, resulting in more than 40,000 optimizations. The most promising setup is applied to the hull-form optimization of a high speed catamaran, for resistance reduction in calm water and at fixed speed, using a potential-flow solver.

Formulation and parameter selection of multi-objective deterministic particle swarm for simulation-based optimization

Abstract Global derivative-free deterministic algorithms are particularly suitable for simulation-based optimization, where often the existence of multiple local optima cannot be excluded a priori, the derivatives of the objective functions are not available, and the evaluation of the objectives is computationally expensive, thus a statistical analysis of the optimization outcomes is not practicable. Among these algorithms, particle swarm optimization (PSO) is advantageous for the ease of implementation and the capability of providing good approximate solutions to the optimization problem at a reasonable computational cost. PSO has been introduced for single-objective problems and several extension to multi-objective optimization are available in the literature. The objective of the present work is the systematic assessment and selection of the most promising formulation and setup parameters of multi-objective deterministic particle swarm optimization (MODPSO) for simulation-based problems. A comparative study of six formulations (varying the definition of cognitive and social attractors) and three setting parameters (number of particles, initialization method, and coefficient set) is performed using 66 analytical test problems. The number of objective functions range from two to three and the number of variables from two to eight, as often encountered in simulation-based engineering problems. The desired Pareto fronts are convex, concave, continuous, and discontinuous. A full-factorial combination of formulations and parameters is investigated, leading to more than 60,000 optimization runs, and assessed by three performance metrics. The most promising MODPSO formulation/parameter is identified and applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions. Its performance is finally compared with four stochastic algorithms, namely three versions of multi-objective PSO and the genetic algorithm NSGA-II.

A Proposal of PSO Particles' Initialization for Costly Unconstrained Optimization Problems: ORTHOinit

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.

Dense orthogonal initialization for deterministic PSO: ORTHOinit+

This paper describes a novel initialization for Deterministic Particle Swarm Optimization (DPSO), based on choosing specific dense initial positions and velocities for particles. This choice tends to induce orthogonality of particles’ trajectories, in the early iterations, in order to better explore the search space. Our proposal represents an improvement, by the same authors, of the theoretical analysis on a previously proposed PSO reformulation, namely the initialization ORTHOinit. A preliminary experience on constrained Portfolio Selection problems confirms our expectations.

Multi-fidelity Adaptive global metamodel of expensive computer simulations

The paper presents a multi-fidelity global metamodel for expensive computer simulations, developed as an essential part of efficient simulation-based design optimization under uncertainty. High- and low-fidelity solvers are managed through a multi-fidelity adaptive sampling procedure. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high- and low-fidelity simulations. The metamodels are based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are placed where the prediction uncertainty is maximum. The prediction uncertainty of both the low-fidelity and the error metamodel is considered for the adaptive refinement of the low- and high-fidelity training set, respectively. The method is demonstrated through three analytical test problems and one simple industrial application in ship hydrodynamics. The fitting error of the multi-fidelity metamodel is used as evaluation metric. The comparison with a high-fidelity-trained metamodel shows the effectiveness of the present method.