Comparison between Deterministic and Stochastic formulations of Particle Swarm Optimization, for Multidisciplinary Design Optimization

Particle Swarm Optimization (PSO) is having a growing space in the optimization community, mainly due to its appreciable qualities of fast initial progress, reduced computational cost and parallel structure, suitable for High Performance Computation (HPC) platforms. Original formulation includes some random co

Resistance reduction of a military ship by variable-accuracy metamodel-based multidisciplinary robust design optimization

A method for simulation-based multidisciplinary robust design optimization (MRDO) affected by uncertainty is presented, based on variable-accuracy metamodelling. The approach encompasses a variable level of refinement of the design of experiments (DoE) used for the metamodel training, a variable accuracy for the uncertainty quantification (UQ), and a variable level of coupling between disciplines for the multidisciplinary analysis (MDA). The results of the present method are compared with a standard MRDO, used as a benchmark and solved by fully coupled MDA and fully accurate UQ, without metamodels. The hull-form optimization of the DTMB 5415 subject to stochastic speed is presented. A two-way steady coupled system is considered, based on hydrodynamics and rigid-body equation of motion. The objective function is the expected value of the total resistance, and the design variables pertain to the modification of the hull form. The effectiveness and the efficiency of the present method are evaluated in terms of optimal design performances and number of simulations required to achieve the optimal design

Resistance reduction of a military ship by variable-accuracy metamodel-based multidisciplinary robust design optimization

A method for simulation-based multidisciplinary robust design optimization (MRDO) affected by uncertainty is presented, based on variable-accuracy metamodelling. The approach encompasses a variable level of refinement of the design of experiments (DoE) used for the metamodel training, a variable accuracy for the uncertainty quantification (UQ), and a variable level of coupling between disciplines for the multidisciplinary analysis (MDA). The results of the present method are compared with a standard MRDO, used as a benchmark and solved by fully coupled MDA and fully accurate UQ, without metamodels. The hull-form optimization of the DTMB 5415 subject to stochastic speed is presented. A two-way steady coupled system is considered, based on hydrodynamics and rigid-body equation of motion. The objective function is the expected value of the total resistance, and the design variables pertain to the modification of the hull form. The effectiveness and the efficiency of the present method are evaluated in terms of optimal design performances and number of simulations required to achieve the optimal design

A proposal of PSO particles' initialization, for costly unconstrained optimization problems: ORTHOinit

Abstract. 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

Initial Particles Position for PSO, in Bound Constrained Optimization

We consider the solution of bound constrained optimization problems, where we assume that the evaluation of the objective function is costly, its derivatives are unavailable and the use of exact derivative free algorithms may imply a too large computational burden. There is plenty of real applications, e.g. several design optimization problems [1,2], belonging to the latter class, where the objective function must be treated as a ‘black-box’ and automatic differentiation turns to be unsuitable. Since the objective function is often obtained as the result of a simulation, it might be affected also by noise, so that the use of finite differences may be definitely harmful. In this paper we consider the use of the evolutionary Particle Swarm Optimization (PSO) algorithm, where the choice of the parameters is inspired by [4], in order to avoid diverging trajectories of the particles, and help the exploration of the feasible set. Moreover, we extend the ideas in [4] and propose a specific set of initial particles position for the bound constrained problem

Penalty Function approaches for Ship Multidisciplinary Design Optimization (MDO)

This paper focuses on the solution of difficult Multidisciplinary Optimization formulations arising in ship design. The latter schemes are by nature the result of the interaction among several optimization problems. Each optimization problem summarizes the issues related to a specic aspect (discipline) of the formulation, and it may be hardly solved by stand-alone methods which ignore the other disciplines. This usually yields very challenging numerical optimization problems, due to the simultaneous solution of dierent schemes. In particular, in our ship design applications we stress the strong interaction between fluid-dynamics and optimization, in order to get remarkable achievements. The ordinary stand-alone methods from mathematical programming prove to be often unsatisfactory on the latter multidisciplinary problems. This scenario requires a specic integration of both Fluid-dynamics and Optimization, where constrained optimization schemes frequently arise. We give evidence that the proper use of Penalty Methods, combined with Global Optimization techniques, may both be a theoretically correct approach, and may yield a fruitful class of techniques for the solution of Multidisciplinary problems. We provide numerical results with dierent penalty functions, over difficult multidisciplinary formulations from ship design. Here, the introduction of penalty methods proved to be a valuable tool since feasibility issues strongly affect the formulation

Mission-based hull-form and propeller optimization of a transom stern destroyer for best performance in the sea environment

An overview is presented of the activities conducted within the NATO STO Task Group AVT-204 to “Assess the Ability to Optimize Hull Forms of Sea Vehicles for the Best Per- formance in a Sea Environment.” The objective is the development of a greater understanding of the potential and limitations of the hydrodynamic optimization tools. These include low- and high-fidelity solvers, automatic shape modification methods, and multi-objective optimiza- tion algorithms, and are limited here to a deterministic application. The approach includes simulation-based design optimization methods from different research teams. Analysis tools include potential flow and Reynolds-averaged Navier-Stokes equation solvers. Design modifica- tion tools include global modification functions, control point based methods, and parametric modelling by hull sections and basic curves. Optimization algorithms include particle swarm optimization, sequential quadratic programming, genetic and evolutionary algorithms. The ap- plication is the hull-form and propeller optimization of the DTMB 5415 model for significant conditions, based on actual missions at sea

On the use of Synchronous and Asynchronous Single-objective Deterministic Particle Swarm Optimization in Ship Design Problems

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 coefficients. 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

Application of derivative-free multi-objective algorithms to reliability-based robust design optimization of a high-speed catamaran in real ocean environment

A reliability-based robust design optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal four-dimensional representation of shape modifications, based on the Karhunen-Loeve expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivative-free multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multi-objective extensions of the deterministic particle swarm optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness.A Reliability-Based Robust Design Optimization (RBRDO) for ship hulls is presented. A real ocean environment is considered, including stochastic sea state and speed. The optimization problem has two objectives: (a) the reduction of the expected value of the total resistance in waves and (b) the increase of the ship operability (reliability). Analysis tools include a URANS solver, uncertainty quantification methods and metamodels, developed and validated in earlier research. The design space is defined by an orthogonal four-dimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull. The objective of the present paper is the assessment of deterministic derivativefree multi-objective optimization algorithms for the solution of the RBRDO problem, with focus on multiobjective extensions of the Deterministic Particle Swarm Optimization (DPSO) algorithm. Three evaluation metrics provide the assessment of the proximity of the solutions to a reference Pareto front and their wideness

Nucleon superfluidity versus thermal states of isolated and transiently accreting neutron stars

The properties of superdense matter in neutron star (NS) cores control NS thermal states by affecting the efficiency of neutrino emission from NS interiors. To probe these properties we confront the theory of thermal evolution of NSs with observations of their thermal radiation. Our observational basis includes cooling isolated NSs (INSs) and NSs in quiescent states of soft X-ray transients (SXTs). We find that the data on SXTs support the conclusions obtained from the analysis of INSs: strong proton superfluidity with T_{cp,max} >= 10^9 K should be present, while mild neutron superfluidity with T_{cn,max} =(2*10^8 -- 2*10^9) K is ruled out in the outer NS core. Here T_{cn,max} and T_{cp,max} are the maximum values of the density dependent critical temperatures of neutrons and protons. The data on SXTs suggest also that: (i) cooling of massive NSs is enhanced by neutrino emission more powerful than the emission due to Cooper pairing of neutrons; (ii) mild neutron superfluidity, if available, might be present only in inner cores of massive NSs. In the latter case SXTs would exhibit dichotomy, i.e. very similar SXTs may evolve to very different thermal states