Andrea Serani

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.

Globally Convergent Hybridization of Particle Swarm Optimization Using Line Search-Based Derivative-Free Techniques

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 simulation-based 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 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.

Nonlinear Methods for Design-Space Dimensionality Reduction in Shape Optimization

In shape optimization, design improvements significantly depend on the dimension and variability of the design space. High dimensional and variability spaces are more difficult to explore, but also usually allow for more significant improvements. The assessment and breakdown of design-space dimensionality and variability are therefore key elements to shape optimization. A linear method based on the principal component analysis (PCA) has been developed in earlier research to build a reduced-dimensionality design-space, resolving the 95% of the original geometric variance. The present work introduces an extension to more efficient nonlinear approaches. Specifically the use of Kernel PCA, Local PCA, and Deep Autoencoder (DAE) is discussed. The methods are demonstrated for the design-space dimensionality reduction of the hull form of a USS Arleigh Burke-class destroyer. Nonlinear methods are shown to be more effective than linear PCA. DAE shows the best performance overall.

Dolphin Pod Optimization

A novel nature-inspired, deterministic, global, and derivative-free optimization method, namely the dolphin pod optimization (DPO), is presented for solving simulation-based design optimization problems with costly objective functions. DPO is formulated for unconstrained single-objective minimization and based on a simplified social model of a dolphin pod in search for food. A parametric analysis is conducted to identify the most promising DPO setup, using 100 analytical benchmark functions and three performance criteria, varying pod size and initialization, coefficient set, and box-constraint method, resulting in more than 140,000 optimization runs. The most promising setup is compared with deterministic particle swarm optimization, central force optimization, and DIviding RECTangles and finally applied to the optimization of a destroyer hull form for reduced resistance and improved seakeeping.

A Multi-objective DIRECT algorithm for ship hull optimization

The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of “hard” nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem.

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.

Simulation-Based Design Optimization by Sequential Multi-criterion Adaptive Sampling and Dynamic Radial Basis Functions

The paper presents a global method for simulation-based design optimization (SBDO) which combines a dynamic radial basis function (DRBF) surrogate model with a sequential multi-criterion adaptive sampling (MCAS) technique. Starting from an initial training set, groups of new samples are sequentially selected aiming at both the improvement of the surrogate model global accuracy and the reduction of the objective function. The objective prediction and the associated uncertainty provided by the DRBF model are used by a multi-objective particle swarm optimization algorithm to identify Pareto-optimal solutions. These are used by the MCAS technique, which selects new samples by down-sampling the Pareto front, allowing for a parallel infill of an arbitrary number of points at each iteration. The method is applied to a set of 28 unconstrained global optimization test problems and a six-variable SBDO of the DTMB 5415 hull-form in calm water, based on potential flow simulations. Results show the effectiveness of the method in reducing the computational cost of the SBDO, providing the background for further developments and application to more complex ship hydrodynamic problems.

Hybrid global/local derivative-free multi-objective optimization via deterministic particle swarm with local linesearch

A multi-objective deterministic hybrid algorithm (MODHA) is introduced for efficient simulation-based design optimization. The global exploration capability of multi-objective deterministic particle swarm optimization (MODPSO) is combined with the local search accuracy of a derivative-free multi-objective (DFMO) linesearch method. Six MODHA formulations are discussed, based on two MODPSO formulations and three DFMO activation criteria. Forty five analytical test problems are solved, with two/three objectives and one to twelve variables. The performance is evaluated by two multi-objective metrics. The most promising formulations are finally applied to the hull-form optimization of a high-speed catamaran in realistic ocean conditions and compared to MODPSO and DFMO, showing promising results.