Hybrid Global/Local Derivative-Free Multi-objective Optimization via Deterministic Particle Swarm with Local Linesearch (original) (raw)
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Hybridization of Multi-Objective Deterministic Particle Swarm with Derivative-Free Local Searches
Mathematics
The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based o...
Simulation Based Design Optimization (SBDO) supports the design of complex engineering systems. The process consists in the application of several numerical simulations with the aim of exploring and assessing the design opportunities among all the feasible design solutions. The multi-objective optimization algorithm manages the search of the best compromise between all the design objectives (such as the resistance and seakeeping of a ship or the drag and weight of an airplane), generally provided in terms of Pareto fronts. The objective functions may be noisy and/or often their derivatives are not directly provided by the simulation tools. Therefore, derivative-free optimization algorithms are used as a viable option for the SBDO process. Local or global optimization algorithms are preferred, whether a fi ne search region is or is not known a priori. The first class of algorithms explores accurately a limited domain region, whereas the second explores efficiently the entire design space, providing approximate solutions to the decision problem. In order to combine the accuracy of local algorithms with the exploration capability of global methods for multi-objective problems, a multi-objective deterministic particle swarm optimization (MODPSO) [4, 5] is combined with a derivative-free multi-objective (DFMO) [3] local optimization algorithm.
Simulation-based design (SBD) optimization assists the designer in the design process of complex engineering systems. In this context, real-world problems are affected by different sources of uncertainties (operational, environmental, geometrical or numerical) and require reliability-based robust design optimization (RBRDO) formulations to identify the optimal solution. RBRDO is usually computationally very costly (especially if high-fidelity simulations are used) and may be achieved by means of metamodels, with efficient optimization algorithms. Herein, a RBRDO for ship design is solved, for real ocean environment including stochastic sea state and speed. The problem is taken from [1] and is formulated as an unconstrained multi-objective optimization problem aimed at (a) the reduction of the expected value of the resistance in wave at sea state 5, varying the speed and (b) the increase of the ship operability, with respect to a set of motion-related constraints. The design space used is a four-dimensional representation of shape modifications, based on the Karhunen-Loève expansion of free-form deformations of the original hull . A metamodel based on stochastic radial basis function [3] is used, trained by URANS simulations. The ship considered is a 100m Delft catamaran, sailing in head waves in the North Pacific ocean.
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 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.
Simulation-based design optimization methods integrate computer simulations, design modification tools, and optimization algorithms. In hydrodynamic applications, often objective functions are com-putationally expensive and noisy, their derivatives are not directly provided, and the existence of local minima cannot be excluded a priori, which motivates the use of deterministic derivative-free global optimization algorithms. The enhancement of two algorithms of this type, DIRECT (DIviding RECTangles) and DPSO (Deterministic Particle Swarm Optimization), is presented based on global/local hybridization with derivative-free line search methods. The hull-form optimization of the DTMB 5415 model is solved for the reduction of the calm-water resistance at Fr = 0.25, using potential flow and RANS solvers. Six and eleven design variables are used respectively, modifying both the hull and the sonar dome. Hybrid algorithms show a faster convergence towards the global minimum than the original global methods and are a viable option for ship hydrodynamic optimization. A significant resistance reduction is achieved both by potential flow and RANS-based optimizations, showing the effectiveness of the optimization procedure.
New global optimization methods for ship design problems
Optimization and Engineering, 2009
The aim of this paper is to solve optimal design problems for industrial applications when the objective function value requires the evaluation of expensive simulation codes and its first derivatives are not available. In order to achieve this goal we propose two new algorithms that draw inspiration from two existing approaches: a filled function based algorithm and a Particle Swarm
Deterministic optimization algorithms are very attractive when the objective function is computation-ally 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.
A multi-objective DIRECT algorithm for ship hull optimization
Computational Optimization and Applications, 2017
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.
Recent Advances in Swarm Intelligence and Evolutionary Computation, Studies in Computational Intelligence, Volume 585, Edited by Xin-She Yang; Chapter 2: pages 25-47; ISBN: 978-3-319-13825-1, 2015
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.