Optimization on Metamodeling-Supported Iterative Decomposition

2015 ◽  
Author(s):  
Kambiz Haji Hajikolaei ◽  
George Cheng ◽  
Gary Wang
Keyword(s):  
Trust Region ◽  
Global Optimum ◽  
High Dimensional ◽  
Step Method ◽  
Direct Optimization ◽  
Decomposition Scheme ◽  
Engineering Problems ◽  
New Strategy ◽  
Iterative Decomposition ◽  
Sample Points

The recently developed metamodel-based decomposition strategy relies on quantifying the variable correlations of black-box functions so that high dimensional problems are decomposed to smaller sub-problems, before performing optimization. Such a two-step method may miss the global optimum due to its rigidity or requires extra expensive sample points for ensuring adequate decomposition. This work develops a strategy to iteratively decompose high dimensional problems within the optimization process. The sample points used during the optimization are reused to build a metamodel called PCA-HDMR for quantifying the intensities of variable correlations by sensitivity analysis. At every iteration, the predicted intensities of the correlations are updated based on all the evaluated points and a new decomposition scheme is suggested by omitting the weak correlations. Optimization is performed on the iteratively updated sub-problems from decomposition. The proposed strategy is applied for optimization of different benchmark and engineering problems and results are compared to direct optimization of the undecomposed problems using Trust Region Mode Pursuing Sampling method (TRMPS), Genetic Algorithm (GA), and Dividing RECTangles (DIRECT). The results show that except for the category of un-decomposable problems with all or lots of strong (i. e., important) correlations, the proposed strategy effectively improves the accuracy of the optimization results. The advantages of the new strategy in comparison with the previous methods are also discussed.

Optimization on Metamodeling-Supported Iterative Decomposition

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Kambiz Haji Hajikolaei ◽  
George H. Cheng ◽  
G. Gary Wang
Keyword(s):  
Trust Region ◽  
Principal Component ◽  
Global Optimum ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Step Method ◽  
Direct Optimization ◽  
Decomposition Scheme ◽  
New Strategy ◽  
Sample Points

The recently developed metamodel-based decomposition strategy relies on quantifying the variable correlations of black-box functions so that high-dimensional problems are decomposed to smaller subproblems, before performing optimization. Such a two-step method may miss the global optimum due to its rigidity or requires extra expensive sample points for ensuring adequate decomposition. This work develops a strategy to iteratively decompose high-dimensional problems within the optimization process. The sample points used during the optimization are reused to build a metamodel called principal component analysis-high dimensional model representation (PCA-HDMR) for quantifying the intensities of variable correlations by sensitivity analysis. At every iteration, the predicted intensities of the correlations are updated based on all the evaluated points, and a new decomposition scheme is suggested by omitting the weak correlations. Optimization is performed on the iteratively updated subproblems from decomposition. The proposed strategy is applied for optimization of different benchmarks and engineering problems, and results are compared to direct optimization of the undecomposed problems using trust region mode pursuing sampling method (TRMPS), genetic algorithm (GA), cooperative coevolutionary algorithm with correlation-based adaptive variable partitioning (CCEA-AVP), and divide rectangles (DIRECT). The results show that except for the category of undecomposable problems with all or many strong (i.e., important) correlations, the proposed strategy effectively improves the accuracy of the optimization results. The advantages of the new strategy in comparison with the previous methods are also discussed.

scholarly journals An Optimization Method for the Configuration of Inter Array Cables for Floating Offshore Wind Farm

2017 ◽  
Author(s):  
Yann Poirette ◽  
Martin Guiton ◽  
Guillaume Huwart ◽  
Delphine Sinoquet ◽  
Jean Marc Leroy
Keyword(s):  
Wind Farm ◽  
Optimization Problem ◽  
Initial Point ◽  
Trust Region ◽  
Optimization Method ◽  
Global Optimum ◽  
Offshore Wind ◽  
Finite Element Software ◽  
Constrained Problems ◽  
Floating Offshore Wind Turbines

IFP Energies nouvelles (IFPEN) is involved for many years in various projects for the development of floating offshore wind turbines. The commercial deployment of such technologies is planned for 2020. The present paper proposes a methodology for the numerical optimization of the inter array cable configuration. To illustrate the potential of such an optimization, results are presented for a case study with a specific floating foundation concept [1]. The optimization study performed aims to define the least expensive configuration satisfying mechanical constraints under extreme environmental conditions. The parameters to be optimized are the total length, the armoring, the stiffener geometry and the buoyancy modules. The insulated electrical conductors and overall sheath are not concerned by this optimization. The simulations are carried out using DeepLines™, a Finite Element software dedicated to simulate offshore floating structures in their marine environment. The optimization problem is solved using an IFPEN in-house tool, which integrates a state of the art derivative-free trust region optimization method extended to nonlinear constrained problems. The latter functionality is essential for this type of optimization problem where nonlinear constraints are introduced such as maximum tension, no compression, maximum curvature and elongation, and the aero-hydrodynamic simulation solver does not provide any gradient information. The optimization tool is able to find various local feasible extrema thanks to a multi-start approach, which leads to several solutions of the cable configuration. The sensitivity to the choice of the initial point is demonstrated, illustrating the complexity of the feasible domain and the resulting difficulty in finding the global optimum configuration.

Multiobjective Optimization for High Dimensional Expensively Constrained Black-Box Problems

2021 ◽  
pp. 1-59
Author(s):  
George Cheng ◽  
G. Gary Wang ◽  
Yeong-Maw Hwang
Keyword(s):  
Multiobjective Optimization ◽  
Trust Region ◽  
Adaptive Strategy ◽  
Black Box ◽  
Superior Performance ◽  
High Dimensional ◽  
Multi Objective Optimization ◽  
Semiconductor Substrate ◽  
Multi Objective ◽  
Computationally Expensive

Abstract Multi-objective optimization (MOO) problems with computationally expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches for MOO are often not suitable for high-dimensional problems and often do not support expensive constraints. In this work, the Situational Adaptive Kreisselmeier and Steinhauser (SAKS) method was combined with a new multi-objective trust region optimizer (MTRO) strategy to form the SAKS-MTRO method for MOO problems with expensive black-box constraint functions. The SAKS method is an approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The MTRO strategy uses a combination of objective decomposition and K-means clustering to handle MOO problems. SAKS-MTRO was benchmarked against four popular multi-objective optimizers and demonstrated superior performance on average. SAKS-MTRO was also applied to optimize the design of a semiconductor substrate and the design of an industrial recessed impeller.

Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

2013 ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Optimization Problems ◽  
Trust Region ◽  
Black Box ◽  
High Dimensional ◽  
Test Problems ◽  
Design Variables ◽  
Low Dimensionality ◽  
Improve Algorithm ◽  
Improved Performance ◽  
Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

A New Simple Micro-PSO for High Dimensional Optimization Problem

2012 ◽  
Vol 236-237 ◽  
pp. 1195-1200
Author(s):  
Wen Hua Han
Keyword(s):  
Optimization Problem ◽  
Optimization Technique ◽  
Pso Algorithm ◽  
Population Based ◽  
Global Optimum ◽  
Stochastic Search ◽  
High Dimensional ◽  
Swarm Optimization ◽  
Search Optimization ◽  
Dimensional Optimization

The particle swarm optimization (PSO) algorithm is a population-based intelligent stochastic search optimization technique, which has already been widely used to various of fields. In this paper, a simple micro-PSO is proposed for high dimensional optimization problem, which is resulted from being introduced escape boundary and perturbation for global optimum. The advantages of the simple micro-PSO are more simple and easily implemented than the previous micro-PSO. Experiments were conducted using Griewank, Rosenbrock, Ackley, Tablets functions. The experimental results demonstrate that the simple micro-PSO are higher optimization precision and faster convergence rate than PSO and robust for the dimension of the optimization problem.

Rapid design optimization of antennas using variable-fidelity EM models and adjoint sensitivities

2016 ◽  
Vol 33 (7) ◽  
pp. 2007-2018 ◽  
Author(s):  
Slawomir Koziel ◽  
Adrian Bekasiewicz
Keyword(s):  
Design Optimization ◽  
Optimization Technique ◽  
Computational Cost ◽  
Trust Region ◽  
Simulation Models ◽  
Direct Optimization ◽  
Content Type ◽  
Variable Fidelity ◽  
Em Simulation ◽  
Conventional Methods

Purpose Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues. Design/methodology/approach The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach. Findings Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods. Research limitations/implications The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes. Originality/value Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

A Composite Framework of Cuckoo Search and PSO Algorithm

2015 ◽  
Vol 713-715 ◽  
pp. 1491-1494 ◽  
Author(s):  
Zhi Qiang Gao ◽  
Li Xia Liu ◽  
Wei Wei Kong ◽  
Xiao Hong Wang
Keyword(s):  
Cloud Model ◽  
Cuckoo Search ◽  
Pso Algorithm ◽  
Global Optimum ◽  
High Dimensional ◽  
Test Results ◽  
Swarm Optimization ◽  
Local Solutions ◽  
Optimum Solution ◽  
Global Optimum Solution

A novel composite framework of Cuckoo Search (CS) and Particle Swarm Optimization (PSO) algorithm called CS-PSO is proposed in this paper. In CS-PSO, initialization is substituted by chaotic system, and then Cuckoo shares optimums in the global best solutions pool with particles in PSO to improve parallel cooperation and social interaction. Furthermore, Cloud Model, famous for its outstanding characteristics of the process of transforming qualitative concepts to a set of quantitative numerical values, is adopted to exploit the surrounding of the local solutions obtained from the global best solution pool. Benchmark test results show that, CS-PSO can converge to the global optimum solution rapidly and accurately, compared with other algorithms, especially in high dimensional problems.

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