Monte Carlo based non-radiating objective function minimization for permittivity profile estimation

2015 ◽  
Author(s):  
Shahed Shahir ◽  
Jeff Orchard ◽  
Safieddin Safavi-Naeini
Keyword(s):  
Monte Carlo ◽  
Objective Function ◽  
Function Minimization ◽  
Profile Estimation

Geometric Optimization of Concentrating Solar Collectors using Monte Carlo Simulation

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
A. J. Marston ◽  
K. J. Daun ◽  
M. R. Collins
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Programming ◽  
Objective Function ◽  
Sample Size ◽  
Optimization Algorithm ◽  
Geometric Optimization ◽  
Trial And Error ◽  
Solar Collectors ◽  
Step Size

This paper presents an optimization algorithm for designing linear concentrating solar collectors using stochastic programming. A Monte Carlo technique is used to quantify the performance of the collector design in terms of an objective function, which is then minimized using a modified Kiefer–Wolfowitz algorithm that uses sample size and step size controls. This process is more efficient than traditional “trial-and-error” methods and can be applied more generally than techniques based on geometric optics. The method is validated through application to the design of three different configurations of linear concentrating collector.

Robust Design Optimization Under Mixed Uncertainties With Stochastic Expansions

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Yi Zhang ◽  
Serhat Hosder
Keyword(s):  
Monte Carlo ◽  
Robust Optimization ◽  
Objective Function ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Technique ◽  
Response Surfaces ◽  
Robust Design Optimization ◽  
Stochastic Expansions ◽  
Mixed Uncertainties

The objective of this paper is to introduce a computationally efficient and accurate approach for robust optimization under mixed (aleatory and epistemic) uncertainties using stochastic expansions that are based on nonintrusive polynomial chaos (NIPC) method. This approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes a weighted sum of the stochastic measures, which are minimized simultaneously to ensure the robustness of the final design to both inherent and epistemic uncertainties. The optimization approach is demonstrated on two model problems with mixed uncertainties: (1) the robust design optimization of a slider-crank mechanism and (2) robust design optimization of a beam. The stochastic expansions are created with two different NIPC methods, Point-Collocation and Quadrature-Based NIPC. The optimization results are compared to the results of another robust optimization technique that utilizes double-loop Monte Carlo sampling (MCS) for the propagation of mixed uncertainties. The optimum designs obtained with two different optimization approaches agree well in both model problems; however, the number of function evaluations required for the stochastic expansion based approach is much less than the number required by the Monte Carlo based approach, indicating the computational efficiency of the optimization technique introduced.

scholarly journals DETERMINATION OF THE OPTIMAL DISTRIBUTION OF SUPPORTS IN THE FLOOR SLABS OF IN-DUSTRIAL BUILDINGS USING STOCHASTIC METHODS

2020 ◽  
Vol 47 (1) ◽  
pp. 138-146
Author(s):  
E. A. Efimenko ◽  
M. Yu. Bekkiev ◽  
D. R. Mayilyan ◽  
A. S. Chepurnenko
Keyword(s):  
Monte Carlo ◽  
Objective Function ◽  
Optimal Location ◽  
Monte Carlo Algorithm ◽  
Thin Plates ◽  
Stochastic Methods ◽  
Industrial Building ◽  
Maximum Deflection ◽  
Optimal Arrangement ◽  
Floor Slab

Abstract. Aim. The purpose of the study is to determine the optimal location of supports used in the floor slab of an industrial building.Method. In order to determine the optimal arrangement of the columns, a Monte Carlo algorithm was used in combination with the finite element method. The calculation was carried out on the basis of the theory of elastic thin plates.Results. The article presents a solution to the problem of determining the optimal location of a given number of point-supports of a floor slab n from the condition of minimum objective function. For the objective function, the maximum deflection of the slab, the potential energy of deformation and the flow rate of reinforcement were selected as variables. The selection of reinforcement was carried out in accordance with current generally-accepted standards for the design of reinforced concrete structures. The calcu-lations were performed using a program developed by the authors in the MATLAB computing environment. The results are given for n = 3,4,5. The algorithm, which has been modified for a large num-ber of supports n, is presented alongside a comparison of the basic and modified algorithm with n = 25. The possibility of a significant reduction in plate deformations with an irregular arrangement of supports compared to a regular distribution is shown.Conclusion. A method is proposed for finding the rational locations of point supports for a floor slab for a given quantity from the condition of min-imum deflection, potential strain energy and consumption of reinforcement materials based on the Monte Carlo method. This technique is suitable for arbitrary slab configurations and arbitrary loads. A modification of the algorithm is presented that is suitable for a large number of supports. The test example shows that the maximum deflection can be reduced by 42% when using an irregular support configuration compared to regular column spacing. In the considered examples, the position of all the supports was previously considered unknown, but the developed algorithm easily allows for stationary supports, whose position does not change.

A New Image Demising Method Based on Partial Differential Equations

2013 ◽  
Vol 443 ◽  
pp. 22-26
Author(s):  
Yong Xing Lin ◽  
Xiao Yan Xu ◽  
Xian Dong Zhang
Keyword(s):  
Image Processing ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Equation ◽  
Objective Function ◽  
Thermal Diffusion ◽  
Minimization Problem ◽  
Iterative Process ◽  
Function Minimization ◽  
Partial Differential

In the paper, we discuss the image demising models, based on partial differential equations. It is through the use of the concept of variations in the calculus of the objective function minimization problem, defines the image processing tasks. The results show that the model expands 2d thermal diffusion equation. Therefore, it is easy to get solution is to use a simple iterative process.

ADVANCES IN DISTRIBUTED OPTIMIZATION USING PROBABILITY COLLECTIVES

2006 ◽  
Vol 09 (04) ◽  
pp. 383-436 ◽  
Author(s):  
DAVID H. WOLPERT ◽  
CHARLIE E. M. STRAUSS ◽  
DEV RAJNARAYAN
Keyword(s):  
Monte Carlo ◽  
Objective Function ◽  
Distributed Optimization ◽  
Joint Probability ◽  
Expected Value ◽  
Joint Probability Distribution ◽  
Mathematical Framework ◽  
Optimization And Control ◽  
Full Rationality ◽  
And Control

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve distributed optimization and control problems. This is done by translating the distributed problem into an iterated game, where each agent's mixed strategy (i.e. its stochastically determined move) sets a different variable of the problem. So the expected value of the objective function of the distributed problem is determined by the joint probability distribution across the moves of the agents. The mixed strategies of the agents are updated from one game iteration to the next so as to converge on a joint distribution that optimizes that expected value of the objective function. Here, a set of new techniques for this updating is presented. These and older techniques are then extended to apply to uncountable move spaces. We also present an extension of the approach to include (in)equality constraints over the underlying variables. Another contribution is that we show how to extend the Monte Carlo version of the approach to cases where some agents have no Monte Carlo samples for some of their moves, and derive an "automatic annealing schedule".

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