scholarly journals Split Common Coincidence Point Problem: A Formulation Applicable to (Bio)Physically-Based Inverse Planning Optimization

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2086
Author(s):  
Charles E. Chidume ◽  
Lois C. Okereke
Keyword(s):  
Optimization Problem ◽  
Coincidence Point ◽  
Point Problem ◽  
Optimization Approach ◽  
Inverse Planning ◽  
Clinical Criteria ◽  
Planning Optimization ◽  
Physically Based ◽  
Treatment Plans ◽  
Optimized Treatment

Inverse planning is a method of radiotherapy treatment planning where the care team begins with the desired dose distribution satisfying prescribed clinical objectives, and then determines the treatment parameters that will achieve it. The variety in symmetry, form, and characteristics of the objective functions describing clinical criteria requires a flexible optimization approach in order to obtain optimized treatment plans. Therefore, we introduce and discuss a nonlinear optimization formulation called the split common coincidence point problem (SCCPP). We show that the SCCPP is a suitable formulation for the inverse planning optimization problem with the flexibility of accommodating several biological and/or physical clinical objectives. Also, we propose an iterative algorithm for approximating the solution of the SCCPP, and using Bregman techniques, we establish that the proposed algorithm converges to a solution of the SCCPP and to an extremum of the inverse planning optimization problem. We end with a note on useful insights on implementing the algorithm in a clinical setting.

Shape and parameter reconstruction for the Robin transmission inverse problem

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Antoine Laurain ◽  
Houcine Meftahi
Keyword(s):  
Inverse Problem ◽  
Shape Optimization ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Optimization Approach ◽  
Reconstruction Method ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity ◽  
Level Set Approach ◽  
Parameter Reconstruction

AbstractIn this paper we consider the inverse problem of simultaneously reconstructing the interface where the jump of the conductivity occurs and the Robin parameter for a transmission problem with piecewise constant conductivity and Robin-type transmission conditions on the interface. We propose a reconstruction method based on a shape optimization approach and compare the results obtained using two different types of shape functionals. The reformulation of the shape optimization problem as a suitable saddle point problem allows us to obtain the optimality conditions by using differentiability properties of the min-sup combined with a function space parameterization technique. The reconstruction is then performed by means of an iterative algorithm based on a conjugate shape gradient method combined with a level set approach. To conclude we give and discuss several numerical examples.

Frequency optimization of laminated functionally graded carbon nanotube reinforced composite quadrilateral plates using smoothed FEM and evolution algorithm

2017 ◽  
Vol 52 (14) ◽  
pp. 1971-1986 ◽  
Author(s):  
T Vo-Duy ◽  
T Truong-Thi ◽  
V Ho-Huu ◽  
T Nguyen-Thoi
Keyword(s):  
Carbon Nanotube ◽  
Optimization Problem ◽  
Volume Fraction ◽  
Differential Evolution Algorithm ◽  
Composite Plates ◽  
Functionally Graded ◽  
Optimization Approach ◽  
Reinforced Composite ◽  
Design Variables ◽  
Evolution Algorithm

The paper presents an efficient numerical optimization approach to deal with the optimization problem for maximizing the fundamental frequency of laminated functionally graded carbon nanotube-reinforced composite quadrilateral plates. The proposed approach is a combination of the cell-based smoothed discrete shear gap method (CS-DSG3) for analyzing the first natural frequency of the functionally graded carbon nanotube reinforced composite plates and a global optimization algorithm, namely adaptive elitist differential evolution algorithm (aeDE), for solving the optimization problem. The design variables are the carbon nanotube orientation in the layers and constrained in the range of integer numbers belonging to [−900 900]. Several numerical examples are presented to investigate optimum design of quadrilateral laminated functionally graded carbon nanotube reinforced composite plates with various parameters such as carbon nanotube distribution, carbon nanotube volume fraction, boundary condition and number of layers.

Qualitative Knowledge and Manufacturing Considerations in Multidisciplinary Structural Optimization of Hybrid Material Structures

2006 ◽  
Vol 10 ◽  
pp. 143-152 ◽  
Author(s):  
Martin Huber ◽  
Horst Baier
Keyword(s):  
Hybrid Material ◽  
Optimization Problem ◽  
Fuzzy Rule ◽  
Optimal Designs ◽  
Design Parameters ◽  
Optimization Approach ◽  
Structural Level ◽  
Design Problems ◽  
Qualitative Knowledge ◽  
Typical Design

An optimization approach is derived from typical design problems of hybrid material structures, which provides the engineer with optimal designs. Complex geometries, different materials and manufacturing aspects are handled as design parameters using a genetic algorithm. To take qualitative information into account, fuzzy rule based systems are utilized in order to consider all relevant aspects in the optimization problem. This paper shows results for optimization tasks on component and structural level.

scholarly journals Optimal design of Vertical-Taking-Off-and-Landing UAV wing using multilevel approach

2020 ◽  
Vol 11 ◽  
pp. 26
Author(s):  
Hao Yue ◽  
David Bassir ◽  
Hicham Medromi ◽  
Hua Ding ◽  
Khaoula Abouzaid
Keyword(s):  
Optimization Problem ◽  
Delta Wing ◽  
Optimization Approach ◽  
Multilevel Optimization ◽  
Distribution Strategy ◽  
Surface Method ◽  
Flight Mode ◽  
Aerial Vehicle ◽  
Computational Fluid Dynamics Cfd ◽  
Cruise Flight

In order to overcome the propre disadvantages of FW(Fixed-Wing) and VTOL(Vertical-Taking-Off-and-Landing) UAV (Unmanned Aerial Vehicle) and extend its application, the hybrid drone is invested more in recent years by researchers and several classifications are developed on the part of dual system. In this article, an innovative hybrid UAV is raised and studied by introducing the canard configuration that is coupled with conventional delta wing as well as winglet structure. Profited by Computational Fluid Dynamics (CFD) and Response Surface Method (RSM), a multilevel optimization approach is practically presented and concerned in terms of cruise flight mode: adopted by an experienced-based distribution strategy, the total lift object is respectively assigned into the delta wing (90–95%) and canard wing(5–10%) which is applied into a two-step optimization: the first optimization problem is solved only with the parameters concerned with delta wing afterwards the second optimization is successively concluded to develop the canard configuration considering the optimized delta wing conception. Above all, the optimal conceptual design of the delta and canard wing is realized by achieving the lift goal with less drag performance in cruise mode.

Proactive Optimization of Intelligent-Well Production Using Stochastic Gradient-Based Algorithms

2016 ◽  
Vol 19 (02) ◽  
pp. 239-252 ◽  
Author(s):  
Morteza Haghighat Sefat ◽  
Khafiz M. Muradov ◽  
Ahmed H. Elsheikh ◽  
David R. Davies
Keyword(s):  
Large Scale ◽  
Optimization Problem ◽  
Stochastic Gradient ◽  
Real Field ◽  
Directional Derivatives ◽  
Optimization Approach ◽  
Layer By Layer ◽  
Monitoring And Control ◽  
Ensemble Size ◽  
Local Optima

Summary The popularity of intelligent wells (I-wells), which provide layer-by-layer monitoring and control capability of production and injection, is growing. However, the number of available techniques for optimal control of I-wells is limited (Sarma et al. 2006; Alghareeb et al. 2009; Almeida et al. 2010; Grebenkin and Davies 2012). Currently, most of the I-wells that are equipped with interval control valves (ICVs) are operated to enhance the current production and to resolve problems associated with breakthrough of the unfavorable phase. This reactive strategy is unlikely to deliver the long-term optimum production. On the other side, the proactive-control strategy of I-wells, with its ambition to provide the optimum control for the entire well's production life, has the potential to maximize the cumulative oil production. This strategy, however, results in a high-dimensional, nonlinear, and constrained optimization problem. This study provides guidelines on selecting a suitable proactive optimization approach, by use of state-of-the-art stochastic gradient-approximation algorithms. A suitable optimization approach increases the practicality of proactive optimization for real field models under uncertain operational and subsurface conditions. We evaluate the simultaneous-perturbation stochastic approximation (SPSA) method (Spall 1992) and the ensemble-based optimization (EnOpt) method (Chen et al. 2009). In addition, we present a new derivation of the EnOpt by use of the concept of directional derivatives. The numerical results show that both SPSA and EnOpt methods can provide a fast solution to a large-scale and multiple I-well proactive optimization problem. A criterion for tuning the algorithms is proposed and the performance of both methods is compared for several test cases. The used methodology for estimating the gradient is shown to affect the application area of each algorithm. SPSA provides a rough estimate of the gradient and performs better in search environments, characterized by several local optima, especially with a large ensemble size. EnOpt was found to provide a smoother estimation of the gradient, resulting in a more-robust algorithm to the choice of the tuning parameters, and a better performance with a small ensemble size. Moreover, the final optimum operation obtained by EnOpt is smoother. Finally, the obtained criteria are used to perform proactive optimization of ICVs in a real field.

scholarly journals On the Sensitivity of Local Flexibility Markets to Forecast Error: A Bi-Level Optimization Approach

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1959
Author(s):  
Delaram Azari ◽  
Shahab Shariat Torbaghan ◽  
Hans Cappon ◽  
Karel J. Keesman ◽  
Madeleine Gibescu ◽  
...  
Keyword(s):  
Distribution System ◽  
Large Scale ◽  
Optimization Problem ◽  
Distribution Networks ◽  
Second Order ◽  
Optimization Approach ◽  
Second Order Cone ◽  
Local Flexibility ◽  
Level Problem ◽  
Relaxation Error

The large-scale integration of intermittent distributed energy resources has led to increased uncertainty in the planning and operation of distribution networks. The optimal flexibility dispatch is a recently introduced, power flow-based method that a distribution system operator can use to effectively determine the amount of flexibility it needs to procure from the controllable resources available on the demand side. However, the drawback of this method is that the optimal flexibility dispatch is inexact due to the relaxation error inherent in the second-order cone formulation. In this paper we propose a novel bi-level optimization problem, where the upper level problem seeks to minimize the relaxation error and the lower level solves the earlier introduced convex second-order cone optimal flexibility dispatch (SOC-OFD) problem. To make the problem tractable, we introduce an innovative reformulation to recast the bi-level problem as a non-linear, single level optimization problem which results in no loss of accuracy. We subsequently investigate the sensitivity of the optimal flexibility schedules and the locational flexibility prices with respect to uncertainty in load forecast and flexibility ranges of the demand response providers which are input parameters to the problem. The sensitivity analysis is performed based on the perturbed Karush–Kuhn–Tucker (KKT) conditions. We investigate the feasibility and scalability of the proposed method in three case studies of standardized 9-bus, 30-bus, and 300-bus test systems. Simulation results in terms of local flexibility prices are interpreted in economic terms and show the effectiveness of the proposed approach.

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