Scalable Optimization Methods for Incorporating Spatiotemporal Fractionation into Intensity-Modulated Radiotherapy Planning

2021 ◽  
Author(s):  
Ali Adibi ◽  
Ehsan Salari
Keyword(s):  
Quadratic Programming ◽  
Large Scale ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Radiotherapy Planning ◽  
Quadratic Program ◽  
Clinical Cancer ◽  
Therapeutic Gain ◽  
Solution Methods ◽  
Quadratically Constrained

It has been recently shown that an additional therapeutic gain may be achieved if a radiotherapy plan is altered over the treatment course using a new treatment paradigm referred to in the literature as spatiotemporal fractionation. Because of the nonconvex and large-scale nature of the corresponding treatment plan optimization problem, the extent of the potential therapeutic gain that may be achieved from spatiotemporal fractionation has been investigated using stylized cancer cases to circumvent the arising computational challenges. This research aims at developing scalable optimization methods to obtain high-quality spatiotemporally fractionated plans with optimality bounds for clinical cancer cases. In particular, the treatment-planning problem is formulated as a quadratically constrained quadratic program and is solved to local optimality using a constraint-generation approach, in which each subproblem is solved using sequential linear/quadratic programming methods. To obtain optimality bounds, cutting-plane and column-generation methods are combined to solve the Lagrangian relaxation of the formulation. The performance of the developed methods are tested on deidentified clinical liver and prostate cancer cases. Results show that the proposed method is capable of achieving local-optimal spatiotemporally fractionated plans with an optimality gap of around 10%–12% for cancer cases tested in this study. Summary of Contribution: The design of spatiotemporally fractionated radiotherapy plans for clinical cancer cases gives rise to a class of nonconvex and large-scale quadratically constrained quadratic programming (QCQP) problems, the solution of which requires the development of efficient models and solution methods. To address the computational challenges posed by the large-scale and nonconvex nature of the problem, we employ large-scale optimization techniques to develop scalable solution methods that find local-optimal solutions along with optimality bounds. We test the performance of the proposed methods on deidentified clinical cancer cases. The proposed methods in this study can, in principle, be applied to solve other QCQP formulations, which commonly arise in several application domains, including graph theory, power systems, and signal processing.

scholarly journals Convex optimization techniques in compliant assembly simulation

2020 ◽  
Vol 21 (4) ◽  
pp. 1665-1690
Author(s):  
Maria Stefanova ◽  
Olga Minevich ◽  
Stanislav Baklanov ◽  
Margarita Petukhova ◽  
Sergey Lupuleac ◽  
...  
Keyword(s):  
Large Scale ◽  
Hessian Matrix ◽  
Linear Complementarity Problems ◽  
Contact Problems ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Active Set ◽  
Assembly Simulation ◽  
The Matrix ◽  
Compliant Parts

Abstract A special class of quadratic programming (QP) problems is considered in this paper. This class emerges in simulation of assembly of large-scale compliant parts, which involves the formulation and solution of contact problems. The considered QP problems can have up to 20,000 unknowns, the Hessian matrix is fully populated and ill-conditioned, while the matrix of constraints is sparse. Variation analysis and optimization of assembly process usually require massive computations of QP problems with slightly different input data. The following optimization methods are adapted to account for the particular features of the assembly problem: an interior point method, an active-set method, a Newton projection method, and a pivotal algorithm for the linear complementarity problems. Equivalent formulations of the QP problem are proposed with the intent of them being more amenable to the considered methods. The methods are tested and results are compared for a number of aircraft assembly simulation problems.

Sequential Quadratic Programming

Acta Numerica ◽  
1995 ◽  
Vol 4 ◽  
pp. 1-51 ◽  
Author(s):  
Paul T. Boggs ◽  
Jon W. Tolle
Keyword(s):  
Quadratic Programming ◽  
Constrained Optimization ◽  
Sequential Quadratic Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Public Domain ◽  
Large Set ◽  
Constrained Optimization Problems ◽  
Nonlinearly Constrained Optimization

Since its popularization in the late 1970s, Sequential Quadratic Programming (SQP) has arguably become the most successful method for solving nonlinearly constrained optimization problems. As with most optimization methods, SQP is not a single algorithm, but rather a conceptual method from which numerous specific algorithms have evolved. Backed by a solid theoretical and computational foundation, both commercial and public-domain SQP algorithms have been developed and used to solve a remarkably large set of important practical problems. Recently large-scale versions have been devised and tested with promising results.

First- and Second-Order Methods for Learning: Between Steepest Descent and Newton's Method

1992 ◽  
Vol 4 (2) ◽  
pp. 141-166 ◽  
Author(s):  
Roberto Battiti
Keyword(s):  
Large Scale ◽  
Feedforward Neural Networks ◽  
Optimization Methods ◽  
Second Order ◽  
Optimization Techniques ◽  
Neural Nets ◽  
Classification Problems ◽  
On Line ◽  
Mutual Relations ◽  
Safety Procedures

On-line first-order backpropagation is sufficiently fast and effective for many large-scale classification problems but for very high precision mappings, batch processing may be the method of choice. This paper reviews first- and second-order optimization methods for learning in feedforward neural networks. The viewpoint is that of optimization: many methods can be cast in the language of optimization techniques, allowing the transfer to neural nets of detailed results about computational complexity and safety procedures to ensure convergence and to avoid numerical problems. The review is not intended to deliver detailed prescriptions for the most appropriate methods in specific applications, but to illustrate the main characteristics of the different methods and their mutual relations.

Biofuel Supply Chain Optimization Using Lévy-Enhanced Swarm Intelligence

2020 ◽  
pp. 169-197
Keyword(s):  
Supply Chain ◽  
Large Scale ◽  
Optimization Techniques ◽  
Optimal Decision ◽  
Supply Chain Optimization ◽  
Industrial Systems ◽  
Planning Optimization ◽  
Biofuel Supply Chain ◽  
Solution Methods ◽  
Optimal Decision Making

Supply chain planning/optimization presents various challenges to decision makers globally due to its highly complicated nature as well as its large-scale structure. Over the years various state-of-the-art methods have been employed to model supply chains. Optimization techniques are then applied to such models to help with optimal decision making. However, with highly complex industrial systems such as these, conventional metaheuristics are still plagued by various drawbacks. Strategies such as hybridization and algorithmic modifications have been the focus of previous efforts to improve the performance of conventional metaheuristics. In light of these developments, this chapter presents two solution methods for tackling the biofuel supply chain problem.

Design optimization of large-scale structures with sequential linear programming

2002 ◽  
Vol 216 (8) ◽  
pp. 799-811 ◽  
Author(s):  
L Lamberti ◽  
C Pappalettere
Keyword(s):  
Linear Programming ◽  
Design Optimization ◽  
Large Scale ◽  
Optimization Technique ◽  
Computational Cost ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Truss Structures ◽  
Large Set ◽  
Sequential Linear Programming

Design optimization of complex structures entails tasks that oppose the usual constraints on time and computational resources. However, using optimization techniques is very useful because it allows engineers to obtain a large set of designs at low computational cost. Among the different optimization methods, sequential linear programming (SLP) is very popular because of its simplicity and because linear solvers (e.g. Simplex) are easily available. In spite of the inherent theoretical simplicity, well-coded SLP algorithms may outperform more sophisticated optimization methods. This paper describes the experience obtained in the design optimization of large-scale truss structures and beams with SLP-based algorithms. Sizing and configuration problems of structures under multiple loading conditions with up to 1000 design variables and 3500 constraints are considered. The relative performance and merits of some SLP-based algorithms are compared and the efficiency of an advanced SLP-based algorithm called ILEAML (improved linearization error amplitude move limits) is tested. ILEAML is also compared to the sequential quadratic programming (SQP) method, which is considered by theoreticians as probably the best theoretically founded optimization technique.

scholarly journals Solving the Real Power Limitations in the Dynamic Economic Dispatch of Large-Scale Thermal Power Units under the Effects of Valve-Point Loading and Ramp-Rate Limitations

2021 ◽  
Vol 13 (3) ◽  
pp. 1274
Author(s):  
Loau Al-Bahrani ◽  
Mehdi Seyedmahmoudian ◽  
Ben Horan ◽  
Alex Stojcevski
Keyword(s):  
Large Scale ◽  
Thermal Power ◽  
Optimization Technique ◽  
Economic Dispatch ◽  
Pso Algorithm ◽  
Search Space ◽  
Economic Benefits ◽  
Optimization Techniques ◽  
Ramp Rate ◽  
Dynamic Economic Dispatch

Few non-traditional optimization techniques are applied to the dynamic economic dispatch (DED) of large-scale thermal power units (TPUs), e.g., 1000 TPUs, that consider the effects of valve-point loading with ramp-rate limitations. This is a complicated multiple mode problem. In this investigation, a novel optimization technique, namely, a multi-gradient particle swarm optimization (MG-PSO) algorithm with two stages for exploring and exploiting the search space area, is employed as an optimization tool. The M particles (explorers) in the first stage are used to explore new neighborhoods, whereas the M particles (exploiters) in the second stage are used to exploit the best neighborhood. The M particles’ negative gradient variation in both stages causes the equilibrium between the global and local search space capabilities. This algorithm’s authentication is demonstrated on five medium-scale to very large-scale power systems. The MG-PSO algorithm effectively reduces the difficulty of handling the large-scale DED problem, and simulation results confirm this algorithm’s suitability for such a complicated multi-objective problem at varying fitness performance measures and consistency. This algorithm is also applied to estimate the required generation in 24 h to meet load demand changes. This investigation provides useful technical references for economic dispatch operators to update their power system programs in order to achieve economic benefits.

scholarly journals Influence of Wind Power on Modeling of Bidding Strategy in a Promising Power Market with a Modified Gravitational Search Algorithm

2021 ◽  
Vol 11 (10) ◽  
pp. 4438
Author(s):  
Satyendra Singh ◽  
Manoj Fozdar ◽  
Hasmat Malik ◽  
Maria del Valle Fernández Moreno ◽  
Fausto Pedro García Márquez
Keyword(s):  
Wind Power ◽  
Electricity Market ◽  
Large Scale ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Optimization Methods ◽  
Bidding Strategy ◽  
Wind Speed Profile ◽  
Gravitational Search ◽  
Modified Gravitational Search Algorithm

It is expected that large-scale producers of wind energy will become dominant players in the future electricity market. However, wind power output is irregular in nature and it is subjected to numerous fluctuations. Due to the effect on the production of wind power, producing a detailed bidding strategy is becoming more complicated in the industry. Therefore, in view of these uncertainties, a competitive bidding approach in a pool-based day-ahead energy marketplace is formulated in this paper for traditional generation with wind power utilities. The profit of the generating utility is optimized by the modified gravitational search algorithm, and the Weibull distribution function is employed to represent the stochastic properties of wind speed profile. The method proposed is being investigated and simplified for the IEEE-30 and IEEE-57 frameworks. The results were compared with the results obtained with other optimization methods to validate the approach.

scholarly journals Enabling Large-Scale Simulations of Quantum Transport with Manycore Computing

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 253
Author(s):  
Yosang Jeong ◽  
Hoon Ryu
Keyword(s):  
Quantum Transport ◽  
Large Scale ◽  
Performance Enhancement ◽  
Silicon Nanowire ◽  
Matrix Multiplication ◽  
Tight Binding ◽  
Optimization Techniques ◽  
Wide Energy Range ◽  
Processing Unit ◽  
Binding Model

The non-equilibrium Green’s function (NEGF) is being utilized in the field of nanoscience to predict transport behaviors of electronic devices. This work explores how much performance improvement can be driven for quantum transport simulations with the aid of manycore computing, where the core numerical operation involves a recursive process of matrix multiplication. Major techniques adopted for performance enhancement are data restructuring, matrix tiling, thread scheduling, and offload computing, and we present technical details on how they are applied to optimize the performance of simulations in computing hardware, including Intel Xeon Phi Knights Landing (KNL) systems and NVIDIA general purpose graphic processing unit (GPU) devices. With a target structure of a silicon nanowire that consists of 100,000 atoms and is described with an atomistic tight-binding model, the effects of optimization techniques on the performance of simulations are rigorously tested in a KNL node equipped with two Quadro GV100 GPU devices, and we observe that computation is accelerated by a factor of up to ∼20 against the unoptimized case. The feasibility of handling large-scale workloads in a huge computing environment is also examined with nanowire simulations in a wide energy range, where good scalability is procured up to 2048 KNL nodes.

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