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At least 1,441 records · Page 80

SU-E-T-234: Modulated Photon Radiotherapy (XMRT):The Impact of Incorporating Energy Modulation Into Intensity Modulated Radiotherapy (IMRT) Optimization

Purpose: To develop a new radiotherapy plan optimization technique that, for a given organ geometry, will find the optimal photon beam energies and fluences to produce a desirable dose distribution. This new modulated (both in energy and fluence) photon radiotherapy (XMRT) was compared with intensity modulated radiotherapy (IMRT) for a simple organ geometry. Methods: The XMRT optimization was formulated using a linear programming approach where the objective function is the mean dose to the healthy organs and dose-point constraints were assigned to each organ of interest. The organ geometry consisted of a target, two organs at risk (OARs), and normal tissue. A seven-equispaced-coplanar beam arrangement was used. For conventional IMRT, only 6 MV beams were available, while XMRT was optimized using 6 and 18 MV beams. A prescribed dose (PD) of 72 GY was assigned to the target, with upper and lower bounds of 110% and 95% of the PD, respectively. Both OARs were assigned a maximum dose of 64 Gy, while the normal tissue was assigned a maximum dose of 66 Gy. A numerical solver, Gurobi, generated solutions for the XMRT and IMRT problems. The dose-volume histograms from IMRT and XMRT solutions were compared. Results: The maximum, minimum, mean, and homogeneity of the dose to the target were comparable between IMRT and XMRT. Though IMRT had improved dose conformity relative to XMRT, XMRT reduced the mean dose to both OARs by more than 1 Gy. For normal tissue, an increase of 5 Gy in mean dose and 27 percent in integral dose was seen for IMRT relative to XMRT. Conclusion: This work demonstrates the benefits of simultaneously modulating photon beam energy and fluence using our XMRT approach in a given phantom geometry. While target coverage was comparable, dose to healthy structures was reduced using XMRT.

07 ISOTOPE AND RADIATION SOURCES↗

Impulsive Control for Continuous-Time Markov Decision Processes: A Linear Programming Approach

In this paper, we investigate an optimization problem for continuous-time Markov decision processes with both impulsive and continuous controls. We consider the so-called constrained problem where the objective of the controller is to minimize a total expected discounted optimality criterion associated with a cost rate function while keeping other performance criteria of the same form, but associated with different cost rate functions, below some given bounds. Our model allows multiple impulses at the same time moment. The main objective of this work is to study the associated linear program defined on a space of measures including the occupation measures of the controlled process and to provide sufficient conditions to ensure the existence of an optimal control.

97 MATHEMATICS AND COMPUTING↗

A novel method for co-optimizing battery sizing and charging strategy of battery electric bus fleets: An application to the city of Paris

Battery-electric buses (BEBs) are a promising technology for replacing diesel buses and reducing their environmental burden. However, their charging process can take several hours, depending on the charging technique and strategy, making them susceptible to schedule disruptions. Furthermore, the selection of the charging strategy and battery size can increase the total capital investment and operational expenses of a BEB fleet, which is a major obstacle to its adoption. Therefore, to minimize the total cost of ownership (TCO) and prevent schedule disruptions, it is essential to establish a well-defined approach to determine an appropriate battery size and charging strategy for BEB fleets. This paper presents a method for reducing the TCO of BEB by determining the optimal battery size and charging strategy for each bus while satisfying operating constraints. The method involves a two-step optimization algorithm that uses Dynamic Programming and Genetic Algorithm. Further, the study applies this approach to the bus fleet serving line 21 in Paris and generates the optimal battery sizing, charging strategy, and required charging infrastructure. The results indicate that 100 kWh batteries offer the best trade-off between capital and operational expenditure for the fleet deployment if used with 65–85 kW chargers at bus terminals.

33 ADVANCED PROPULSION SYSTEMS↗

A sequential linear optimization approach for controller design

A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

Horta, L. G.↗

Multidisciplinary optimization of a controlled space structure using 150 design variables

A controls-structures interaction design method is presented. The method coordinates standard finite-element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structure and control system of a spacecraft. Global sensitivity equations are used to account for coupling between the disciplines. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Design problems using 15, 63, and 150 design variables to optimize truss member sizes and feedback gain values are solved and the results are presented. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporation of the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables.

James, Benjamin B.↗

Improving Mathematical Exposition of an Industrial-Scale Linear Program

Industrial-scale models require considerable setup time; hence, once built, they are used in myriad ways to consider closely related cases. In practice, the code for these models frequently evolves without appropriate notational choices, largely as a result of the lengthy development time of, and the number of individuals contributing to, their formulation. This leads to inefficiencies and obfuscates model structures that might be leveraged to expedite solutions. In this paper, we advocate for an emerging literature on model formulation “best practices” and present the reformulation of a widely used industrial-scale linear program. The efficient mathematical expression of this linear program, used to plan capacity expansion in the energy sector, allows for greater transparency of model structures and enhanced ability to identify computational performance improvements, as well as a lucid interpretation of its solutions. This type of formulation is employed in several mathematical programming courses at our university as an example of the advantages of best practices; the model more broadly is used widely to inform policy in the U.S. energy sector.

97 MATHEMATICS AND COMPUTING↗

Mathematical programming formulations for satellite synthesis

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Bhasin, Puneet↗

Application of digital computer APU modeling techniques to control system design.

Study of the required controls for a H2-O2 auxiliary power unit (APU) technology program for the Space Shuttle. A steady-state system digital computer program was prepared and used to optimize initial system design. Analytical models of each system component were included. The program was used to solve a nineteen-dimensional problem, and then time-dependent differential equations were added to the computer program to simulate transient APU system and control. Some system parameters were considered quasi-steady-state, and others were treated as differential variables. The dynamic control analysis proceeded from initial ideal control modeling (which considered one control function and assumed the others to be ideal), stepwise through the system (adding control functions), until all of the control functions and their interactions were considered. In this way, the adequacy of the final control design over the required wide range of APU operating conditions was established.

Bailey, D. A.↗

Damage tolerant composite wing panels for transport aircraft

Commercial aircraft advanced composite wing surface panels were tested for durability and damage tolerance. The wing of a fuel-efficient, 200-passenger airplane for 1990 delivery was sized using grahite-epoxy materials. The damage tolerance program was structured to allow a systematic progression from material evaluations to the optimized large panel verification tests. The program included coupon testing to evaluate toughened material systems, static and fatigue tests of compression coupons with varying amounts of impact damage, element tests of three-stiffener panels to evaluate upper wing panel design concepts, and the wing structure damage environment was studied. A series of technology demonstration tests of large compression panels is performed. A repair investigation is included in the final large panel test.

Smith, Peter J.↗

A strategy for reducing turnaround time in design optimization using a distributed computer system

There is a need to explore methods for reducing lengthly computer turnaround or clock time associated with engineering design problems. Different strategies can be employed to reduce this turnaround time. One strategy is to run validated analysis software on a network of existing smaller computers so that portions of the computation can be done in parallel. This paper focuses on the implementation of this method using two types of problems. The first type is a traditional structural design optimization problem, which is characterized by a simple data flow and a complicated analysis. The second type of problem uses an existing computer program designed to study multilevel optimization techniques. This problem is characterized by complicated data flow and a simple analysis. The paper shows that distributed computing can be a viable means for reducing computational turnaround time for engineering design problems that lend themselves to decomposition. Parallel computing can be accomplished with a minimal cost in terms of hardware and software.

Young, Katherine C.↗

Convex quadratic relaxations for mixed-integer nonlinear programs in power systems

Here, this paper presents a set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems. The considered models are motivated by hybrid discrete/continuous applications where existing approximations do not provide optimality guarantees. The new relaxations offer computational efficiency along with minimal optimality gaps, providing an interesting alternative to state-of-the-art semidefinite programming relaxations. Finally, three case studies in optimal power flow, optimal transmission switching and capacitor placement demonstrate the benefits of the new relaxations.

42 ENGINEERING↗

The Heuristic Dynamic Programming Approach in Boost Converters

In this study, a heuristic dynamic programming controller is proposed to control a boost converter. Conventional controllers such as proportional-integral-derivative (PID) or proportional-integral (PI) are designed based on the linearized small-signal model near the operating point. Therefore, the performance of the controller during the start-up, the load change, or the input voltage variation is not optimal since the system model changes by varying the operating point. The heuristic dynamic programming controller optimally controls the boost converter by following the approximate dynamic programming. The advantage of the HDP is that the neural network-based characteristic of the proposed controller enables boost converters to easily cope with large disturbances. An HDP with a well-trained critic and action networks can perform as an optimal controller for the boost converter. To compare the effectiveness of the traditional PI-based and the HDP boost converter, the simulation results are provided.

24 POWER TRANSMISSION AND DISTRIBUTION↗

On the robust optimization to the uncertain vaccination strategy problem

In order to prevent an epidemic of infectious diseases, the vaccination coverage needs to be minimized and also the basic reproduction number needs to be maintained below 1. This means that as we get the vaccination coverage as minimum as possible, thus we need to prevent the epidemic to a small number of people who already get infected. In this paper, we discuss the case of vaccination strategy in term of minimizing vaccination coverage, when the basic reproduction number is assumed as an uncertain parameter that lies between 0 and 1. We refer to the linear optimization model for vaccination strategy that propose by Becker and Starrzak (see [2]). Assuming that there is parameter uncertainty involved, we can see Tanner et al (see [9]) who propose the optimal solution of the problem using stochastic programming. In this paper we discuss an alternative way of optimizing the uncertain vaccination strategy using Robust Optimization (see [3]). In this approach we assume that the parameter uncertainty lies within an ellipsoidal uncertainty set such that we can claim that the obtained result will be achieved in a polynomial time algorithm (as it is guaranteed by the RO methodology). The robust counterpart model is presented.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Algorithmic Perspectives on Problem Formulations in MDO

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.

Alexandrov, Natalia M.↗

Auto Design

SPAR, a computer program developed by Lewis, is used to optimize the design of body panels by Chrysler Corporation. The program is interactive, easy to use, and fast.

Source record↗

Enhanced Fuel-Optimal Trajectory-Generation Algorithm for Planetary Pinpoint Landing

An enhanced algorithm is developed that builds on a previous innovation of fuel-optimal powered-descent guidance (PDG) for planetary pinpoint landing. The PDG problem is to compute constrained, fuel-optimal trajectories to land a craft at a prescribed target on a planetary surface, starting from a parachute cut-off point and using a throttleable descent engine. The previous innovation showed the minimal-fuel PDG problem can be posed as a convex optimization problem, in particular, as a Second-Order Cone Program, which can be solved to global optimality with deterministic convergence properties, and hence is a candidate for onboard implementation. To increase the speed and robustness of this convex PDG algorithm for possible onboard implementation, the following enhancements are incorporated: 1) Fast detection of infeasibility (i.e., control authority is not sufficient for soft-landing) for subsequent fault response. 2) The use of a piecewise-linear control parameterization, providing smooth solution trajectories and increasing computational efficiency. 3) An enhanced line-search algorithm for optimal time-of-flight, providing quicker convergence and bounding the number of path-planning iterations needed. 4) An additional constraint that analytically guarantees inter-sample satisfaction of glide-slope and non-sub-surface flight constraints, allowing larger discretizations and, hence, faster optimization. 5) Explicit incorporation of Mars rotation rate into the trajectory computation for improved targeting accuracy. These enhancements allow faster convergence to the fuel-optimal solution and, more importantly, remove the need for a "human-in-the-loop," as constraints will be satisfied over the entire path-planning interval independent of step-size (as opposed to just at the discrete time points) and infeasible initial conditions are immediately detected. Finally, while the PDG stage is typically only a few minutes, ignoring the rotation rate of Mars can introduce 10s of meters of error. By incorporating it, the enhanced PDG algorithm becomes capable of pinpoint targeting.

Acikmese, Behcet↗

Mixed Integer Programming and Heuristic Scheduling for Space Communication

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

Lee, Charles H.↗

Multidisciplinary optimization of controlled space structures with global sensitivity equations

A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.

Padula, Sharon L.↗