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At least 91 records · Page 5

A statistical-based scheduling algorithm in automated data path synthesis

In this paper, we propose a new heuristic scheduling algorithm based on the statistical analysis of the cumulative frequency distribution of operations among control steps. It has a tendency of escaping from local minima and therefore reaching a globally optimal solution. The presented algorithm considers the real world constraints such as chained operations, multicycle operations, and pipelined data paths. The result of the experiment shows that it gives optimal solutions, even though it is greedy in nature.

Jeon, Byung Wook

A Most Probable Point-Based Method for Reliability Analysis, Sensitivity Analysis and Design Optimization

A major step in a most probable point (MPP)-based method for reliability analysis is to determine the MPP. This is usually accomplished by using an optimization search algorithm. The optimal solutions associated with the MPP provide measurements related to safety probability. This study focuses on two commonly used approximate probability integration methods; i.e., the Reliability Index Approach (RIA) and the Performance Measurement Approach (PMA). Their reliability sensitivity equations are first derived in this paper, based on the derivatives of their respective optimal solutions. Examples are then provided to demonstrate the use of these derivatives for better reliability analysis and Reliability-Based Design Optimization (RBDO).

Hou, Gene J.-W.

Optimal reentry guidance for aeroassisted orbit transfer vehicles

A three-state model is presented for analyzing the problem of optimal changes in heading with minimum energy loss for a hypersonic gliding vehicle. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy of the vehicle. A separate boundary-layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary-layer problem, three guidance laws are obtained, each having a feedback form. The guidance laws are evaluated for a hypothetical vehicle, and compared to an optimal solution obtained using a multiple shooting algorithm.

Calise, Anthony J.

Surrogate Modeling and Optimization of a Combustor with an Interdigitated Flushwall Injector

Design and Analysis of Computer Experiments (DACE) methods are applied and used to perform surrogate modeling and optimization of a simplified combustor flowpath with an interdigitated flushwall injector. The objectives of the optimization are the thrust potential and combustion efficiency, which are evaluated across a range of flight Mach numbers, duct heights, spanwise spacings, and injection angles. The focus of this work is to highlight the application of a sequential learning approach, in order to learn about the responses of the objective functions over the design space and to identify local regions of interest for further analysis. This approach is contrasted to a previous effort where only a single sampling set was used to fit surrogate models and perform optimization. The optimal solutions resulting from the previous and present approaches are different, due to surrogate model-guided local refinement of the design space allowed by the sequential learning method. The values of the global error estimates between the previous and present approaches are comparable, but the sequential method proved more computationally cost-effective. Further refinement in the optimal regions might be needed to improve predictive capability of surrogate models and to obtain the optimal solutions sets.

Rajiv R Shenoy

Postoptimality Analysis in the Selection of Technology Portfolios

This slide presentation reviews a process of postoptimally analysing the selection of technology portfolios. The rationale for the analysis stems from the need for consistent, transparent and auditable decision making processes and tools. The methodology is used to assure that project investments are selected through an optimization of net mission value. The main intent of the analysis is to gauge the degree of confidence in the optimal solution and to provide the decision maker with an array of viable selection alternatives which take into account input uncertainties and possibly satisfy non-technical constraints. A few examples of the analysis are reviewed. The goal of the postoptimality study is to enhance and improve the decision-making process by providing additional qualifications and substitutes to the optimal solution.

prioritization

Preliminary Work for Examining the Scalability of Reinforcement Learning

Researchers began studying automated agents that learn to perform multiple-step tasks early in the history of artificial intelligence (Samuel, 1963; Samuel, 1967; Waterman, 1970; Fikes, Hart & Nilsonn, 1972). Multiple-step tasks are tasks that can only be solved via a sequence of decisions, such as control problems, robotics problems, classic problem-solving, and game-playing. The objective of agents attempting to learn such tasks is to use the resources they have available in order to become more proficient at the tasks. In particular, each agent attempts to develop a good policy, a mapping from states to actions, that allows it to select actions that optimize a measure of its performance on the task; for example, reducing the number of steps necessary to complete the task successfully. Our study focuses on reinforcement learning, a set of learning techniques where the learner performs trial-and-error experiments in the task and adapts its policy based on the outcome of those experiments. Much of the work in reinforcement learning has focused on a particular, simple representation, where every problem state is represented explicitly in a table, and associated with each state are the actions that can be chosen in that state. A major advantage of this table lookup representation is that one can prove that certain reinforcement learning techniques will develop an optimal policy for the current task. The drawback is that the representation limits the application of reinforcement learning to multiple-step tasks with relatively small state-spaces. There has been a little theoretical work that proves that convergence to optimal solutions can be obtained when using generalization structures, but the structures are quite simple. The theory says little about complex structures, such as multi-layer, feedforward artificial neural networks (Rumelhart & McClelland, 1986), but empirical results indicate that the use of reinforcement learning with such structures is promising. These empirical results make no theoretical claims, nor compare the policies produced to optimal policies. A goal of our work is to be able to make the comparison between an optimal policy and one stored in an artificial neural network. A difficulty of performing such a study is finding a multiple-step task that is small enough that one can find an optimal policy using table lookup, yet large enough that, for practical purposes, an artificial neural network is really required. We have identified a limited form of the game OTHELLO as satisfying these requirements. The work we report here is in the very preliminary stages of research, but this paper provides background for the problem being studied and a description of our initial approach to examining the problem. In the remainder of this paper, we first describe reinforcement learning in more detail. Next, we present the game OTHELLO. Finally we argue that a restricted form of the game meets the requirements of our study, and describe our preliminary approach to finding an optimal solution to the problem.

Clouse, Jeff

Existence of the time optimal control for robotic manipulators

Using Filipov's Theorem, it is shown that the conditions oif nonfinite escape of trajectories, reachability, and convexity of the dynamics over all admissible controls are needed for the existence of a time optimal solution for the robotic equation. With a lower bound for the finite-escape time established using a Liapunov approach, and an upper bound for the time to reach the target established using the exact linearization idea, a single inequality is found which is closely related to the coriolis and the centrifugal terms, the absence of which implies that the domain of existence of the optimal solution can be made arbitrarily large with a large torque constraint. As the work space is finite, this is essentially a global result in practical situations.

Wen, J.

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION

A survey of methods of feasible directions for the solution of optimal control problems

Three methods of feasible directions for optimal control are reviewed. These methods are an extension of the Frank-Wolfe method, a dual method devised by Pironneau and Polack, and a Zontendijk method. The categories of continuous optimal control problems are shown as: (1) fixed time problems with fixed initial state, free terminal state, and simple constraints on the control; (2) fixed time problems with inequality constraints on both the initial and the terminal state and no control constraints; (3) free time problems with inequality constraints on the initial and terminal states and simple constraints on the control; and (4) fixed time problems with inequality state space contraints and constraints on the control. The nonlinear programming algorithms are derived for each of the methods in its associated category.

Polak, E.