scholarly journals Two-Stage Spline-Approximation with an Unknown Number of Elements in Applied Optimization Problem of a Special Kind

2021 ◽  
Vol 9 (4) ◽  
pp. 411-420
Author(s):  
V. I. Struchenkov ◽  
D. A. Karpov
Keyword(s):  
Optimization Problem ◽  
Spline Approximation ◽  
Special Kind ◽  
Two Stage ◽  
Unknown Number ◽  
Applied Optimization

Two Stage Mini-Max Algorithm for Grid-Based Wind Farm Layout Optimization

2017 ◽  
Author(s):  
Ning Quan ◽  
Harrison Kim
Keyword(s):  
Power Output ◽  
Wind Farm ◽  
Optimization Problem ◽  
Layout Optimization ◽  
Discrete Optimization Problem ◽  
Real World Data ◽  
Two Stage ◽  
Wind Farm Layout ◽  
Wind Farm Layout Optimization ◽  
Grid Based

The power maximizing grid-based wind farm layout optimization problem seeks to determine the layout of a given number of turbines from a grid of possible locations such that wind farm power output is maximized. The problem in general is a nonlinear discrete optimization problem which cannot be solved to optimality, so heuristics must be used. This article proposes a new two stage heuristic that first finds a layout that minimizes the maximum pairwise power loss between any pair of turbines. The initial layout is then changed one turbine at a time to decrease sum of pairwise power losses. The proposed heuristic is compared to the greedy algorithm using real world data collected from a site in Iowa. The results suggest that the proposed heuristic produces layouts with slightly higher power output, but are less robust to changes in the dominant wind direction.

scholarly journals End-to-End Game-Focused Learning of Adversary Behavior in Security Games

2020 ◽  
Vol 34 (02) ◽  
pp. 1378-1386
Author(s):  
Andrew Perrault ◽  
Bryan Wilder ◽  
Eric Ewing ◽  
Aditya Mate ◽  
Bistra Dilkina ◽  
...  
Keyword(s):  
Expected Utility ◽  
Optimization Problem ◽  
Predictive Accuracy ◽  
Experimental Results ◽  
Limited Data ◽  
Two Stage ◽  
Security Games ◽  
End To End ◽  
Feature Values ◽  
Adversary Model

Stackelberg security games are a critical tool for maximizing the utility of limited defense resources to protect important targets from an intelligent adversary. Motivated by green security, where the defender may only observe an adversary's response to defense on a limited set of targets, we study the problem of learning a defense that generalizes well to a new set of targets with novel feature values and combinations. Traditionally, this problem has been addressed via a two-stage approach where an adversary model is trained to maximize predictive accuracy without considering the defender's optimization problem. We develop an end-to-end game-focused approach, where the adversary model is trained to maximize a surrogate for the defender's expected utility. We show both in theory and experimental results that our game-focused approach achieves higher defender expected utility than the two-stage alternative when there is limited data.

A Study on Efficient Computing Budget Allocation for a Two-Stage Problem

2021 ◽  
pp. 2050044
Author(s):  
Tianxiang Wang ◽  
Jie Xu ◽  
Jian-Qiang Hu
Keyword(s):  
Optimization Problem ◽  
Simulation Optimization ◽  
Risk Measure ◽  
Budget Allocation ◽  
Optimal Decision ◽  
Two Stage ◽  
Second Stage ◽  
Allocation Procedure ◽  
Optimal Computing Budget Allocation ◽  
Sequential Allocation

We consider how to allocate simulation budget to estimate the risk measure of a system in a two-stage simulation optimization problem. In this problem, the first stage simulation generates scenarios that serve as inputs to the second stage simulation. For each sampled first stage scenario, the second stage procedure solves a simulation optimization problem by evaluating a number of decisions and selecting the optimal decision for the scenario. It also provides the estimated performance of the system over all sampled first stage scenarios to estimate the system’s reliability or risk measure, which is defined as the probability of the system’s performance exceeding a given threshold under various scenarios. Usually, such a two-stage procedure is very computationally expensive. To address this challenge, we propose a simulation budget allocation procedure to improve the computational efficiency for two-stage simulation optimization. After generating first stage scenarios, a sequential allocation procedure selects the scenario to simulate, followed by an optimal computing budget allocation scheme that determines the decision to simulate in the second stage simulation. Numerical experiments show that the proposed procedure significantly improves the efficiency of the two-stage simulation optimization for estimating system’s reliability.

scholarly journals Risk-Based Two-Stage Stochastic Optimization Problem of Micro-Grid Operation with Renewables and Incentive-Based Demand Response Programs

Energies ◽  
2018 ◽  
Vol 11 (3) ◽  
pp. 610 ◽  
Author(s):  
Pouria Sheikhahmadi ◽  
Ramyar Mafakheri ◽  
Salah Bahramara ◽  
Maziar Damavandi ◽  
João Catalão
Keyword(s):  
Stochastic Optimization ◽  
Demand Response ◽  
Optimization Problem ◽  
Two Stage ◽  
Stochastic Optimization Problem ◽  
Micro Grid ◽  
Grid Operation ◽  
Demand Response Programs

scholarly journals Analysis of Loop Programs Using Generalization

2021 ◽  
Author(s):  
◽  
Glenn Colman
Keyword(s):  
Artificial Intelligence ◽  
Symbolic Execution ◽  
Two Stage ◽  
Second Stage ◽  
Unknown Number ◽  
Extensive Search ◽  
Number Of Iterations ◽  
Artificial Intelligence Systems

<p>This thesis describes a symbolic execution system, PAN, that is able to symbolically execute loops. PAN achieves this by generalizing the effect of a few loop iterations to predict the effect of an unknown number of iterations. PAN operates on relatively unstructured loops that include 'go to' type constructs, allowing multiple exits from a loop. PAN uses a two stage generalization approach using techniques developed in Artificial Intelligence systems. The first stage uses models of expected loop effects and requires only limited search to generalize the effect of simple loops The second stage uses a less constrained approach that can generalize the effects of more complex loops by using extensive search. Fundamental to PAN's generalization method is the sequence. These are identified using models and used in both stages of the generalization process.</p>

scholarly journals On the Optimality of Affine Policies for Budgeted Uncertainty Sets

2021 ◽  
Author(s):  
Omar El Housni ◽  
Vineet Goyal
Keyword(s):  
Robust Optimization ◽  
Structural Properties ◽  
Optimization Problem ◽  
Hardness Of Approximation ◽  
Uncertain Parameters ◽  
Two Stage ◽  
Uncertainty Sets ◽  
Adjustable Robust Optimization ◽  
Robust Optimization Problem ◽  
Budgeted Uncertainty

In this paper, we study the performance of affine policies for a two-stage, adjustable, robust optimization problem with a fixed recourse and an uncertain right-hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets, widely used in practice, in which we can specify a budget on the adversarial deviations of the uncertain parameters from the nominal values to adjust the level of conservatism. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than [Formula: see text] even for budget of uncertainty sets in which [Formula: see text] is the number of decision variables. Affine policies, in which the second-stage decisions are constrained to be an affine function of the uncertain parameters provide a tractable approximation for the problem and have been observed to exhibit good empirical performance. We show that affine policies give an [Formula: see text]-approximation for the two-stage, adjustable, robust problem with fixed nonnegative recourse for budgeted uncertainty sets. This matches the hardness of approximation, and therefore, surprisingly, affine policies provide an optimal approximation for the problem (up to a constant factor). We also show strong theoretical performance bounds for affine policy for a significantly more general class of intersection of budgeted sets, including disjoint constrained budgeted sets, permutation invariant sets, and general intersection of budgeted sets. Our analysis relies on showing the existence of a near-optimal, feasible affine policy that satisfies certain nice structural properties. Based on these structural properties, we also present an alternate algorithm to compute a near-optimal affine solution that is significantly faster than computing the optimal affine policy by solving a large linear program.

scholarly journals On the Sparse Beamformer Design

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3536
Author(s):  
Mingjie Gao ◽  
Ka Yiu ◽  
Sven Nordholm
Keyword(s):  
Optimization Model ◽  
Optimization Problem ◽  
Numerical Results ◽  
Minimal Effect ◽  
Two Stage ◽  
Filter Length ◽  
Length Increase ◽  
Beamformer Design

In designing acoustic broadband beamformers, the complexity can grow significantly when the number of microphones and the filter length increase. It is advantageous if many of the filter coefficients are zeroes so that the implementation can be executed with less computation. Moreover, the size of the array can also be pruned to reduce complexity. These problems are addressed in this paper. A suitable optimization model is proposed. Both array pruning and filter thinning can be solved together as a two-stage optimization problem to yield the final sparse designs. Numerical results show that the complexity of the designed beamformers can be reduced significantly with minimal effect on performance.

Sign in / Sign up

Export Citation Format

Share Document