Stochastic optimization

Résumé

Stochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involves random objective functions or random constraints. Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. Stochastic optimization methods generalize deterministic methods for deterministic problems. Methods for stochastic functions Partly random input data arise in such areas as real-time estimation and control, simulation-based optimization where Monte Carlo simulations are run as estimates of an actual system, and problems where there is experimental (random) error in the measurements of the criterion. In such cases, knowledge that the function values are contaminated by random "noise" leads natur

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https://en.wikipedia.org/wiki/Stochastic_optimization

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Centralized and Decentralized Electricity Markets: Assessment of Operational and Economic Aspects

Farzaneh Abbaspourtorbati, Anneta Matenli

This paper presents the comparison of decentralized and centralized market settings in terms of economic efficiencies, particularly price signals, and operating aspects. The decentralized dispatch consists of an energy auction separated from a contingency analysis. The centralized setting is the conventional economic dispatch. This comparison includes deterministic and stochastic formulations (source of uncertainty is wind generation) applied on the Swiss power system.

Ieee2016

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Design of a tensegrity structure using stochastic search

Elodie Schmidt

2009

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Stochastic Optimization of Sailing Trajectories in an America's Cup Race

Frédéric Dumas

The main objective of the thesis is the study and the determination of an optimal navigation strategy, for a sailboat in an America's Cup race, by methods of stochastic optimization. Such methods are appropriate because the sailing team expects the wind to fluctuate over time in an unpredictable manner. Two preliminary models are designed as "proof of concept": they assume a shifty wind with two possible directions. The first model limits the potential actions of the yacht, by only allowing it either to continue on its current bearing or to tack. The second model allows additional bearings and aims at studying the concept of Wally. The third model is the main contribution of the thesis. It is based on a realistic wind model and a wide range of allowed yacht actions. It is designed for use during the first upwind leg of a regatta and can be used in real time, producing the trajectory recommendation which minimizes the expected time to the top mark that ends the leg. Other information is also provided, which quantifies the loss related to using non optimal actions or the advantage/disadvantage of other positions in the race field. Using Monte-Carlo simulations, we produce information about the probability of winning against the opponent, in terms of his current position. The last part of the thesis is dedicated to the implementation of an algorithm that stabilizes the output of a laser gun used on board the yacht during the races to determine the precise position of the opponent's yacht, which leads to estimates of direction and velocity. For this, we have developped a robust stabilization and automated filtering algorithm. We test this algorithm on real data.

EPFL2010

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