212,489 research outputs found
Stochastic Constraint Programming
To model combinatorial decision problems involving uncertainty and
probability, we introduce stochastic constraint programming. Stochastic
constraint programs contain both decision variables (which we can set) and
stochastic variables (which follow a probability distribution). They combine
together the best features of traditional constraint satisfaction, stochastic
integer programming, and stochastic satisfiability. We give a semantics for
stochastic constraint programs, and propose a number of complete algorithms and
approximation procedures. Finally, we discuss a number of extensions of
stochastic constraint programming to relax various assumptions like the
independence between stochastic variables, and compare with other approaches
for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial
Intelligenc
Time Blocks Decomposition of Multistage Stochastic Optimization Problems
Multistage stochastic optimization problems are, by essence, complex because
their solutions are indexed both by stages (time) and by uncertainties
(scenarios). Their large scale nature makes decomposition methods appealing.The
most common approaches are time decomposition --- and state-based resolution
methods, like stochastic dynamic programming, in stochastic optimal control ---
and scenario decomposition --- like progressive hedging in stochastic
programming. We present a method to decompose multistage stochastic
optimization problems by time blocks, which covers both stochastic programming
and stochastic dynamic programming. Once established a dynamic programming
equation with value functions defined on the history space (a history is a
sequence of uncertainties and controls), we provide conditions to reduce the
history using a compressed "state" variable. This reduction is done by time
blocks, that is, at stages that are not necessarily all the original unit
stages, and we prove areduced dynamic programming equation. Then, we apply the
reduction method by time blocks to \emph{two time-scales} stochastic
optimization problems and to a novel class of so-called
\emph{decision-hazard-decision} problems, arising in many practical situations,
like in stock management. The \emph{time blocks decomposition} scheme is as
follows: we use dynamic programming at slow time scale where the slow time
scale noises are supposed to be stagewise independent, and we produce slow time
scale Bellman functions; then, we use stochastic programming at short time
scale, within two consecutive slow time steps, with the final short time scale
cost given by the slow time scale Bellman functions, and without assuming
stagewise independence for the short time scale noises
Stochastic utility-efficient programming of organic dairy farms
Opportunities to make sequential decisions and adjust activities as a season progresses and more information becomes available characterise the farm management process. In this paper, we present a discrete stochastic two-stage utility efficient programming model of organic dairy farms, which includes risk aversion in the decision maker’s objective function as well as both embedded risk (stochastic programming with recourse) and non-embedded risk (stochastic programming without recourse). Historical farm accountancy data and subjective judgements were combined to assess the nature of the uncertainty that affects the possible consequences of the decisions. The programming model was used within a stochastic dominance framework to examine optimal strategies in organic dairy systems in Norway
Stochastic Utility-Efficient Programming of Organic Dairy Farms
Opportunities to make sequential decisions and adjust activities as a season progresses and more information becomes available characterize the farm management process. In this paper, we present a discrete stochastic two-stage utility efficient programming model of organic dairy farms, which includes risk aversion in the decision maker's objective function as well as both embedded risk (stochastic programming with resource) and non-embedded risk (stochastic programming without recourse). Historical farm accountancy data and subjective judgments were combined to assess the nature of the uncertainty that affects the possible consequences of the decisions. The programming model was used within a stochastic dominance framework to examine optimal strategies in organic dairy systems in Norway.agriculture, risk analysis, stochastic programming, stochastic dominance, organic farming, Livestock Production/Industries, Q12, C61,
Recommended from our members
Software tools for stochastic programming: A Stochastic Programming Integrated Environment (SPInE)
SP models combine the paradigm of dynamic linear programming with
modelling of random parameters, providing optimal decisions which hedge
against future uncertainties. Advances in hardware as well as software
techniques and solution methods have made SP a viable optimisation tool.
We identify a growing need for modelling systems which support the creation
and investigation of SP problems. Our SPInE system integrates a number of
components which include a flexible modelling tool (based on stochastic
extensions of the algebraic modelling languages AMPL and MPL), stochastic
solvers, as well as special purpose scenario generators and database tools.
We introduce an asset/liability management model and illustrate how SPInE
can be used to create and process this model as a multistage SP application
Stochastic Programming with Probability
In this work we study optimization problems subject to a failure constraint.
This constraint is expressed in terms of a condition that causes failure,
representing a physical or technical breakdown. We formulate the problem in
terms of a probability constraint, where the level of "confidence" is a
modelling parameter and has the interpretation that the probability of failure
should not exceed that level. Application of the stochastic Arrow-Hurwicz
algorithm poses two difficulties: one is structural and arises from the lack of
convexity of the probability constraint, and the other is the estimation of the
gradient of the probability constraint. We develop two gradient estimators with
decreasing bias via a convolution method and a finite difference technique,
respectively, and we provide a full analysis of convergence of the algorithms.
Convergence results are used to tune the parameters of the numerical algorithms
in order to achieve best convergence rates, and numerical results are included
via an example of application in finance
- …