Robust Optimization VS Stochastic Optimization
2016-01-12 22:52
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1. Robust optimization addresses optimization problems with uncertain parameters that are not described using probability distributions but uncertainty sets.
2. A robust optimization problem seeks to determine a solution to an optimization problem that is feasible for any realization of the uncertain parameters within the uncertainty set, and optimal for the worst-case realization
of these uncertain parameters.
a stochastic programming problem 的缺点:
(1) the number of scenarios太多,导致问题规模增大
(2) distribution functions很难描绘不确定变量的特性
Robust Optimization优点:
computationally efficient and modelling flexibility
代价:At the cost of reduced flexibility
可以用对偶变换来变成 single-level的问题来求解,但一个重要前提是最里层的优化问题是convex的
对比:
Stochastic:
Random vector λ is then modeled as a set Ω of plausible outcomes or scenarios
ω, where each ω ∈ Ω has an associated probability of occurrence πω such that
ω∈Ω πω = 1.
Stochastic Programming Problems with Recourse
The simplest recourse problem is the two-stage stochastic programming problem,
in which decisions are divided into two groups, namely:
• Decisions that have to be made before the realization of uncertain parameters:
first-stage or here-and-now decisions and do not depend on the realization of the random parameters. 联系动态经济调度中,t=1时的优化叫first-stage,变量叫 here-and-now decision variables。
• Decisions that are made after the actual values of uncertain parameters are
disclosed.
“second-stage, wait-and-see, or recourse decisions”
2. A robust optimization problem seeks to determine a solution to an optimization problem that is feasible for any realization of the uncertain parameters within the uncertainty set, and optimal for the worst-case realization
of these uncertain parameters.
a stochastic programming problem 的缺点:
(1) the number of scenarios太多,导致问题规模增大
(2) distribution functions很难描绘不确定变量的特性
Robust Optimization优点:
computationally efficient and modelling flexibility
代价:At the cost of reduced flexibility
可以用对偶变换来变成 single-level的问题来求解,但一个重要前提是最里层的优化问题是convex的
对比:
Stochastic:
Random vector λ is then modeled as a set Ω of plausible outcomes or scenarios
ω, where each ω ∈ Ω has an associated probability of occurrence πω such that
ω∈Ω πω = 1.
Stochastic Programming Problems with Recourse
The simplest recourse problem is the two-stage stochastic programming problem,
in which decisions are divided into two groups, namely:
• Decisions that have to be made before the realization of uncertain parameters:
first-stage or here-and-now decisions and do not depend on the realization of the random parameters. 联系动态经济调度中,t=1时的优化叫first-stage,变量叫 here-and-now decision variables。
• Decisions that are made after the actual values of uncertain parameters are
disclosed.
“second-stage, wait-and-see, or recourse decisions”
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