247,246 research outputs found
Wasserstein robust combinatorial optimization problems
This paper discusses a class of combinatorial optimization problems with
uncertain costs in the objective function. It is assumed that a sample of the
cost realizations is available, which defines an empirical probability
distribution for the random cost vector. A Wasserstein ball, centered at the
empirical distribution, is used to define an ambiguity set of probability
distributions. A solution minimizing the Conditional Value at Risk for a worst
probability distribution in the Wasserstein ball is computed. The complexity of
the problem is investigated. Exact and approximate solution methods for various
support sets are proposed. Some known results for the Wasserstein robust
shortest path problem are generalized and refined
Modelling and Optimization of a Non-Constrained Multi-objective Problem having Multiple Utility Functions using Bayesian Theory
One of the multi-objective optimization methods makes use of the utility function for the objective functions. Utility function creating the most satisfaction answers for decision makers (DMs) by considering the priorities of the DMs; in an available studies; there are only one utility function for each objective function. But due to practical situation in different decision making environments in an industry or trade lead each goal has multiple utility functions. This paper presents a model of multi- objective problem in which each of the objective function has multiple utility function applying Bayesian theory. This model allows DMs to calculate the probability of these utilities using conditional probability in conditions of uncertainty. In addition, examples are given to illustrate the usefulness of this model
Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization
We propose a data-driven method to solve a stochastic optimal power flow
(OPF) problem based on limited information about forecast error distributions.
The objective is to determine power schedules for controllable devices in a
power network to balance operation cost and conditional value-at-risk (CVaR) of
device and network constraint violations. These decisions include scheduled
power output adjustments and reserve policies, which specify planned reactions
to forecast errors in order to accommodate fluctuating renewable energy
sources. Instead of assuming the uncertainties across the networks follow
prescribed probability distributions, we assume the distributions are only
observable through a finite training dataset. By utilizing the Wasserstein
metric to quantify differences between the empirical data-based distribution
and the real data-generating distribution, we formulate a distributionally
robust optimization OPF problem to search for power schedules and reserve
policies that are robust to sampling errors inherent in the dataset. A simple
numerical example illustrates inherent tradeoffs between operation cost and
risk of constraint violation, and we show how our proposed method offers a
data-driven framework to balance these objectives
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