Unanswered Questions
55 questions with no upvoted or accepted answers
9
votes
0
answers
230
views
Solving large-scale stochastic mixed integer program
What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
- 1,687
6
votes
0
answers
226
views
Airline revenue management re-solving problem
I am considering a bid prices (shadow price of the capacity constraint) problem (from Chen, L. and Homem-de Mello, T. (2009)., page 14) where the acceptable classes for booking requests for ...
- 165
6
votes
0
answers
95
views
Sample Average Approximation vs. Numerical Integration
In the sense of the calculation of the expected value of objective functions, we have two choices to evaluate the value; 1. Sample Average Approximation (SAA):
$$
\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).
$$...
- 155
6
votes
0
answers
53
views
What are useful plots/statistics/metrics when analyzing the solution sensitivity in multi-objective optimization?
Consider an optimization problem with $n>3$ objectives.
For handling this there exists often two approaches:
a) some weighting of the objectives,
b) fix an order of objectives and then optimize ...
- 5,442
5
votes
1
answer
162
views
Numerically stable way to optimize a lexicographical preference between two objective functions?
I am solving a mixed-integer program whose decision variables are $x \in \{0, 1\}^n$ and $y \in \mathbb{R}^m$, where $0 \leq y_j \leq u_j$ for constant upper bounds.
My primary objective function is ...
CommunityBot
- 1
5
votes
0
answers
154
views
Chance constrained optimization - interpretation
Suppose that we have a stochastic vector $\psi$ and $S$ realisations of $\psi$ given by $\psi_1,\dots,\psi_S$ with equal probability of occurrence. In addition, we have constraints of the form
\begin{...
- 2,463
5
votes
0
answers
80
views
Best method to optimize the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?
I am looking to optimize the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...
- 1,895
4
votes
0
answers
164
views
Stochastic optimization for inventory management
The deterministic problem is to minimize operational cost subject to constraints in demand, supply and capacity. The ordering policy is periodic review, order-up-to.
The stochastic version of the ...
- 1,895
4
votes
0
answers
54
views
How to find range of values for the first-stage decisions resulting in the same cuts in two-stage stochastic programming?
Suppose we have a two-stage stochastic program as follows:
\begin{equation}
\begin{split}
\min \ & c^Tx + \mathbb{E}_\xi[Q(x,\xi)] \\
& \text{where}\\
&Q(x,\xi)=\min q(\xi)^Ty\\
&Tx+...
- 2,160
4
votes
0
answers
251
views
How can I formulate this multi-objective optimization problem?
Now, for each system $X$ $(X=A,B,C,E)$, my objective is
$$\max\min\frac{s_{x_u}}{d_{x_u}}$$
here, $x=a$ for system A, $x=b$ for system B and follows...
and for the whole system, my objective is
$$\max\...
CommunityBot
- 1
3
votes
0
answers
124
views
Continuous optimization with a Euclidean TSP objective
I am trying to solve a problem of the form $$\min_{x_1,\dots,x_n} f(x_1,\dots,x_n)$$ subject to a constraint that $\mathrm{length}(\mathrm{TSP}(x_1,\dots,x_n))\leq c$, where $x_1,\dots,x_n$ are all ...
- 33.1k
3
votes
0
answers
100
views
Pygmo2: What is the point of evolving an archipelago in a loop if number of generations already set in algo
I want to solve a multi-objective problem with nsga2 or moead taking advantage of the parallelism available in pygmo library. I have seen a very nice example on github posted below. However I am not ...
- 31
3
votes
0
answers
50
views
Control variables and cofounding effects in stochastic programming/,model predictive control/reinforcement learning
How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable?
Since the term control variable ...
3
votes
0
answers
117
views
Multiserver Queue Theory Optimization problem
I have a design optimization problem where I need to connect a customer with a server via call. The scenario is as follows:
Customer-1 is connected with $N$ servers out of a total pool of $P$ servers....
- 31
3
votes
0
answers
89
views
Derivative of sup(max) functions in distributionally robust optimization
In the distributionally robust optimization problem
\begin{aligned}
\min_{x\in X}\sup_{P\in\mathfrak{P}}\mathbb{E}_P[f(x,\xi)],
\end{aligned}
where $f:\mathbb{R}^n\to\mathbb{R}$ and $P$ is a ...
- 155