Most Popular
1500 questions
5
votes
0 answers
Linear programming approach to dynamic programming - an initial pair of state-decisions
I aim to solve the following Bellman equation:
\begin{equation}
v(\vec{s}) = \min_{\vec{x} \in \Xi_{\vec{s}}} \big\{c(\vec{s}, \vec{x}) + \lambda \times \sum_{\vec{s}^{'}\in S} p(\vec{s}^{'} | \vec{s}, \vec{x}) \times v(\vec{s}^{'})\big\}
…
mdslt
- 615
- 3
- 8
5
votes
2 answers
Assembly line balancing: What does machine precedence mean?
I am looking at the looking at the following classical integer programming model for assembly line balancing:
R.R.Vemuganti's "Applications of Set Covering, Set Packing and Set Partitioning Models: A Survey", in Handbook of Combinatorial…
user2153235
- 223
- 1
- 5
5
votes
1 answer
Can we linearize the division of a binary variable by a continuous variable?
I'm trying to solve an MINLP problem where the following division term is appearing in the objective:
$$z_r = \frac{x_{ry}}{\sum_r d_r x_{ry}}, \forall r, y,$$ where $x_{ry}$ is a 2D binary variable and $d_r$ is a non-zero real number. In addition,…
Sourav Mondal
- 95
- 3
5
votes
2 answers
Why is it called the "Simplex" Algorithm/Method?
I have been trying to learn more about the Simplex Algorithm/Method. In particular, I am interested in knowing why this algorithm is called the "Simplex Algorithm".
For instance, when reading the Wikipedia Page…
stats_noob
- 1,831
- 7
- 30
5
votes
1 answer
How to handle a non-separable bilinear objective function in the special case of decoupled constraints?
I have a large number of (10000+) non-negative, real decision variables $x_i$ and $y_j$.
Let $I$ and $J$ be the index sets associated with $x$ and $y$, respectively.
Let $\bar{I}$ and $\bar{J}$ be non-empty subsets of $I$ and $J$, respectively.
The…
Displayed_Name
- 135
- 4
5
votes
1 answer
How to handle a bilinear objective function in the special case of decoupled constraints?
I have decision variables $x_i$ and $y_j$, real positive variables.
I would like to minimize objective function
\begin{aligned}
\min \quad & \sum_{ij} x_iy_j \\
\end{aligned}
All constraints are linear and decoupled/separable in the sense that each…
Displayed_Name
- 135
- 4
5
votes
1 answer
Lazy-Constraints for modelling soft-constraints (CPLEX + rejectCandidate semantics)
I basically have a (somewhat bloated) assignment-problem on a boolean-matrix: (N_WORKERS, N_TASKS). Let's assume, we only look at one specific worker and therefore we have a 1d boolean assignment-vector: x.
I'm trying to model a soft-constraint…
sascha
- 505
- 4
- 11
5
votes
2 answers
Regularization in Machine Learning : Constraint Optimization in Disguise?
I have the following question on "Regularization vs. Constrained Optimization" :
In the context of statistical modelling, we are often taught about "Regularization" as a method of dealing with the "Bias-Variance Tradeoff" (i.e. stabilizing the…
stats_noob
- 1,831
- 7
- 30
5
votes
2 answers
is there any recommended "rolling horizon in optimization" literature for beginners?
I am relatively new to optimization and mathematical programming. I am looking for literature on rolling horizon. When I search for it on the internet, I find many articles like:
Lukas Glomb et al.
Javier Silente et al.
Tareq Al-Ameri et al.
and…
Andre
- 303
- 1
- 5
5
votes
2 answers
Is Traveling Salesman Problem "Combinatorial Optimization" or "Integer Optimization"?
I am looking at the Traveling Salesman Problem and I can not figure out if this problem is a type of "Integer Optimization Problem", or is a type of "Combinatorial Optimization Problem"?
It seems like this is a Combinatorial Optimization Problem. Is…
stats_noob
- 1,831
- 7
- 30
5
votes
2 answers
What is the newest MIP and CP solver?
What is the newest MIP or CP solver (which is model based exact solver)?
I want to follow and wonder developments on solvers. But finding new developed solvers (experimental, academic, commercial etc.) with search is not enough, and sometimes can be…
kur ag
- 815
- 5
- 14
5
votes
1 answer
Is the Travelling Salesman Problem Considered as "Gradient Free Optimization"?
I was thinking about the Traveling Salesman Problem the other day - for such types of discrete combinatorial optimization problems, do they have a "loss function"?
It seems that there is some "vague" function which takes inputs as different…
stats_noob
- 1,831
- 7
- 30
5
votes
2 answers
Linearizing $x^2/(1-x)$ by partitioning the interval $0
We have two decision variables
\begin{align}
& 0
user9659
5
votes
1 answer
CPLEX gives different solutions of MILP every run
I am solving a mixed-integer (binary) linear problem using CPLEX as a solver (branch-and-bound method). But I encountered the following issue. Each run I get a different solution at a different node of MILP. However, these solutions are very close…
errenmike1806
- 91
- 6
5
votes
1 answer
Can I print the linear programming sensitivity analysis report using google or-tools?
One can solve the linear programs using google or-tools with GLOP solver. I wonder if there is a way to print the sensitivity report (like shadow prices etc.).
Manu K. Gupta
- 59
- 2