Questions tagged [optimization]
For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.
459
questions
2
votes
2answers
158 views
Pyomo + Ipopt. Speed Issue
I am using Pyomo + Ipopt as solver to solve a NLP problem. The problem is not extremely complex in terms of dimensionality and ...
2
votes
1answer
311 views
Divisibility constraint in Integer programming
I have a simple question regarding the divisibility in integer programming
suppose the objective function is
$\text{max}\quad x_1 + x_2$
where the constraint is that the sum of $x_1$ and $x_2$ are ...
2
votes
1answer
105 views
How can I have minimum amount of resources wasted in this resource allocation problem?
I have a demand, $d$
I also have supply from 1000 sources. The supplies from those $N$ (for example, $N=1000$) sources are given by
$s_1,s_2,s_3,\cdots,s_N$. So,the total supply is : $s_1+s_2+\cdots+...
2
votes
1answer
129 views
Defining and comparing utilization rates for delivery service
I'm currently working on a case for a food delivery service and wondered whether my notion of "driver utilization" makes any sense.
My data set contains an hourly overview of the
number of active ...
2
votes
1answer
60 views
Constraining flow into a node and out of a node using Min Cost Flow input
Let's say I have a graph $G=(V,E)$ where each vertex has an edge going both into and out of it (i.e. cyclic, akin to the kidney donor pair problem). Now suppose we have a capacity $u_{ij} = 1 \forall(...
2
votes
1answer
73 views
Which is better to minimize w.r.t a lower bound or an upper bound of an objective function?
Suppose there is a optimization problem that aims at minimizing an objective function $X$ but we can't develop a mathematical model for minimizing $X$. However, there are two objective functions $Y$ ...
2
votes
1answer
48 views
Logical equivalencies to modeling an indicator decision variable in transportation problem
I am formulating a model that seeks to minimize the cost of shipping goods from factories to warehouses, where the cost of shipping is independent of the type or amount of goods being shipped (except ...
2
votes
1answer
79 views
Formulating “more complicated” objectives in Python Gurobi
I am currently learning how to use Gurobi for Python using their official tutorial found here. In this example, they appear to formulate the objective by simply specifying a cost dictionary to the <...
2
votes
1answer
55 views
Reformulating to locate the second largest decision variable of a set of decision variables
Consider a set of $A_{vn}$ decision variables such that $A_{v1},A_{v2},\cdots,A_{vn}<A$. While this is the standard formulation finding the maximum value of $A_{vn}$, I would also like to find the ...
2
votes
1answer
95 views
Problem with implementing squared terms in the objective function
I'm trying to implement either one of these objective functions, but I'm having a hard time with the squared terms. I'm attaching both so you can take a look at the structure and see if you can give ...
2
votes
1answer
147 views
2
votes
1answer
130 views
Representing Date Variables in Pulp
I am working on an optimisation problem that involves minimising shipping demurrage. I am struggling to model how to represent the difference, (x-y) between dates where the ship is ready to be loaded ...
2
votes
1answer
168 views
Does this problem fall into any common problem definition…Knapsack maybe?
I am struggling to find a representative problem formulation for this optimization challenge. I have implemented a MILP in Matlab, but the run time is taking more then a day. My goal is to see if it ...
2
votes
1answer
70 views
What is the state of the art on the Weber problem?
I'm trying to get up to speed on the Weber problem. I'm very much not an expert, unfortunately. I would really appreciate recent literature recommendations / surveys / potted histories, however ...
2
votes
1answer
42 views
warmstarting simplex algorithm- how much can problems differ from each other?
I'm working on an implementation of the simplex algorithm.
I want to solve problems in real time every 30 minutes. They could be interpreted as a classic transportation problem.
I couldn't really say ...
2
votes
1answer
63 views
Impose binary constraint on integer matrix with CVXPY
So I have the following matrix:
\begin{equation}
P_{i,j}=
\begin{bmatrix}
x_0 & x_1 & x_2 \\
y_0 & y_1 & y_2 \\
z_0 & z_1 & z_2
\end{bmatrix}
\end{equation}
where ...
2
votes
3answers
74 views
Link a binary variable to continuous variable in Java Gurobi
I have the following problem:
Depending on my continuous optimization variable $S_m$, I would like to introduce a binary variable $x_m$, which, depending on the value of $S_m$ (greater or less than 0) ...
2
votes
2answers
62 views
Parallel scheduling with precedence constraints and variable job length
I have $N$ jobs and $M$ machines and want to minimize the makespan, i.e. the total time to finish all jobs. Some jobs have precedence constraints and can only be started once other jobs are finished. ...
2
votes
1answer
62 views
How to build a GAMS model in python
I looked at the GAMS python API but the documentation only describing already predefined models (run .gms with some tweaking options).
My question is now: Can I somehow build a gams model from scratch ...
2
votes
1answer
78 views
confusing results of two models with different complexity
i have two models that address the same problem.
the first one is :
the second one is:
for different instances for the same size (n=30) i found the following results ( the first column on the left ...
2
votes
1answer
67 views
MIP for assigning tasks with prerequisite tasks
I have a modified assignment problem for which I'm having difficulty formulating the constraints mathematically.
I have a set of workers and a set of tasks which should be completed in the minimum ...
2
votes
1answer
116 views
Is my formulation correct and how to formulate this IF-THEN constraint?
I have system with $N_U$ users and $N_T$ transmitters. Multiple transmitters can transmit to a single users and one transmitter can transmit to many users, i.e., two sets of transmitters serving two ...
2
votes
3answers
204 views
Is there any OR way to solve this problem?
For each observations there are 207 variables (binary, either a 'symptom' happened or not), class variable is also binary.
For each variable or symptom there is a weight attached (currently set ...
2
votes
1answer
50 views
Specify the criteria of the optimal solution
I have three variables $x_{1},x_{2},x_{3}$ and a function $f : D \rightarrow \mathbb{R}$ where $D$ is defined as such :
$$D = (x_{1},x_{2},x_{3})$$ such that $$x_{1}+x_{2}+x_{3}=1$$ and $$x_{1}>x_{...
2
votes
1answer
84 views
Specific usecase of two-phase simplex algorithm
The problem below aims to find to most optimal way to transport the fuel :
A company Er must transport a type of fuel from its two refineries Ra and Rb to its two points of sale PV1 and PV2. The ...
2
votes
1answer
43 views
How to define a stationary point of the MINLP problem?
As we all know, KKT point and stationary point are well defined when the optimization variables are continuous in the problem.
Now, I want to know whether there exist some special points except for ...
2
votes
1answer
38 views
Question about theorems of the form “Any limit point of the sequence is a minimum of the problem”
In Optimization, we have problems of the form
\begin{align*}
&\min f(x)\\
&\text{s.t. }\hspace{0.2cm} x \in S
\end{align*}
and many theorems are of the form "If the problem satisfies ...
2
votes
1answer
60 views
Formulating indicator constraint set
I am having difficulty formulating the indicator constraints for the following:
Consider a set of $A_{n}$ decision variables such that $A_{1},A_{2},⋯,A_{n}<A$. While all of them are integers that ...
2
votes
1answer
64 views
Quasi-convex function must be “partially monotonic”?
$f(x)$ is quasi-convex,
$$x^*\in\arg\min_{x\in C}f(x).$$
How to prove that, for any $a\in C$, $f(x) $ is weakly monotonic in the direction of $(x^*-a)$?
Is this simple result a part of an ancient ...
2
votes
1answer
74 views
AdaGrad - Sparsity of parameters
I read on Wikipedia:
AdaGrad (for adaptive gradient algorithm) is a modified stochastic gradient descent algorithm with per-parameter learning rate, first published in 2011. Informally, this ...
2
votes
1answer
97 views
Safety stock calculation with production forecast variance
I am trying to find an safety stock calculation where the expression incorporates:
Lead time variance
Sales demand variance &
Production forecast variance
My calculation so far is based on the ...
2
votes
1answer
57 views
Normalization approaches to manufacturing data
I’m hoping someone would be able to help with insight to a normalization approach, I am tasked with identifying the relative difficulty between stages in a manufacturing process.
The processes can be ...
2
votes
0answers
29 views
How to use NEOS without using Pyomo
I am new to modelling language and specifically NEOS server. I aim to solve MINLP using Baron, through the NEOS server. So, far I have been able to write model file, data file and command file as ...
2
votes
0answers
51 views
How to model non-zero minimum constraint?
I found following way to model a minimum constraint but in my case I need a non-zero minimum value. So in this figure, if any value of x_i is 0 then answer is 0 (assume x_i >=0) but I need non-zero ...
2
votes
0answers
35 views
Hardness Reduction for assigning Users to Servers
Suppose there are $x$ servers, and $y$ users. The $y$ users are to be assigned to the $x$ servers similar to classic scheduling problems. The cost of using servers is given by $c(|x|)$ which is an ...
2
votes
0answers
126 views
Solving systems of equations with simple implicit functional relations
I am attempting to solve five variables from a system of equations. Let the variables be $x_1,x_2,x_3,x_4,x_5$. Let the problem have the form:
$\exp(x_1)+x_1^6=x_3+x_4+x_5 \tag{1}$
$\exp(x_2)+x_2^6=...
2
votes
0answers
72 views
Solving transportation problem by the Network Simplex
I am trying to solve the following problem using Network Simplex method. But I have questions.
My attempt:
Basis Matrix$(B)$
Rows: 1, 2, 3, 4, 5
Column: (1,3) (1,4) (1,5) (2,3) (2,4) (2,5)
$$
\...
2
votes
0answers
52 views
CPU time on Linux with Gurobi
I am solving a MILP model in C++ using Gurobi 10.1.
I retrieve the CPU time of my C++ program under Linux via the following commands:
...
2
votes
0answers
128 views
modify pickup and delivery problem to only delivery scenario in google OR-tools
I am using Google OR Tools for solving the capacitated vehicle routing problem.I want to implement optimization solution for delivery problem.For example there is one storage location which load all ...
2
votes
0answers
61 views
Dynamic Programming problem of affecting equipment with budget constraint
I have a problem that I must formulate as a DP problem and solve.
A hospital is split up into 4 sections, each section has 1 or 2 or 3 backup generators. We have to maximize the likelihood that no ...
2
votes
0answers
57 views
Node ordering in Graph optimization
I'm solving a network optimization problem which is modeled as a graph $G=(V,E)$. Solving this problem using Pulp and NetworkX in Python and ordering the graph's nodes in a certain order (i.e. (1,2,3,...
2
votes
0answers
61 views
Reading MPS file for linear programming and reconstructing the Optimization model
Are you aware of any tutorial that can help me learn on how to reconstruct the objective function and constraints from a MPS file once it's loaded in MATLAB. I can load the mps file given to me and ...
2
votes
0answers
26 views
MDP model for a unique system
Let's assume that we have a system where there are two exogenous factors, name $a$ and $b$, that can affect the system state. At each decision epoch either $a$ or $b$ occurs and it is not possible ...
2
votes
0answers
53 views
How to set solver options in Pyomo with GAMS Python API?
Did anyone have experiences with Pyomo and GAMS as solver? I had looked into the pyomo documentation (GAMSShell Solver) and in the CPLEX Manuals, but doesnt find the correct syntax.
My Code looks like:...
2
votes
0answers
36 views
Algorithms for finding step sizes which satisfy the Wolfe conditions?
I am a student studying optimization, and I am interested in algorithms which finds step sizes satisfying the Wolfe (or strong Wolfe) conditions. I do know of one book which provides such an algorithm:...
2
votes
0answers
148 views
Operation hours optimization for circular schedule
Here is my problem. A store has X = 15 electical devices with the ability to work non-stop, fully charged, up to 8 hours. Their battery charge lasts 2 hours and the operating hours of the store differ ...
2
votes
0answers
46 views
Algorithm for Trainyard Marshall optimization problem
The problem I am trying to solve is the 2014 RAS problem. The link is the following
The problem
Trains come to the humpyard where each compartment of a train gets humped or disassembled and then each ...
2
votes
0answers
45 views
Decision-making algorithm for dynamic load balancing
I'm researching a subject of balancing the load between two black-box systems (with some twists). I thought that I could record latest response time log from each of those systems and process such a ...
2
votes
0answers
62 views
Density Optimization by Fitting an Circle to a Field - Monte Carlo Method
Given: I have 2D non-parametric formula that provides instantaneous intensity at certain (x,y) location.
Required: I want to en-circle a region where the density is high via optimization. In other ...
2
votes
0answers
58 views
Weapon Target Assignment Problem + Time Windows
So I am very familiar with the WTAP it the static case. What I am wondering, is there a formulation that has "time windows" as well? Let's say you have some weapons and some targets, you know the ...
