Questions tagged [constraint]

For questions related to constraints, i.e. any restriction or relation a set of decision variables has to satisfy.

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MIP formulation for a lower semi-continuous function

How can I formulate in mixed linear programming (a set of constraints) the following issue. I have a maximization function on x, g(x). I need to convert a ...
Di Al's user avatar
  • 1
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1 answer
45 views

Sum only over weekend days

I would like to adjust my constraint so that the x are only ever added for the weekend of a week, i.e. days 6,7 and then 13,14 and 20,21 etc.. That would be my previous formulation, but how can I ...
mingabua's user avatar
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2 answers
62 views

What is the best way to constrain a binary matrix so that at most one row has positive values?

I have a binary variable $x_{i,j}$ for $i\in\{1,\ldots,m\}$ and $j\in\{1,\ldots,n\}$ and the constraint is to have at most one row that has ones. I wrote this as: $$x_{i,j}+x_{i',j'}\leqslant1,\forall ...
Jika's user avatar
  • 101
4 votes
1 answer
73 views

How to identify constraints that are good candidates for being lazy constraints?

I am working on reducing the solving time of the optimization problem I am working on. One of the ideas I am exploring is the usage of Lazy constraints. As solver, I am using Gurobi, so both pre-...
cholo14's user avatar
  • 223
2 votes
1 answer
68 views

Compute time between tasks

I am trying to solve an optimization problem in which there is a set of tasks, $S$, where $s_i$ and $e_i$ are the starting and ending time of task $i \in S$. Each task $i $ must be done within its own ...
Christopher Expósito Izquierdo's user avatar
1 vote
1 answer
108 views

How to linearize the following constraints

Given the following two expressions: $ x - \frac{1}{T}\sum_{i} y_{i}$ $ x - \frac{1}{Q}\sum_{i} \beta_{i} y_{i}$ where $x \in \mathbb{Z}_{+}$, $y \in \mathbb{R}_{+}$, and $T$, $Q$ and $\beta_{i}$ ...
CHE's user avatar
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2 answers
180 views

Starting with HiGHS

I have been messing about with HiGHS and trying to get a hang of its capability. Here is an example of a simple model from their github repo https://github.com/ERGO-Code/HiGHS/blob/master/examples/...
Erin Walter's user avatar
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1 answer
143 views

Production scheduling

I'm formulating a scheduling problem with the following decision variables: $$X_t \space \text{is power sold to market in time period t} \\ Y_t \space \text{is power used for production in time period ...
fikacoder's user avatar
1 vote
1 answer
303 views

Discrete point inside a polygon formed by set of vertices

I am working on a problem where I have a set of 2D vertices and a test point. I want to chek whether the test point lies inside ...
Ken Adams's user avatar
1 vote
2 answers
221 views

How to properly tackle a big model using weak constraints

I'm currently working on a model that has a large number of variables (around 200k), and I don't know what the proper way to handle such a big problem is. One suggestion I got is to use lazy ...
Marco's user avatar
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3 votes
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Which solvers provide an IIS feature?

I am well aware that commercial solvers CPLEX and GUROBI provide an IIS (irreducible infeasible set) feature. @batwing mentions FICO Xpress in the comment section as well, and @RobPratt mentions SAS. ...
Kuifje's user avatar
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1 answer
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How to calculate the duration of a task in each shift?

I am solving a job scheduling problem with three shifts, the duration of all shifts are assumed to be known (and might be equal): The tasks can start from any shift We know the duration of each task ...
Optimization team's user avatar
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2 answers
35 views

Scheduling next shift such its not within X hours of previous shift

Hey i have this constraint that i am trying to code in python: "scheduling next shift such its not within X hours of previous shift" Given that i have start, end time of each shift and the ...
user12443's user avatar
2 votes
1 answer
108 views

How to select intermediate nodes in a network?

I have a network where nodes are connected as shown in the Figure . Nodes 2 and 4 have a connection to the cloud node. I am writing constraints where at least one node with a connection to the cloud ...
bsha's user avatar
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1 vote
2 answers
149 views

Linearizing if else conditions in ILP

We are given three binary indicator variables $X_{ij}, Y_{jk}$ and $Z_{jl}$. Write linear constraints such that, a) if $X_{ij}$ is equal to 1, then for that $j$ when $X_{ij} = 1$, exactly one $Y_{jk} =...
ephemeral's user avatar
  • 897
4 votes
2 answers
1k views

Which solvers should I use to solve large, but extremely sparse LP problems with 100-500 thousand variables?

I would like to solve the following type of LP problems: where M and N are very large numbers, they are on the order of a few hundreds of thousands and tens of thousands, respectively. As is clear ...
TobiR's user avatar
  • 143
2 votes
1 answer
70 views

Question About Fritz John Theorem and Slater Constraint Qualification

Background Information I am studying constraint qualifications. Here are two theorems leading to my question: Theorem 1$\space\space\space\space$ [Fritz John Theorem] Suppose that $f, g_1, \dots, g_k$...
Beerus's user avatar
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1 vote
1 answer
50 views

Is there any literature on constrained nonlinear optimization where constraint returns have to be queried from an oracle?

I am looking at literature considering constrained optimization problems of the form: $\min_{x\in X\subseteq R^n} f(x), \text{ subject to } g_{oracle}(x) \leq 0$ The optimization algorithm doesn't ...
Shourya Bose's user avatar
2 votes
1 answer
207 views

Compute overlapping time

I am trying to solve an optimization problem in which there is a set of tasks, $S$, where $s_i$ and $e_i$ are the starting and ending time of task $i \in S$. Each task $i $ must be done within its ...
Christopher Expósito Izquierdo's user avatar
2 votes
1 answer
145 views

SET game: how to generate all sets with a MIP?

I am playing around with the game called Set: In the game, certain combinations of three cards are said to make up a "set". For each one of the four categories of features — color, number, ...
SetPlayer's user avatar
1 vote
0 answers
24 views

Nesterov Acceleration in Proximal Iteration with Strictly Positive Variable?

I have a cost function of the form $f(x) - \log(x)$, where $f$ is some smooth function mapping $\mathbb{R}^n_+\to\mathbb{R}$and $x$ is restricted to be nonnegative by the problem constraints (and for ...
John Madden's user avatar
1 vote
1 answer
100 views

Constraints to avoid disjointed solutions in a MIP

Given an directed graph $G= (N,E)$, where $N$ is the set of nodes and $E$ is the set of all edges, each associated with a direction. $G$ is a connected graph but not necessarily a complete graph. A ...
CHE's user avatar
  • 111
1 vote
3 answers
201 views

MIP constraints with chronological ordering

I am using a MIP formulation to decide which dates and locations (i.e. stops) should be chosen for a route that maximizes the total revenue over all chosen stops. My decision variable $X$ is the ...
3Li's user avatar
  • 35
7 votes
1 answer
612 views

How can one model a binary variable?

I am looking for the formulation of a constraint that does the following. I want to introduce a new binary variable $\kappa_{it}$ that takes the value 1 if the sum of the other binary variable $\...
nflgreaternba's user avatar
-1 votes
1 answer
65 views

Literature for the Big-M constraint method

I've come across the possibility of introducing binary variables in linear programming with the Big-M method here several times now. Here is an example: \begin{align} &(1-x_{i})\le \sum_i y_i\\ &...
marvelfab12's user avatar
0 votes
1 answer
181 views

LP - How to model binary variable that indicates a switch

I have the following question / concern. I have a modeling problem with the decision variable $d_{ptm}$ which indicates whether product $p$ was serviced by machine $m$ in period $t$. It takes the ...
marvelfab12's user avatar
2 votes
1 answer
59 views

epigraphs for quadratic constraints

I have a constraint of the following form \begin{equation} x^{\top}x + y^{\top}y \leq t \end{equation} where x, y are vector variables and t is a scalar variable. I can augment the variables x and y, ...
Kumar's user avatar
  • 153
1 vote
1 answer
40 views

How to sum over periods till Period t?

I am trying to set up a constraint that does the following. I a binary variable $p_{it}$ that indicates whether a student $i$ passed the test in $t$. 1 if yes and 0 if no. Now I want to set up a ...
nflgreaternba's user avatar
0 votes
1 answer
52 views

Help finding linear constraint - LP

I have the following question. I have two variables $w_{nds}$ and $m_{nd}$. The first variable indicates whether a nurse $n$ works shift $s$ on day $d$. The second one indicates the motivation of ...
nflgreaternba's user avatar
1 vote
3 answers
112 views

How to linearize a chain of if-then constraints?

How can I express the process of converting a series of if-then constraints into a linear form? Let's assume that we have integer variable $x_i$, non-negative variables $y_i^d$, and binary variables $\...
linkho's user avatar
  • 177
4 votes
2 answers
384 views

union of constraints

How to solve problems like $\min_x f(x) \\ g(x) < 0 \ or \ h(x)<0$? I think we can solve $\min_x f(x) \\ g(x) < 0 $ and $\min_x f(x) \\ h(x) < 0 $, then we compare the solutions from these ...
StupidMan's user avatar
1 vote
2 answers
82 views

Grouping variables to take same value

Assume we have 50 variables that we want to split into 3 groups and each group should have at least 5 variables. How to formulate that all variables in the same group take the same values? I used the ...
milad's user avatar
  • 21
1 vote
2 answers
162 views

how to satisfy time constraints with meeting points?

I have a specific pickup and delivery problem to work on and am thinking how to incorporate time windows effectively. The problem has some driver with some time window [$a_d, b_d$] which is the start ...
Hemfri's user avatar
  • 33
3 votes
0 answers
68 views

constrained optimization with decreasing constraint thresholds -Literature tips

consider a constrained optimization problem (typically c=0), with f highly nonlinear: \begin{equation} \text{minimize}_x f(x) \\\\ s.t \ \ \ \ g(x) \leq c \end{equation} I experimented a bit and found ...
Lukas Schroth's user avatar
2 votes
1 answer
215 views

it is possible to have a constraint that does not contain any decision variables

I had formulated an optimization model, and along the way I had to change a variable into a parameter. In doing so, one of my constraints that contained the variable I changed no longer contained a ...
orion's user avatar
  • 23
1 vote
1 answer
119 views

Sigmoidal programming

I plan to use sigmoidal programming from the git repo https://github.com/madeleineudell/SigmoidalProgramming.jl There are some issues with the implementation of this repo. It requires me to pass $A, b,...
Meet Saiya's user avatar
3 votes
2 answers
371 views

How to model this binary constraint?

I have an optimization problem that has a variable in the matrix form. The variable is a binary matrix. It has size $M \times N = 10 \times 50$ where $M$ is the number of machines and $N$ is the ...
TheExerminate's user avatar
2 votes
2 answers
373 views

Representing "and"/"or" relationships into constraints

How do I represent the following constraints in terms of equations? For each i, either (1) holds or (2) holds- $$ x_{1}^i \geq x_{2}^i \quad and \quad x_{3}^i \geq x_{4}^i \quad {(1)} $$ $$ x_{1}^i \...
T_k's user avatar
  • 77
3 votes
3 answers
248 views

Equivalence between constraints in ILP

Let's have binary variables $x$ and $y$. I'd like to define a helping binary variable $z$ such that $$ z = 1 \; \;\; \mathrm{iff} \; \; \; x + y = 2.$$ If I wanted to express the equivalence between ...
tomashauser's user avatar
1 vote
1 answer
160 views

Linearize conditional constraint

Consider a variable c from the domain {-1,0,1}. I have the following constraint: IF $c = 1 \Rightarrow x = 1 $ ELSE $x = 0$ How do I linearize this constraint?
Waldo's user avatar
  • 19
1 vote
0 answers
78 views

How to speed up state of charge constraint in Pyomo model

Context: I am working on a small electricity market model in Pyomo. It optimizes the capacity of different technologies and generation in at least 43800 hours. One of the technologies is a battery. ...
funkypenguin's user avatar
2 votes
2 answers
58 views

How to restrict the amount of consecutive assignments

I'm working on a scheduling/rostering problem. In this scenario the shifts are predefined with a starting and ending date and time. The problem basically assigns people to shifts with a binary ...
Daniel Baquero's user avatar
0 votes
1 answer
64 views

Maximization problem with preferences on variables

Consider the following trivial, theoretical model: $$ \max x+2y+3z \qquad s.t. $$ $$ x \leq b_x $$ $$ y \leq b_y $$ $$ z \leq b_z $$ $$ x+y+z = 1 $$ $$ x,y,z \in \{0, 1\} $$ and $b_x$, $b_y$ and $b_z$ ...
Libra's user avatar
  • 937
1 vote
1 answer
76 views

Multiplicity-Constraint in Constraint Programming Solvers

I need to solve a CSP with a constraint imposing upper bounds on the multiplicity of variables in a list. More precisely, I need a constraint of the form ...
guigux's user avatar
  • 113
0 votes
1 answer
96 views

Meaning difference between SUMMATION and not in the MIP model

I'm asking you a question because I was confused about MIP while reading the paper. This paper is about dual crane optimization. In the MIP model of the paper, equations (7) and (8) are used to model ...
Kim's user avatar
  • 1
2 votes
3 answers
143 views

Efficient formulation of flexible job-shop scheduling constraints

I am working on a flexible job-shop scheduling problem, where indices are as follows: $i$: Index of operations $j$: Index of jobs $m$: Index of machines $p$: Index of operation sequences on a machine ...
mdslt's user avatar
  • 573
4 votes
2 answers
221 views

how to ensure minimum output of a generator (else zero output) in linear programming?

I want to ensure, that a generator (in my case a heat generator, for example a boiler) first starts to output thermal energy, when a certain minimum output can be realized. Otherwise the output should ...
Andre's user avatar
  • 293
3 votes
3 answers
298 views

Set null the next set of N values

I'm dealing with a problem I already modelled by using linear programming. The already existing constraints set at 1 groups of contiguous variables (for ex: ...
devOn's user avatar
  • 33
3 votes
2 answers
453 views

Binary integer programming with dynamic costs and total resource constraint

I am trying to find a suitable paradigm under which my discrete optimisation problem falls into. This looks similar to integer programming, so the goal is to find a binary vector $\bar{x}$. However, ...
shiftyscales's user avatar
2 votes
1 answer
103 views

Prove MF-Constraint Qualification but not LICQ is satisfied

Let $g_1(x):=(x_1-1)^2+(x_2-1)^2-2\leq 0, g_2(x):=(x_1-1)^2+(x_2+1)^2-2\leq 0, g_3(x):=-x_1\leq 0$ be given constraints. Show that the Mangasarian-Fromovitz Constraint Qualification (MFCQ) is ...
Uhmm's user avatar
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