Questions tagged [constraint]
For questions related to constraints, i.e. any restriction or relation a set of decision variables has to satisfy.
144
questions
3
votes
1answer
113 views
If-then condition formulation to avoid variable multiplication
I'm trying to formulate the following logic:
If $y_i =1$, then $c_i \leq x_i$
If $y_i =0$, then $c_i \leq 0$
Where $y_i$, $c_i$, and $x_i$ are decision variables.
The easy way would be to write:
$$c_i ...
3
votes
1answer
153 views
Complicated constraint with logical operators in PuLP
I have an optimization problem that I am trying to solve with PuLP.
All the variables are Booleans.
The variables that are "selected" will be true, all others false.
Objective function is ...
1
vote
1answer
61 views
Tuples OPL in VRP
I am trying to build a constraint of the form x[i j] +x[j i] <y[i][j] where x is a decision variable if arc ...
1
vote
0answers
41 views
Minimizing total number of banners used in the cover buildings problem modelled
I was watching a video about Google OR-Tools where they were solving this cover building problem from Codility challenges using constraint programming.
In short, you have a list of building heights, e....
5
votes
2answers
333 views
The importance of evaluating the number of constraints
If I introduce a problem, say as an ILP formulation, should I also discuss the number of introduced constraints? If yes, why?
2
votes
1answer
45 views
How to model a cumulative resource constraint with same family condition?
Assume that we have 3 tasks to schedule : $x_{a1}, x_{a2}, x_{b3}$. They all use the same cumulative resource : $r_1$. Each activity increases $r_1$ by $1$ at it starts time and decreases $r_1$ by $1$ ...
3
votes
2answers
129 views
Defining multiple constraints compactly where some index combinations are not defined
My question is about how usual/strange defining constraints compactly can be (in a scientific document). Formally, I define constraints
$$f_{i,j,k}(x) \leq 0, \quad \forall i \in [I], \ \forall j \in [...
1
vote
1answer
50 views
Represent the minimum between two terms as a continuous constraint
Let's consider the following minimization problem:
\begin{align}
\min_{x,a,b}&\quad X\tag1\\
\text{s.t.}&\quad X = \min(A,B)\tag2\end{align}
with $A,B$ functions that depend on $X$.
Is there a ...
4
votes
1answer
182 views
How do constraints become redundant in a Big-M conjunction?
The following Big-M conjunction appears on page 14:3 of The Path&Cycle Formulation for the Hotspot Problem in Air Traffic Management:
\begin{align*}
\text{(i)} \quad t_{(g, \; s)} - t_{(f, \; s+...
4
votes
2answers
98 views
Deriving order/rank variable from another decision variable
There is a decision variable $x_i$ which denotes the time when a person is allowed to do his work.
The objective function is
$\min (x_i - a_i)$
where $a_i$ is the time when the person arrives at the ...
4
votes
1answer
123 views
Constrain Mixed-Integer problem such that a graph is fully connected
I have a problem (see my questions about Architectural layouts which poses an interesting abstract question) where there exists an implicit (symmetric) graph whose values in the adjacency matrix are ...
2
votes
1answer
49 views
Can we take the constraints from one model and plug them into the other model in pyomo?
I am implementing data-driven robust optimization methodology introduced in this article in python. Somewhere of the method, I need to use pyomo for each constraint whose parameters are uncertain to ...
7
votes
3answers
218 views
How to model a non-overlap constraint between 2 groups of tasks?
Let $T$ be a set of tasks. Each task $t \in T$ has a duration $d_t$.
Let $T_1 \subset T$ and $T_2 \subset T$ such as $T_1 \cap T_2 = \emptyset $
How can I model the following constraint : all tasks ...
1
vote
1answer
117 views
Operator error in operating cost model constraint
I have built a model to minimize the operating cost and when I coded a model in CPLEX, it gave an error at Cons09: ...
1
vote
0answers
67 views
vehicle routing optimization, Big M method of reformulation of constraints
Please excuse me for the long question, if I dont prrovide this info. my post gets removed!
The following optimization problem is called Mixed-Integer Quadratically Constrained Programming
(MIQCP) ...
4
votes
2answers
141 views
How to model: If $X\ge\epsilon$ then $X\ge Y$
Let $0\le X\le\bar X$ and $0\le Y\le\bar Y$ be nonnegative continuous variables. Let $\epsilon$ be a small positive number. How can the constraint $X\ge\epsilon\implies X\ge Y$ be modeled?
2
votes
0answers
60 views
How to write the constraint matrix for this blending problem?
Below is a model for maximizing a utility function, a blending of, 3 ingredients $(A, B,C)$ to obtain 3 mixes of fertilizer, with the recipe given as proportions. Ingredients cost $A=130,\ B=150,\ C=...
4
votes
1answer
92 views
Lot-sizing problem variant
I have a the following optimization problem: I have mandates,(e,g. to deliver 100 tonnes of products) that I need to schedule its delivery during the month (day 2: deliver 40 Tonnes, day 15: deliver ...
4
votes
1answer
381 views
Gurobi: how to add a constraint to make there be only one non-integer value
line1
line2
line3
line4
A
2.3
0
3.1
0
B
0
4
2.2
0
C
1.1
0
0
4.6
Let's say after optimization with certain constraints, my model will generate an optimal production allocation table similar to ...
1
vote
0answers
126 views
Adding sequence constraints to the assignment problem- Python
This is an online assignment problem and yet can be considered as an assignment problem with a sequence. Assume that workers are coming into the system sequentially and I want to assign a task to them ...
4
votes
1answer
144 views
Constraintlist with two Options Pyomo
I recently started with Pyomo and I have the following Problem:
I want to construct a ConstraintList with an if statement.
I already learned, that it's not possible. But the problem still exists...
My ...
3
votes
1answer
57 views
How to specify an objective function that prohibits trading in both directions linearly
I am building a small model that trades water and buys water. For simplicity reasons, I am only discussing the relevant constraints: $\sf varWaterIn_h$ is the amount in litres of water bought per hour,...
0
votes
0answers
76 views
Products distribution planning model
I have a problem of planning the distribution of products for a month. I have different unique products. A Mandate is provided for each product, and the Mandated quantity for each product is to be ...
1
vote
1answer
151 views
How do I write the following constraint?
I have defined the index for time to be T = [1,2,3,4,5,6]. I want that that the demand that to be addressed twice in a given a time period, when the difference between the time the demand is addressed ...
6
votes
2answers
130 views
Linearise $\max\{ y_{t-1} + a_t - z_t ,0\}$
I'm trying to linearise these constraints, but I am not able to do correctly do it.
$$y_t = \max\{ y_{t-1} + a_t - z_t, 0 \} $$
My attempt was this:
\begin{align}y'_t &\geq a_t - z_t\\y'_t &\...
1
vote
1answer
83 views
Formulate a constraint set to identify the number of overlapping operations
Let assume we have operation $r \in R$, machine $n \in N$ and day $t \in T$. $S_{r}$ is the service duration of operation $r$. Note that $S_{r}$ can be defined based on time slot (e.g., $S_{1}$ can be ...
4
votes
1answer
119 views
How do I formulate constraints that check if a parameter is between certain values, using binary variables?
I have $3$ parameters $a_1,a_2,a_3$ and a variable $d$ and $3$ binary variables $b_1,b_2,b_3$ and a "result" variable $s$. How do I model constraints so that:
If $d$ is between $0$ and $a_1$...
1
vote
0answers
98 views
How do I write the following constraints in Pyomo?
I'm currently trying to replicate a vehicle routing problem paper, and I'm facing trouble writing the said constraints in the paper in Pyomo. I've been able to generate the data as required by the ...
2
votes
1answer
90 views
Linearly independent rows in simplex
I'm having some trouble understanding about the independent rows in a basic solution. In the book Introduction to linear optimization by B&T, the authors give the definition of a basic solution as ...
5
votes
1answer
91 views
if $x = 0$ then $y \ne b$
I'm trying to model the following:
if $x=0$ then $y \ne b$
$y$ is a positive integer number( $y\le U$) and $x$ is binary and $b$ is a constant.
3
votes
2answers
220 views
How to make following constraint a convex one?
I would like to write a constraint as follows, where $x,y>0$ are optimization variables, and $a,b,c,d,A$ are positive constants. How to make it a convex constraint?
\begin{equation}
\frac{{ax}}{{\...
2
votes
1answer
81 views
CPLEX Indicator Constraints in Java API
I'm using the Java API of CPLEX (12.6.1 version) to solve a MILP problem.
This is how I create 'normal' constraints:
...
0
votes
1answer
84 views
How to create constraint-equations in Pyomo with empty set inputs
I would like to crate an constraint-equation that depends on 4 sets. For that I use the following code:
...
6
votes
1answer
136 views
Two equivalent soft constraint implementations
Take the following optimization problem:
\begin{align}\min_x&\quad f(x)\\\text{s.t.}&\quad g(x)\le0\end{align}
with $f$ and $g$ nonlinear functions. Suppose I want to relax the constraint by ...
1
vote
2answers
123 views
Show the total unimodularity of constraints matrix
I have a model as below.
I have constructed the matrix of its constraints as below. I need to show the total unimodularity of its constraints matrix. However, the determinant of the below submatrix (...
2
votes
3answers
90 views
Convex optimization on the unit hypercube with gradients and a bounded minimum
I'd like to find the minimum of a smooth, continuous function inside the unit hypercube (the dimensionality of which could go into the hundreds or even thousands). The function is convex (Hessian $\...
4
votes
3answers
162 views
How to couple a binary variable to a continuous variable to indicate values greater 0
I have a continuous variable $x_t$. A binary variable $b_t$ should be coupled to $x_t$ such that $b_t$ has the value $1$ if $x_t$ has a value greater than $0$ and $b_t$ has the value $0$ if $x_t$ has ...
5
votes
1answer
212 views
How to set a limit for a switch to 0 of a variable for 2 variables combined
I have a follow up question to another question of mine How to set a limit for a switch to 0 of a variable about counting the number of switches to 0 of one decision variable. Now I would like to ask ...
4
votes
1answer
351 views
Is there any automatic way to spot contradictory constraints in linear programming?
Let's have the following trivial linear program: \begin{align}\max&\quad z=20A+30B\\\text{s.t.}&\quad A\le60\\&\quad B\le50\\&\quad A+2B\ge220\\&\quad A,B\ge0\end{align}
It's easy ...
2
votes
1answer
42 views
How to write the following constraint? [duplicate]
I would like to write the following constraint, where $varBuyWater$ and $varSellWater$ are decision variables on how much water to buy and to sell. However, I do not want the solver to buy and sell ...
5
votes
1answer
202 views
How to set a limit for a switch to 0 of a variable
I would like to know how to define a constraint to set a limit for switching to 0 for a decision variable? So I have a linear variable $x(t)$ which quantifies the modulation degree of a heating device....
3
votes
1answer
108 views
Constraints that set values to binary variables depending on other binaries
I am trying to write a mathematical problem that involves some conditions based on binary variables. More specifically, I have a set of three binary variables $d_1$, $d_2$, $d_3$ and depending on ...
3
votes
1answer
684 views
How to find out which constraint causes problems in Pyomo
I have a Pyomo model with many constraints and variables. When solving it with Gurobi, I get the message "Model is infeasible or unbounded". Now I would like to find out which constraints ...
0
votes
0answers
639 views
Use if-statements when defining a constraint in Pyomo
I would like to define the value of a variable model.variable_costsPerTimeSlot [t] in pyomo and I would like to use if-statements. Depending on the value of the if-...
1
vote
1answer
62 views
How to assure a range for a specific variable in Pyomo
I would like to specify a certain range for a variable for a certain timeslot in Pyomo. I have a temperature variable $T(t)$ that is defined by using the difference equation $$T(t) = T(t-1) + \cdots,\...
2
votes
1answer
58 views
Piecewise Constraint in Abstract Model
I would like to write a piecewise constraint for an Abstract Model in Pyomo.
$$\operatorname{pu}_i(t_i^{'v})=\begin{align}\begin{cases}\rho_1(e_i'-t_i^{'v})+\rho_2(e_i-e_i'),\quad& t_i^{'v}\le e_i'...
0
votes
0answers
28 views
Correct way to define constraints in Pyomo
Can I know if the constraint below can be defined as follows in Pyomo for convex optimization.
W and G are arrays of dimension M x N.
...
2
votes
1answer
476 views
Can I define constraints in Pyomo as a list?
I would like to define the following constraint in Pyomo $$W^\top{\bf 1}\le\hat w=\begin{bmatrix}\hat{w}_1&\hat{w}_2&\ldots&\hat{w}_N\end{bmatrix}^\top$$ where $W$ is a $2\times4$ matrix. ...
7
votes
2answers
178 views
Index of element in MILP vector decision variable that equals 1
Consider a decision variable in a MILP constrained:
$$\sum_i p_i = 1$$
$$p_i\ \in \{0, 1\}$$
Obviously one element in $p$ is 1 and all others are 0. How can I set a decision variable to the index i of ...
2
votes
1answer
143 views
Matrix Singularity Constraint
I'm using CVXPY. Given a $2\times2$ matrix $A$, is it possible to add a singularity constraint?
Anything equivalent to:
$|A| = 0$: The determinant is $0$
$\operatorname{rank}(A) \leq 1$
Smallest ...
