Questions tagged [constraint]
For questions related to constraints, i.e. any restriction or relation a set of decision variables has to satisfy.
130
questions
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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
122 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
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51 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
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1answer
89 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 ...
3
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1answer
257 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 ...
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56 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
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1answer
99 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
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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,...
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75 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
147 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
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2answers
123 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
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1answer
79 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
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1answer
112 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 $a_1$...
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59 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
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1answer
85 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
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1answer
88 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
217 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
68 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
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1answer
56 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
133 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
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2answers
106 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
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3answers
80 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
137 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
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1answer
210 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
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1answer
323 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
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1answer
41 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
195 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
63 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
344 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
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0answers
269 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
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1answer
33 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 $$T(t) = T(t-1) + \cdots,\...
2
votes
1answer
42 views
Piecewise Constraint in Abstract Model
I would like to write a piecewise constraint for an Abstract Model in Pyomo.
$$\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'...
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0answers
25 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.
...
1
vote
1answer
119 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
164 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
135 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 ...
2
votes
1answer
127 views
MILP constrained by the minimum number of satisfied constraints
I have an MILP where we have
$$
t_k = \sum_i P_i\cdot C_{ik} : P_i\ \in \{0,1\}, C_{ik} \in I^+
$$
and our model is constrained by the number of times $t_k$ is bigger than a certain value $T_k$.
$$
\...
3
votes
1answer
116 views
Maximizing a piecewise-linear convex function
Note: Initially posted on MathOverflow.
I am working on an optimization problem where some of the terms of the objective function to maximize are expressed as a piecewise linear function of variables:...
4
votes
2answers
430 views
Modeling a constraint such that a set of binary decision variables do not equate to 1 simultaneously
I would like to seek some advice on modeling the following logical condition:
I would like to ensure that a group of binary variables do not equate to 1 simultaneously, i.e., $\omega_{1}=1, \omega_{2}=...
4
votes
1answer
95 views
Linearize $\max x_i\ge1$
I'm trying to linearize this optimization problem ($S_j$ is a subset of variables): \begin{align}\min&\quad\sum_{x_i \in X} x_i\\\text{s.t.}&\quad\max_{i \in S_j}x_i\geq 1\quad\forall S_j\\&...
3
votes
0answers
101 views
Two binding constraints - Linear Programming
I'm having some troubles to continue solving my system, I'm used to solve such systems but with "one" binding constraint, if someone could give me some helpful hints so I can solve it I will ...
3
votes
2answers
316 views
If-then constraint with continuous variables
I was usually using if-then constraints with integer variables but ended up using continuous variables and got confused. I have variables $x_{ij}\in\mathbb{R}_{\geq 0}$, and would like to force the ...
2
votes
2answers
100 views
Should I process the data or add a new constraint to achieve the target?
I have an MILP as below
$\begin{equation}
\begin{array}{*{35}{l}}
\underset{d_{u,c}}{\max}\hspace{1mm}\hspace{1mm}\sum_{u=1}^{U}\sum_{c=1}^{C}d_{u,c}\omega_{u,c}\\
\text{}\text{subject to }\text{ C1:}...
2
votes
1answer
123 views
How to define constraints in Pyomo using sets and variables
I am trying to model the transportation problem of Dantzig in Pyomo (see the GAMS code here https://www.gams.com/latest/gamslib_ml/libhtml/gamslib_trnsport.html or the description here https://www....
3
votes
2answers
270 views
Hard to soft constraint
What are all necessary changes to the below model so that constraint set $(2)$ becomes soft?
Give the new full model. $\alpha_{ij}$ are parameters. Eqn. $(1)$ refers to an already existing function of ...
2
votes
0answers
74 views
How to linearize this multiplicative constraint?
I have a constraint in the form
$\sqrt{|\sum_{c\in C}{h_cw_c}|^2}\ge\sqrt{x}\zeta$
Here, $h_c$ is s row vector (know), $w_c$ is a column vector (variable).
$x$ and $\zeta$ are also optimization ...
2
votes
1answer
70 views
How to model these constraints correctly
$W$ is a vector of $N$ complex elements.
$D$ is a binary variable
The requirements are:
when $D==1$, $L_{\min}\le ||W||_2^2\le L_{\max}$
and when $D==0$, $||W||_2^2=0$
I have formulated the following ...
2
votes
2answers
104 views
Constraint to handle the machine-configuration's change between initial position and its first occurrence in the process
I am working with a kind of a reconfigurable process planning, meaning that the same machine can have different configurations and perform multiple operations. Each machine has an initial ...
1
vote
1answer
59 views
Priority Constraint
Suppose I have the following set of binary variables:
$X_i$: $I$ ranges from {1,..,4} Highest priority among the three variables $X$ , $Y$ and $Z$
$Y_j$: $J$ ranges from {1,..,3}
$Z_k$: $K$ ranges ...
2
votes
1answer
116 views
How can I perform discrete optimisation of a variable over a data set
This question relates directly to a dataset I've generated for Fantasy Premier League, but I'm also curious how I can apply this to a more general case.
Data
I have a list of premier league players, ...
