Questions tagged [constraint]

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

Filter by
Sorted by
Tagged with
1
vote
1answer
26 views

Python, Google OR-Tools, OnlyEnforceIf() method

I am trying to solve a basic puzzle by using Google OR-Tools, this is my first try with OR-Tools and I am trying to learn. I completed almost everything and was ready to conclude the program until I ...
-4
votes
0answers
46 views

How to treat with equality constraints in whale optimization algorithm? [duplicate]

Whale optimization is one of the metaheuristic algorithms which used to find the optimal solution to unconstrained optimization problems. I have an objective function : $x_1+2 x_2−6 x_3≥0$, subject to ...
3
votes
3answers
173 views

How to handle an equality constraint in metaheuristic algorithms (like GA, PSO)?

Metaheuristic algorithms are generally used to find the optimal solution to unconstrained optimization problems. I would like to maximize $x_1+3x_2-x_3\ge0$ while respecting the equality constraint $...
5
votes
0answers
198 views

Substituting inequality by equality constraints

Let $\mathbf{A}=\left(a_{ij}\right)$ be a $n\times J$ matrix with $a_{ij}\geq 0$, $n>J$ and such that no row or column has all its entries equal to zero. Let also $\mathbf{k}=\left(k_j\right)$ be a ...
4
votes
1answer
47 views

How do you turn an abstract set constraint into equality constraints?

I am reading from Nonlinear Programming by Bertsekas, and in the section on ADMM, he says: Consider the problem $$\text{min} \sum _{i=1} ^ m f_i(x)$$ $$\text{s.t. }x \in \cap _{i = 1}^m X_i,$$ where $...
5
votes
2answers
302 views

Failing to meet a constraint in a NLP problem

I have a NLP problem at hand, which I am trying to solve via Pyomo + ipopt. I try to run several different instances of the optimizer with different conditions, out ...
8
votes
1answer
401 views

Adding a constraint in constraint programming

Is it true that the more we add constraint to a constraint programming solver the more efficient it will be? How does this compare to adding constraints in integer programming solvers.
5
votes
1answer
73 views

Combined arc capacity constraints in network flows

Consider the network flow polyhedron for a directed graph $G = (N, A)$. Along with the standard flow-balance and single-arc capacity constraints, we are faced with additional constraints which enforce ...
0
votes
0answers
33 views

Linearizing max constraint Problem [duplicate]

I want to linearize a max constraint as below: In which x_(i,t),are binary decision variables and T is a constant. How can I linearize this constraint?
2
votes
1answer
59 views

distance specific constraint

I have some points with determined coordinates $(a_i,b_i)$. A vehicle can move between these points based on rectangular distance. In more detail, we consider that the path between points is an ...
3
votes
2answers
115 views

Model “If, then” constraint

How to model the following "If, then" type constraint? If $\sum\limits_{i \in I}x_i = 0$ then $\sum\limits_{j \in J}x_{j} = n$ where $x$ are binary variables, $n$ is a known parameter and $...
2
votes
1answer
56 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 ...
4
votes
2answers
124 views

Faster implementation of “or” constraints in ILP

I have implemented a set of "or" constraints in my ILP using binary decision variables (as in this method). It works fine for smaller problems, but when I try to increase the number of ...
5
votes
1answer
97 views

Minimize binary variable's distance with respect to the index values

For a given binary decision variable $x[i,j,k]$ my goal is to get as dense results in terms of k for successive values of j. Distance of k value to be kept as close as possible throughout j values: $d ...
3
votes
3answers
115 views

Possibility of indexing decision variables with 2 indices using a set of tuples in Pyomo

I am currently attempting to solve a network problem that is not fully connected.Thus, I have attempted to do some preprocessing of data so as to form a set of tuples, e.g. $\{(a,b), (c,e),\ldots\}$, ...
3
votes
1answer
78 views

View of Constraints and Decision Variables in Pyomo

I have just attempted to construct my first Pyomo model. However, I was unable to locate any documentation that shows how to view constraints, decision variables. As my model is big, I need to see ...
3
votes
3answers
198 views

SLSQP Optimisation loop takes several iterations to compute error function despite jacobian

I have an error function $f : w \rightarrow f(w)$ that I want to minimize, $w$ being a vector of length 211. There are some constraints on $w$. I managed to compute the jacobian $J$ and even with it ...
3
votes
1answer
88 views

Pyomo: Help setting up my model

I have been working with a model for the past couple of weeks, but I am not sure what am I doing wrong as every time Pyomo returns that is infeasible or ...
3
votes
0answers
117 views

SDP relaxation with greater-than and less-than inequalities at the same time

I am dealing with the following nonconvex fractional quadratic optimization problem \begin{align} & \min_{\boldsymbol{x}} && \max_{t \in \mathcal{T}} \frac{\boldsymbol{a}_t^T \boldsymbol{...
1
vote
1answer
69 views

Pyomo: Struggling to get a constraint to work

I am trying to model an Electric Vehicle scheduling to minimise the electricity bill. Of course, the EV will only be able to charge every time that is plugged into a charging station (i.e. it cannot ...
3
votes
1answer
112 views

Space constraint in scheduling problem

I'm studying an MIP model with a scheduling problem and I'm wondering if the space constraint is correct. If there is space in the factory at that time, the block can be processed, where $i$ is the ...
1
vote
0answers
75 views

Question on quadratically constrained quadratic program

If the constrained optimization problem is a quadratically constrained quadratic program of the form \begin{align}\min&\quad x^HQx-a(x+x^H)+b|z^Hx|^2\\\text{s.t.}&\quad\|x\|^2\le1\end{align} ...
1
vote
3answers
205 views

Using big M values for a constraint

I want to enforce $x_{i,j}=x_{k,j}\implies z_i \neq z_k$ where $k = i-1$ so I used \begin{align}z_k + 1 - (x_{i,j} - x_{k,j})) \leq z_i \leq z_k - 1 - (x_{i,j} - x_{k,j})\quad\text{for each $j$}\end{...
1
vote
1answer
36 views

Enforcing discontinuous range for a variable

I want to enforce the following ranges for a set of variables, where the ranges for each variable are discontinuous. For example, I have two sets of ranges for each variable, \begin{align}\sf LB_1 &...
4
votes
1answer
118 views

Buying shares in increments

I constructed an optimisation model which objective is to find highest return on available stocks. Now want to add a constraint that allows to buy stocks only in $2000 increments, how can I do it? i.e ...
4
votes
1answer
84 views

How to convert non-normal probabilistic constraints to deterministic ones for mathematical modelling?

I am working on a chance-constrained optimisation model that takes into account uncertainty. I am aware of how to convert constraints that are of a probabilistic nature into the equivalent ...
4
votes
0answers
48 views

Confused in how to insert a slack variable in a constraint inequality

According to my understanding, we should put a slack variable to equate an inequality constraint by inserting the slack variable in the side that is less than the other side. For example, if we have $...
9
votes
3answers
456 views

Is there a better way to formulate this constraint?

Let $x_{r}^{j}=1\iff$ the machine schedules job $j$ using resource $r$. My constraint says that: a resource cannot be used twice, i.e., if $x_{r}^{j}=1$, then $x_{r}^{j'}=0$ for $j'\neq j$. I write ...
3
votes
2answers
111 views

Minimizing a variable over the intersection of simplex and linear constraints

I am solving: \begin{align} \begin{array}{rll} y^* = \min & y & \\ \mathrm{s.t.} & a_i^\top x \leq y, & i=1,\ldots,m \\ & x \succeq 0,\ \mathbf{1}^\top x = 1. & \end{array} \...
4
votes
1answer
100 views

Constraint programming in OPL: intervals covering time slots

I am trying to model the following: There is a shop open from xx AM to yy PM. In each 30 min time slot, there have to be demand[timeSlot] = x employees present. E.g. the shop is open from 08am to ...
-4
votes
2answers
94 views

How can I model this binary logic?

I am looking for a constraint to express the following: IF W1 = 0 AND W2 = 0 THEN Y = 0 IF W1 = 0 AND W2 = 1 THEN Y = 1 IF W1 = 1 AND W2 = 0 THEN Y = 0 IF W1 = 1 AND W2 = 1 THEN Y <= 1 ...
6
votes
2answers
207 views

How can this be expressed as a MILP constraint?

I am looking for a constraint to express the following: IF W1 = 0 AND W2 = 0 THEN Y = 1 IF W1 = 0 AND W2 = 1 THEN Y = 1 IF W1 = 1 AND W2 = 0 THEN Y = 0 IF W1 = 1 AND W2 = 1 THEN Y <= 1 ...
7
votes
1answer
767 views

How to find the idle intervals in integer programming?

I have a scheduling problem with one machine and one job. I defined a binary variable $z_t$ that is 1 iff the job is scheduled at time $t$ (the job can be served in multiple times that are not ...
3
votes
1answer
56 views

Iterative calculus with Excel - N° 2

In continuation with the previous post, I propose you another problem. I have this model: \begin{align}\min&\quad F\\\text{s.t.}&\quad F-(1150x_{B_{1}}+1000x_{B_{2}}+1350x_{B_{3}}-S_{1})=430\...
3
votes
1answer
237 views

Iterative calculus with Excel

I have this model: \begin{align}\max&\quad\small{(0.2(1.07)^{-1}+0.2(1.07)^{-2}+0.9(1.07)^{-3})x_A+0.4(1.07)^{-1}+0.5(1.07)^{-2}+0.3(1.07)^{-3})x_B}\\&\quad 0.2x_{A}+0.4x_{B}\geq300\,000 \\&...
7
votes
2answers
253 views

The general meaning of “constraint relaxation” in the context of the Shortest Path Problem

I've read that in the context of the Shortest Path Problem, the use of the term "relaxation" ("relaxing edges") [...][the use of the term "relaxation"] is historical. The outcome of a relaxation ...
8
votes
3answers
621 views

Bin packing variant

I am currently struggling with a bin packing variant, where we have fuel and compartments of a tank truck. Some industry constraints apply, but the whole picture is that you must fit the total volume ...
5
votes
1answer
204 views

TSP with constraints in OR Tools

I am completely new to OR Tools, but what I have tried so far seems very powerful. I have, however, run into a problem that I cannot seem to figure out how to solve. I am trying to model a TSP ...
5
votes
1answer
153 views

How to model shipment size constraint?

I am working on an LP problem where I have to model a constraint as: "The total number of units of product A and B should be shipped in multiples of $1200$" e.g. $700\text{(product A)} + 500\text{(...
5
votes
1answer
397 views

Single KKT solution for a simple problem: proof of being minimizer

I have a very simple problem: $$ \begin{align*} \begin{array}{ll} \min\limits_{x_1,x_2} & -x_1x_2 \\ \text{s.t.} & x_1 + x_2 - 2 = 0. \end{array} \end{align*} $$ The KKT system gives me $x_1^*...
5
votes
2answers
657 views

Integer programming problem

I have the following exercise: Stockco is considering four investments. Investment 1 will yield a net present value (NPV) of \$16,000; investment 2, an NPV of \$22,000; investment 3, an NPV of \$12,...
7
votes
2answers
257 views

shadow prices associated with nonnegativity constraints

Why are shadow prices associated with nonnegativity constraints also called as reduced costs, even if they have the same interpretation as shadow prices associated with an optimal solution? Why the ...
12
votes
3answers
1k views

Does it make sense to use strict equality constraint in optimization?

Once I learned from some post that the strict equality constraint in optimization problem does not make much sense. We should always use $\le$ constraint. How far this is true. If I must have a ...
5
votes
1answer
126 views

Precedence constraints using binary variables - DOCPLEX

I would like to establish a precedence constraint to ensure the precedence relation of tasks. I have a set of tasks available, but required tasks are not always the same. It means, the tasks executed ...
7
votes
2answers
143 views

Linear constraint formulation (OR-statement)

I have the decision variable $X_{iz}$ And I have two parameters $T_i\in\{0,1\}$ and $IT_z\in\{0,1,2\}$. I can only assign $i$ to $z$ if the following holds: for $T_i=0$, $IT_z$ needs to be $0$ or $2$...
10
votes
2answers
171 views

Linearization $\max(c_1 x_2, c_2 x_2, \ldots, c_nx_n) \geq q$ constraint

I have a MIP minimization problem where I have a maximization in the constraints: $$\max(c_1x_2,\, c_2x_2,\, \ldots,\, c_nx_n) \geq q$$ Where: $c_n$ constants $x_n$ binary variables $q$ constant $...
10
votes
1answer
342 views

Linear programming with if-then-else (big-M)

I am trying to formulate the following in linear programming. \begin{cases}\text{if}\,\,a>b\,\,\text{then}\,\,c=a\\\text{else}\,\,c=b.\end{cases} I tried some things with big $M$, like $$a + my &...
11
votes
1answer
170 views

Example satisfying Mangasarian-Fromovitz CQ but not LICQ

On Wikipedia's page for the KKT conditions, it is stated that Mangasarian-Fromovitz constraint qualification (MFCQ) is weaker than linear independent constraint qualification (LICQ). What is a ...
8
votes
1answer
187 views

Minizinc: How to use a predicate in an assert statement?

Trying to use minizinc builtins to do some basic validation of data inputs but I get a type error ...
12
votes
1answer
299 views

Which ML algorithms work by solving constrained optimisation problems?

As far as I know, most machine learning algorithms solve unconstrained optimisation problems, i.e., if we were to unroll all the neurons into symbolic expressions we would end up with a massive ...