# Questions tagged [constraint-programming]

For questions on modeling satisfaction or optimization problems in languages designed for expressing (often high-level) constraints on decision variables.

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### Adding a variable makes the model unsatisfiable in MiniZinc

I have the following model. ...
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I am just not able to grasp how can I use the addElement constraint of OR-Tools. I am trying to model the following constraint written in MiniZinc: ...
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### 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 $1$ ...
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### Scheduling when task duration longer than working interval

I'm trying to modify the job shop example for CP-SAT solver. (https://developers.google.com/optimization/scheduling/job_shop) I'm limited to 8 hours working day, So I defined a list of NewIntervalVar()...
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### Set value based on if other variable is in specific range

I have the following problem. number_of_machines is controlled by other constraints. I need to set line variable to specific value based on "range" ...
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### ILOG CPOptimizer soft constraints (multiple solves reusing searched space)

I'm trying to feed information retrieved from my neural network to my CP model to help narrow down the search on big instances of my problem. However, I also want to remove the additional imposed ...
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### Convex Optimization Problem with norm inequality constraint

Consider the following optimization problem: \begin{align} \inf_{x,y}&\quad(x-x_0)^\top A(x-x_0) + (y-y_0)^\top B(y-y_0) \\\text{s.t.}&\quad x^\top a\geq0,\\ & \quad y^\top b\geq0, \\& ...
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### VRP through constraint programming

I am with a problem that consists of determining whether a VRP instance is feasible, this question is a continuation of an older thread. In order to do it, I was thinking of using Constraint ...
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### Dual of quadratic program with linear objective

Let $c$ and $k$ be element-wise positive $n\times 1$ vectors and let $A$ be a element-wise positive and positive-definite matrix. Consider the optimization problem \begin{align} \max_{p\in\mathbb{R}^n}...
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### Print Intermediate Solutions of Scheduling Problem and tackling FLAGS in jupyter notebook

I tried this code and it goes on and I'm clueless when it'll end so I manually interrupt it. Is there any way we can see intermediate solutions that are feasible solutions and can we limit time or ...
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### Multiple Depot/Crew Office Bus Driver Scheduling Modelling

I'm working on Bus Driver Schedule with multiple add-on constraints that are complex and hence trying to figure out how this can be achieved. Reference of Bus Driver Scheduling using OR-Tools:- https:/...
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### 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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### Consistency Level of Constraints

Recently I started using CP and translated my first MIP model into a CP model with the IBM CP Optimizer. Lately I was confronted with a question I could not answer: "What is the consistency level ...
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### Extracting CNF representation of my problem from SAT solver

As I know, any SAT solver such as or-tools or cplex cp optimizer converts a given problem to CNF form in the first place. Is it possible to extract the resulting CNF representation from or-tools or ...
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I'm totally new to the world of optimization and I have an optimization problem that I think it can be formulated as Mixed Integer Quadratically Constrained Quadratic Program (QCQP) but I'm not sure ...
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### Solver Recommendation : Discrete Variables and Quadratic Constraints

I would like some solver recommendations to solve a problem with boolean/integer variables, mostly linear constraints but also some quadratic constraints. I also have an objective to minimize which is ...
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### Multiple If else constraints in Mixed integer programming

How to formulate the following as constraints in MILP? a = y, if x= 0, a = 0, if x != 0, . . . . a[i][j] = b[i][j-1] + y, if x[j]=i, a[i][j] = a[i][j-1], if x[j] != i, ... . . . b...
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### OR-Tools, How to avoid dividing by zero

Problem: There is an order to fabricate some products of total number, let's say 200 (all products are the same). We have some number of factories, let's say 5. Every factory has different number of ...
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### How to visit a subset of network nodes in a single trip?

I have a connected network where I want to visit a set of destinations which may require visiting intermediate nodes as well because there may be no direct edge between source and destination nodes. I ...
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### Scheduling optimisation constraint on consecutive shifts & consecutive night shifts (python)

I am trying to write a program to schedule a team of 8 individuals into shifts. I want to know how to model that every individual must get at least one night shift break, and must not work two ...
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### Scheduling: Tasks changing the state of the executing machine

I have a scheduling problem in which machines consume their battery when executing tasks and charge their battery when not executing tasks. A single task has to be executed in one go (no recharging ...
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### What is a good approach to deciding which jobs (from a list of HPC jobs) should be ran locally vs. on the cloud given time & cost constraints?

Cloud computing has transformed the landscape of compute operations. Of course, there are still many labs/businesses with local, large-scale compute clusters. For those businesses who keep the ...
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### Modeling in integer programming vs modeling in constraint programming

I have some experience with linear and integer programming modeling (I read Model Building In Mathematical Programming by Williams). Now I am trying to learn how to model with constraint programming. ...
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### 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 ...
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### How can I formulate this specific if-then constraint?

IF $\sum\limits_d X_{i,d}\ge6$ THEN $Y_i = 1$ (strictly) AND IF $\sum\limits_d X_{i,d}<6$ THEN $Y_i = 0$ (strictly) $X$ and $Y$ are binary variables. What I'm actually trying to do is to charge the ...
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### Constraint programming and scheduling issues

I have a constraint problem that I need to resolve, but I did not how know to model the problem: I have 11 employees, I will name them from $a$ to $k$: $\{a,b,c,d,e,f,g,h,i,j,k\}$. I have a small ...
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### How to know which constraint in CP-SAT did not meet the feasibility gap

Is there any systematic way to retrieve some information on the constraint that caused infeasibility in Or.Tools CP-SAT? ...
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### How to model a set of integer variables getting assigned different values than another set of integer variables

Assume we have variables $x_1, x_2, x_3, x_4$ that each can belong to $\{1,2,...,10\}$. How can we model a constraint that variables $x_1, x_2$ get assigned different values than $x_3, x_4$? Because ...
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### Integer decision variables as index

The following problem has only two integer variables; however, they appear in the index of the parameters. Appreciate it if anyone has any efficient idea to transform it into a canonical integer ...
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### Constraint programming resources

I am looking for resources to learn constraint programming. I will divide the resources I am looking for in three types: Modeling Is there resources (books, articles, courses, etc.) that are ...
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### Mixed integer programming vs Constraint programming

I see that certain studies are comparing MIP and constraint programming (CP) performances. And generally, they claim that CP outperforms MIP. But I believe that it is not completely true. Because ...
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### Fixed cost associated to SlackVar(waiting time cost) [CVRPTW]

I'm modeling a CVRPTW with some features: Each type of vehicle has a cost per km and a fixed cost per trip. To calculate these costs, I am using these methods for this: ...
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### How to use the least number of colours to colour different routes of a bus route such that no two intersecting routes will have the same colour

I would like to know of a method in which if provided say 10 routes with details regarding which route intersects with which another route, we can use the least number of colours to colour the routes, ...
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### Derived variables of when a decision variable appears?

I am dealing with a multi-travelling passenger problem. $x_{i,j}$ is a binary variable that allocate a passenger $i$ to a vehicle $j$, every vehicle can carry only $n_{pv}$ passenger where \$i \in \{1,...
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### Could DOcplex.CP recognize that it solves the graph coloring minimization problem?

I created a graph coloring DOcplex.CP model inspired by this example. However, I do not know the number of colors in advance. The goal is to minimize the number of colors (i.e., get as close as ...