# 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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### How to measure model quality in OR-Tools?

After creating my model for a problem, what steps should I take to test if a change in the model is actually helpful or not? In Python, ...
• 1,414
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### What is the newest MIP and CP solver?

What is the newest MIP or CP solver (which is model based exact solver)? I want to follow and wonder developments on solvers. But finding new developed solvers (experimental, academic, commercial etc.)...
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### Cumulative Constraint OR-Tools

I'm trying to solve an rcpsp model. I can't find documentation for the AddCumulative function of OR-Tools. How should this function be used? I want to write this ...
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### In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
• 481
I have five integer variables, and I need to write some constraints on them: $x_0$ , $[x_1, x_2, x_3, x_4 ]$. $1 \leq x_i \leq 3$ if $x_0 =1$ then no constraint on $[x_1, x_2, x_3, x_4 ]$ if x_0 =... • 1,378 4 votes 2 answers 2k views ### 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 ... • 149 4 votes 1 answer 1k views ### How exactly does OptionalIntervalVar work in OR-Tools? I created OptionalIntervals for a number of tasks: ... 4 votes 1 answer 596 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 ... 4 votes 1 answer 179 views ### How do I formulate constraints that check if a parameter is between certain values, using binary variables? I have3$parameters$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... • 43 4 votes 1 answer 325 views ### Creating constraints dynamically in pyomo abstract model I have a networkX graph with few nodes and these nodes have attributes such as "demand". ... 4 votes 1 answer 153 views ### Mathematically formulating formal problem of a cloud service scheduler So, I have been tasked to create a formal mathematical description of problem statement on a cloud service scheduler for my team's university project, which is, honestly, a little weird of a thing to ... • 79 4 votes 1 answer 265 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 1 answer 467 views ### Machine Allocation & optimal Utilization using python Problem statement: Meet the demand which can be met across 2 facilities each having multiple machines where several components are made. The objective is to find the optimal solution to meet the ... 4 votes 0 answers 107 views ### Modelling issue with rcpsp and boolean expressions I'm trying to solve an RCPSPDc problem in OR-Tools with CP-SAT solver. In my RCPSPDc model (with discount rate) i want to set this objective: $$\max_{s}\sum_{j\in J}\text{profit}_{j}\cdot \frac{1}{(1+... 3 votes 2 answers 353 views ### 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. ... 3 votes 2 answers 676 views ### What is the difference bewteen CP and MILP approaches in Job Shop Scheduling? My understanding is Constraint programming (CP) is a sub-set of MILP but in MILP we not only try to find a feasible solution (like CP) but also we should optimize an objective function. I do have a ... • 1,378 3 votes 2 answers 804 views ### How to avoid similar solutions? I have a problem like this x_1 +x_2 +x_3 =10 let's assume 0 \leq x_i \leq 10 It is obvious that this problem has more than one solution For example : Solution 1 : x_1 =0 , x_2= 1 , x_3 =9 ... • 1,378 3 votes 2 answers 794 views ### What are the solvers that give a feasible solution within a given time? What are the solvers that take the maximal computation time as a parameter and gives the best found feasible solution within this time. • 567 3 votes 1 answer 511 views ### 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 ... • 815 3 votes 2 answers 289 views ### 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 ... 3 votes 1 answer 306 views ### How to write a LP/MIP to mark the items in a time-series list after a fixed delta? I have a time series list like this. ... • 203 3 votes 1 answer 655 views ### Of what size should I expect to be able to solve an integer linear program with Pyomo? So I am solving a purely integer linear optimization problem with Pyomo on a single computer (core i-5, 12 GB RAM). The problem has around 10000 variables and 300 constraints. For doing this, I am ... • 199 3 votes 2 answers 152 views ### Vehicle passenger assignment with capacity constraint Problem Summary To match passengers (the number of passengers) to capacitated vehicles such that the profit is increased. All the vehicles have the same capacity c. It is not important to track ... • 33 3 votes 2 answers 368 views ### OR-Tools CP-SAT solver: is it possible to name a constraint like in GUROBI I try to implement cp model with OR-tools CP-SAT solver. Please, is it possible to name constraints for being able to manage conflict later like for variables: ... • 65 3 votes 2 answers 294 views ### Simple Integer Optimization Problem: docplex CP model works but equivalent PuLP+CBC model is infeasible? I have an integer optimization problem with one constraint per decision variable and no objective function. It can be coded and solved using docplex, however I am ... • 145 3 votes 1 answer 306 views ### Unexpected runtime error I have a model that contains the sets (both ordered and Days also circular): Days and Personnel, and I'm trying to make a restriction run exaclty once per Day for every member of Personnel. I'm using ... 3 votes 2 answers 69 views ### Constrained shift assignment problem using ilogcp solver can´t find an optimal solution IĀ“ve been trying to solve a contrained assignation problem given a set of constraints based in a real-world problem. I modeled the problem in AMPL as follows: ... 3 votes 2 answers 310 views ### 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 ... 3 votes 2 answers 56 views ### Constrained optimization with heuristic algorithm in actual production In a real production problem, if you decide to use a heuristic algorithm (such as GA), what are the mainstream methods to deal with constraints in constraint optimization? I mean, I knew that there ... 3 votes 2 answers 248 views ### how to count the number of values that are greater than zero in OR-Tools I am using OR-Tools for an employees scheduling problem. I have a dictionary that is defined as an IntVar, where such dictionary contains the number of hours that will be assigned to each employee, ... • 31 3 votes 2 answers 263 views ### Limit number of switches in employee scheduling problem Here is a scheduling problem I need to solve. Given the demand for 2 positions in 1 week with 3 shifts per position, I need to allocate the employees accordingly with some extra operational ... 3 votes 1 answer 195 views ### ValidateModel or tools in c++ and proto problems I'm trying to validate my model, this is the relevant part of my code: ... 3 votes 1 answer 355 views ### Force gaps between tasks, tasks are scheduled within their job's time windows in Jobshop problem The problem I'm trying to solve is a modification of the original Jobshop problem. The additional constraints are: There is only one machine for all jobs and their tasks. Each job has a priority (... 3 votes 1 answer 72 views ### Optimize parametric Log-Likelihood with a Tree Suppose there are some objects with features, and the target is parametric density estimation. Density estimation is model-based. Parameters are obtained by maximizing log-likelihood.$$\operatorname{... • 31 3 votes 1 answer 2k 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 ... 3 votes 1 answer 136 views ### 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 ... 3 votes 1 answer 317 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 ... 3 votes 1 answer 227 views ### On what kind of problems a local search may perform better than MIP / CP techniques? [closed] In combinatorial optimization, on what type of problem a local search may lead to better & quicker solutions than usual mixed-integer programming and constraint programming techniques ? By type ... • 63 3 votes 1 answer 67 views ### Finding a starting ellipsoid and a minimum volume to approximate a convex optimization problem Suppose we have a convex optimizatiom program: \begin{align} \min &\quad f_0(x)\\ s.t. &\quad h_i(x) = 0 && i=1,\ldots, p\\ &\quad g_i(x) \leq 0 && i=1,\ldots, m\\ &\... 3 votes 3 answers 150 views ### Constraint programming problem with matrix of integers I am trying to solve the following problem. SupposeA$is an$m \times n$matrix of integers with entries in$\{1, \dots, k\}. There are two kinds of constraints on the entries of this matrix: For ... 3 votes 1 answer 4k views ### SLSQP vs Trust Region Constrained Algorithms I have gone through scipy constrained algos explanation, however, not much is mentioned about the differences, pros and cons of the 'trust-const' and 'slsqp' methods. I particularly wanted to know ... • 139 3 votes 0 answers 463 views ### Circuit constraints in ortools I am looking to assign tasks to people. Each successive task should be started after the first one is finished and should be started at the same location as the preceding task. While the time ... 3 votes 0 answers 156 views ### 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, \\& ... • 215 3 votes 0 answers 198 views ### Power of variable or tools I'm working with OR Tools in Python and I need to define the objective function an expression of the variables. In particular, the objective function is $$\frac{c_j}{1.7^{s_j}}$$ withc_j$... • 131 2 votes 3 answers 608 views ### How to model two variables to NOT to belong to the same set partition using Constraint Programming Assume we have two variables$x,y \in S$where$S=\{1,2, \dots, 1000\}$. Also, we are given a partition of set$S$as:$S_1 = \{1,2, \dots, 249\},S_2 = \{250, \dots, 499\},S_3 = \{500, \dots, ...
Let's assume we have event $i=1,2,\cdots,k$, denoted as $\text{event}_i$. We know for a fact that $\text{event}_i$ is smaller then $\text{event}_{i+1}$ i.e., $\text{event}_i \leq \text{event}_{i+1}$. ...