# Questions tagged [constraint-programming]

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### Constraint programming scheduling problem [on hold]

I am trying to find a programmatic solution to the following problem: There are 6 teachers for this room Each teacher must work for 8 hours a day Each teacher must have a 30 minute lunch break ...
1answer
85 views

### Conditional milp formulation

I have two binaries, $\alpha_{ts,it}$ and $\alpha_{ts,gshp} \in \{0,1\}$, and two reals $T_{it}$ and $T_{ts}$ which have upper and lower bounds. How can I model $\alpha_{ts,it}=1$ if the following ...
1answer
61 views

### (M)ILP overlap of two intervals

I got an ILP Model where $c_i$ represents the starting time for a visit$_i$. $c_i$ is already constraint by a number of constraints, one is $c_i > 0$. I have now outside of my model 0 or multiple ...
1answer
96 views

### Which AC-3 algorithm is being used here?

This is the illustration of the AC-3 algorithm for four queens from exhaustive study of essential constraint satisfaction problem techniques based on N-Queens problem by Md. Ahsan Ayub, Kazi A Kalpoma,...
2answers
957 views

### CSP Forward checking with n-ary (and binary) constraints

I have implemented my own CSP solver using a Backtracking algorithm. Within the Backtracking algorithm I apply a Forward Checking algorithm (reducing domains of connected, unnasigned variables) that ...
1answer
13 views

### Constraint propagation using Projection rule

I've found this example of constraint propagation using projection rule We have C = { x1 ≠ x2, x1 ≥ x2 } < C; x1 ∈ {1,2,3}, x2 ∈ {1,2,3} > They say that ...
4answers
3k views

### Can constraint satisfaction problems be solved with Prolog?

Is "party attendance" type of problems solvable in Prolog? For example: Burdock Muldoon and Carlotta Pinkstone both said they would come if Albus Dumbledore came. Albus Dumbledore and Daisy ...
0answers
11 views

### How to apply AC-3(Arc-consistency 3) algorithm in N-Queen problem?

I am building N-Queen Solver with java. I confused with AC-3 algorithm. I heard that AC-3 can be applied with backtracking algorithm before processing and during the search.The latter is called MAC-3 ...
0answers
15 views

### Constraint headers format in CHR

I'm new to CHR and I was wondering if it makes sense to have have functions as arguments for constraint heads in a rule. I know that in the body of the rule this is possible. E.g. Is ...
2answers
2k views

### AC-3 Algorithms on CSP problem, What is happened when enocunter to an empty domain variable?

Suppose We Applying Arc-Consistency (AC3) algorithms on one Constraint Satisfaction Problem, if domain of one variable be empty, what is the next step of this algorithm? According to This Link and to ...
1answer
33 views

### How to model equality in Integer Linear Programming

How to implement v=(a==b) using Linear Programming? $$v= \begin{cases} True, a=b\\ False, a≠b\\ \end{cases}$$ Until now I tried the big M-Method. To show a≤b: $$a-b+Mv≤M$$ $$-a+b-Mv≤-1$$ To show ...
0answers
12 views

### How to calculate constraint check in BT of 4-Queens problem?

I have seen number of constraint check in paper of CSPs. The constraint checking is counted as followed: when a value of a variable x is checked against a value of variable y, this is counted as ...
0answers
19 views

### What is the time complexity of FC_MRV algorithm?

I am studying CSP and read the papers on it.I wanted to know the time complexity of Forward checking with Minium Remaining Value algorithm.
0answers
21 views

### Channeling Constraints in Constraint Handling Rules (CHR)

Suppose we have a constraint satisfaction problem that can be defined as its constraints in two different viewpoints $V_1$ and $V_2$. Moreover, there are two variables $A$ and $B$ from $V_1$ and $V_2$ ...
0answers
35 views

### Projection operator for constraints

I was looking at HM(X) framework, Hindley-Milner parameterized by a constraint system X, and I was struggling to understand what does the projection operator $\exists \alpha$ does for a constraint. ...
0answers
26 views

### What approach to solve an open shop problem with following constraints

Say we have an open shop scheduling problem with following constraints : No wait-time between operations of a job Multiple job types (meaning each job type has different set of operations eventhough ...
1answer
39 views

### Modelling of minimal NOR-circuit problem with CP

I'm currently working on a Constraint Programming problem which I find difficult to model. Here 's the definition of the problem : " Given a specification of a Boolean function f(x1, ..., xn) in the ...
1answer
40 views

1answer
39 views

### Algorithm to solve constraint satisfaction problems

I have group of people. Each person can be described by few characteristics: age, occupation, city, favorite_color I would like to generate 60 random people and ...
0answers
59 views

### Can somebody suggest what is wrong with these constraint? [closed]

I have written two constraints for Mixed integer linear problem. I am working on the scheduling problem i.e., Scheduling of hybrid appliances. For example, the washing machine is appliance indicated ...
2answers
46 views

### How to create constraints for Mixed integer linear problem?

i am a beginner to Discrete optimization domain. I am working on the real world problem, i.e., Scheduling of hybrid appliances. I have hybrid appliances which can ...
1answer
77 views

### Shift Organization algorithms (Constraint Programming + Marriage problem)

I want to assign people to cover shifts considering a set of constraints and preferences. Here's the problem definition: Daily shifts must be covered by workers, who are divided in three groups: ...
1answer
75 views

### How do you proceed if your milp is not solvable

We are currently developing an ilp/milp model to fit the best routes with given resources (people) in a given timeframe and given visits and costs to travel from one visit to another (asymetrical). ...
1answer
158 views

### Constraint Satisfaction: maximizing total value with no overlaps

Suppose we have a bunch of bars, which can represent anything (time slots, paths, physical items...) and each of them has a start point, an end point, and an associated value. Out of all the bars ...
1answer
40 views

1answer
200 views

### How to encode a sequence of non-decreasing integers with an integer without redundancy, loops, and recursions

How to encode a sequence of n non-decreasing integer of [0, ..., m] fulfilling the following conditions: no or minimal redundancy only use 1 integer variable or k independent integer variables with a ...
0answers
63 views

### (Historical perspective) CSP and SAT inter-fertilization

[Disclaimer: this is a rather specialized question] It is known that techniques like Conflict-Driven Clause Learning (CDCL) and back-jumping -- which improved the Satisfiability (SAT) strategies ...
0answers
44 views

### Using Genetic Algorithms for volatile problems

Suppose I am looking at an optimization problem with a large number of interconnected constraints, but the solution is - in some regions - extremely volatile (With volatile I mean: small mutations ...
1answer
327 views

### Blob detection as Constraint satisfaction problem?

In image processing I have a black and white image which is represented by matrix {0,1}, I have to find blob (a region of connected pixels) in it. I'm confused, can this problem be reduced to ...
0answers
120 views

### n-queen puzzle with no 3 queens on same line

I am trying to solve n-queen puzzle with an additional stronger condition that no 3 queens can be on the same line. Right now my algorithm is, Generate a random permutation of ...
1answer
82 views

### Maximum set of equalities, subject to some inequalities

I have $n$ variables $x_1,\dots,x_n$. I'm given a set $E$ of equalities (each of the form $x_i=x_j$ for some $i,j$) and a set $I$ of inequalities (each of the form $x_i \ne x_j$ for some $i,j$). I ...
1answer
2k views

### When to use SAT vs Constraint Satisfaction?

If I have a hard problem, one standard approach is to express it as a SAT instance and try running a SAT solver on it. Another standard approach is to express it as a constraint satisfaction problem, ...
2answers
510 views

### How to impose Euclidean distance constraint in a constraint satisfaction problem without quadratic constraints?

Best reference I could find is this one. However, I could not quite understand this one since there is no numerical example. What I am trying to achieve with one sentence How can I answer the ...
2answers
385 views

### A tentative satisfiability algorithm

General satisfiability (with a few exceptions such as Horn Clauses) is not believed to have an algorithmic solution. However, the following algorithm appears to be a solution for general ...
3answers
142 views

### Isn't Domain of a variable nothing but a constraint?

In Constraint programming we have Variables and their Domains and then all the constraints, but if you at the concept of a domain of a variable it is nothing but another type of constraint, you are ...
1answer
45 views

### Help Understanding the Type and Complexity of my Programming Task [closed]

I'm working on a programming task that I, without good evidence, have a sneaking suspicion is NP-Complete. With that said, I would like confirmation on this if possible, as well as some suggestion for ...
1answer
140 views

### In Constraint Programming, are there any models that take into account the number of variable changes?

Consider a CSP model where changing the value of a particular variable is expensive. Is there any work where the objective function also considers the number of changes in the value of the variable ...
1answer
136 views

### Requiring at least one alldiff constraint to be satisfied converted to SAT

For generating certain hard puzzles, I am trying to model a problem (ultimately) in SAT. I don't know how to do that, so I am starting with CSP because it's more expressive. In CSP, there is a global ...
1answer
362 views

### Efficient algorithm to fulfil a set of coordinate constraints

I have a set of labelled points and a set of distance constraints between pairs of points, consisting of a lower and upper distance bound. There is definitely an arrangement of the points in 3D space ...
1answer
94 views

### How to decide if CSP is ambiguous?

When you pick up some reading about CSP the main focus is how to solve it. My goal is to compute/decide if CSP is ambiguous (has 2 or more solutions) or not (has 1 solution). Of course brute-force ...
0answers
214 views

### Steiner tree wiring problem

I’m trying to find an algorithm that can give me an approximate solution for a wiring problem that I have been asked to look at. I believe this is closely related to finding a node weighted Steiner ...
1answer
738 views

### Forward checking with conflict directed backjumping [closed]

Can somebody explain me how can I join forward checking with conflict directed backjumping in my CSP solver? I understand that when the consistency fails when I add a value to a variable, I should ...