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1. Top results related to define constraint satisfaction problem

   • understanding constraint satisfaction problem: map coloring algorithm

     Top Answer

     Answered Oct 07, 2018 · 0 votes

     So after rehashing some college literature (Peter Norvig's Artificial Intelligence: A Modern Approach), it turns out the problem in your hands is the application of Recursive Backtracking as a way to find a solution for the Graph Coloring Problem, which is also called Map Coloring (given its history to solve the problem of minimize colors needed to draw a map). Replacing each country in a map for a node and their borders with edges will give you a graph where we can apply recursive backtracking to find a solution.

     Recursive backtracking will descend the graph nodes as a depth-first tree search, checking at each node for whether a color can be used. If not, it tries the next color, if yes, then it tries the next unvisited adjacent node. If for a given node no color satisfies the condition, it will step back (backtrack) and move on to a sibling (or the parent's sibling if no siblings for that node).

     So,

     I assume that since assignment is inputted as an empty dictionary {}, that this will return the solution, that is, the dictionary that contains states and their colors ... Would it be something like checking the size of the dictionary against the number of states?

     Yes and yes. Once the dictionary contains all the nodes of the graph with a color, you'll have a solution.

     The input csp class contains a list of states, I assume this could just be var equal to popping off a value in the list?

     That pseudocode syntax is confusing but the general idea is that you'll have a way to find out a node of the graph that hasn't been colored yet. One simply way is to return a node from the dictionary that doesn't have a value assigned to it. So if I understand the syntax correctly, var would store a node. VARIABLES[csp] seems to me like a representation of the list of nodes inside your CSP structure.

     I'm not sure what the parameters (VARIABLES[csp], assignment, csp) are doing, given my input

     The assignment parameter is a dictionary containing the nodes evaluated so far (and the future solution), as mentioned above, and csp is the structure containing a,b and c.

     Again, confused on what the inputs of (var, assignment, csp) are doing exactly. But I assume that it'll go through each value (neighbor) in dictionary of the state?

     ORDER-DOMAIN-VALUES appears to be a function which will return the ordered set of colors in your CSP structure. The FOR loop will iterate over each color so that they're tested to satisfy the problem at that level.

     if value is consistent with assignment given CONSTRAINT[csp] then-

     Here, what you're doing is testing the constraint with that value, to ensure it's true. In this case you want to check that any nodes adjacent to that node does not have that color already. If an adjacent node has that color, skip the IF and iterate the for loop to try the next color.

     If no adjacent nodes have that color, then enter the IF body and add that node var with color value to the assigment dictionary (I believe {var = value} is a tuple representation, which I would write {var,value}, but oh well). Then call the function recursive backtracking again, recursively. If the recursive call returns non-failure, return its results (it means the solution has been found).

     If it returns a failure (meaning, it tried all the colors and all of them happened to be used by another adjacent node), then remove that node ({var,value}) from the assignment (solution) array and move on to the next color. If all colors have been exausted, return failure.

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   • constraint satisfaction in java

     Top Answer

     Answered Sep 16, 2012 · 1 votes

     You could perhaps do this through the use of some helper methods from the google commons collect library. It would look something like this:

     I'm assuming that the tuples (0,0,0) etc are tuples of the input to the constraint, (x0, x1, x2) for constraint1, (x2, x4) for constraint2 etc.

     So, for constraint1, first we fill a list with all possible combinations:

     final List<int[]> allCombos = new ArrayList<int[]>(); for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { for (int k = 0; k < 3; k++) { allCombos.add(new int[] {i, j, k}); } } } for (final int[] i : allCombos) { System.out.println(i[0] + ", " + i[1] + ", " + i[2]); }

     Next, we want to filter so we'll be left with the tuples that are allowed by constraint1:

     final List<int[]> constraint1 = ImmutableList.copyOf(Iterables.filter(allCombos, new Predicate<int[]>() { @Override public boolean apply(@Nullable final int[] input) { return input[0] + input[1] > input[2]; } })); for (final int[] i : constraint1) { System.out.println(i[0] + ", " + i[1] + ", " + i[2]); }

     This might need a little explanation.

     ImmutableList.copyOf is a method that creates a copy of a given list. To this method, we pass the result of Iterables.filter(), which takes a list (the input to be filtered), and a Predicate, which has an overridden method apply(), where you decide which element of the input list that are supposed to be part of the result list. Here, we basically just code the constraint itself, and the cases where the apply method returns true will be part of the filtered list. (I've chosen to represent the tuples as an array, you could use the filter-strategy with any tuple-representation..)

     The result of the last printouts (the filtered list) will be:

     0, 1, 00, 2, 00, 2, 11, 0, 01, 1, 01, 1, 11, 2, 01, 2, 11, 2, 22, 0, 02, 0, 12, 1, 02, 1, 12, 1, 22, 2, 02, 2, 12, 2, 2

     I'll leave it up to you to do the same for the other constraints..

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   • Constraint Satisfaction Problems (CSP) in Artificial Intelligence

     Finding a solution that meets a set of constraints is the goal of constraint satisfaction problems (CSPs), a type of AI issue. Finding values for a group of variables that fulfill a set of restrictions or rules is the aim of constraint satisfaction problems. For tasks including resource allocation, planning, scheduling, and decision-making, CSPs are frequently employed in AI.

     There are mainly three basic components in the constraint satisfaction problem:

     Variables:    The things that need to be determined are variables. Variables in a CSP are the objects that must have values assigned to them in order to satisfy a particular set of constraints. Boolean, integer, and categorical variables are just a few examples of the various types of variables Variables, for instance, could stand in for the many puzzle cells that need to be filled with numbers in a sudoku puzzle.

     Domains:     The range of potential values that a variable can have is represented by domains. Depending on the issue, a domain may be finite or limitless. For instance, in Sudoku, the set of numbers from 1 to 9 can serve as the domain of...

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   • Backtracking search for constraint satisfaction problem implementation

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     Answered Nov 10, 2018 · 0 votes

     The first step is to create a knowledge model for the domain. This can be done with a domain specific language (DSL). In the DSL syntax a possible solution to the problem is formulated. The wanted side effect of a domain specific language is, that a grammar has to be created which can parse the language. This grammar can be used in the reverse order which is called a "generative grammar". The aim is to include as much domain knowledge as possible in the DSL which makes it easier for the solver to test out all states.

     Unfortunately, the question has only a few information about the domain itself. According to the description there are three variables which can be on or off. This would generate a possible statespace of 2x2x2=8 which seems a bit too easy for a domain, because the solver is done if he tested out all 8 states. So i would guess, that the problem is bit harder but not explained in the description. Nevertheless, the first step is to convert the problem into a language which can be parsed by a grammar.

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   • Define contraints for specific exact cover problem

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     Answered Aug 02, 2019 · 0 votes

     (Completely rewrote answer.)

     Although it might be possible to cast this problem as an exact cover problem and (in principle) solve it with Algorithm X, in practice that turns out to be impractical and there is a better way.

     First to answer your question as asked: Recall the exact cover problem: given a bunch of “items” (to be covered) and a bunch of “options” (each of which covers a set of items), the problem is to find a set of options such that each item is covered exactly once.

     In your case, if you pick the (20) players as items and groups-of-four-players as options, then, as you found, any algorithm for the exact cover problem will find ways of scheduling one round of the tournament.

     But in fact you don't need that at all, as (in the absence of further constraints) you can write down all solutions explicitly: there are (20 choose 4)=4845 ways of choosing the first group-of-4, then (16 choose 4)=1820 ways of choosing another group-of-4 from the remaining, and so on, and finally you don't care about the ordering among the five groups-of-4 you find, so the number of ways you can partition a set of 20 people into five groups-of-4 is

     (choose(20, 4) * choose(16, 4) * choose(12, 4) * choose(8, 4) * choose(4, 4)) / (5 * 4 * 3 * 2 * 1) = 2546168625.

     (Equivalently: (20!)/((4!)^5 * 5!) = 2546168625, as we can write down a list of 20 players, then reorder within each group of 4 and also reorder the groups.)

     If you'd like to generate all of them with a program, you can write each of them in canonical order: suppose you call the 20 players 'A' to 'T', then you can write each group-of-4 in lexicographic order (thus, the group {F, J, B, Q} would be written “BFJQ”), and finally you can write down the five groups themselves in lexicographic order (thus the first group will start with "A", the second group with the earliest letter not in the first group, etc).

     Next, if you want to cover multiple rounds, to frame it as something like an exact-cover problem again, you'd need to have the above number (≈2.5 billion) of “options” (rows). It's not clear what the items would be, but this is clearly going to be impractical, so it's not worth pursuing this line of thought.

     Instead, it turns out that your problem is well-studied, originally under the name of Kirkman's schoolgirl problem (scheduling, from 15 people, groups of 3 as many times as possible — turns out to be 7) (see Ray Toal's page here), and more recently as the “social golfer problem” (see Markus Triska's page here):

     The Social Golfer Problem (SGP) is a combinatorial optimisation problem. The task is to schedule g × p golfers in g groups of p players for w weeks such that no two golfers play in the same group more than once. An instance of the SGP is denoted by the triple g-p-w. The original problem asks for the maximal w such that the instance 8-4-w can be solved.

     And your question here asks for the maximal w such that the instance 5-4-w can be solved. The answer turns out to be w=5, and the MathWorld page on the problem gives exactly this 5-4-5 instance:

     Mon ABCD EFGH IJKL MNOP QRSTTue AEIM BJOQ CHNT DGLS FKPRWed AGKO BIPT CFMS DHJR ELNQThu AHLP BKNS CEOR DFIQ GJMTFri AFJN BLMR CGPQ DEKT HIOS

     See also Warwick Harvey's page which has (had) the best known solutions for many different parameters. It records that 5 is both the upper- and lower-bound for this problem, i.e. it is known how to schedule 5 rounds (you found one yourself!) and known that it is not possible to schedule more than 5 rounds.

     You can search the literature for “social golfer problem” to find more approaches to solving it by computer. More generally, problems like this are studied in the vast area of combinatorics known as Combinatorial Designs. One great reference I found while writing an earlier answer is the book Handbook of Combinatorial Designs, which has chapters like VI.3 Balanced Tournament Designs, and VI.51 Scheduling a Tournament.

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2. www.geeksforgeeks.org › constraint-satisfactionConstraint Satisfaction Problems (CSP) in Artificial ...

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   Jun 8, 2023 · Constraint Satisfaction Problems (CSP) in Artificial Intelligence. Last Updated : 08 Jun, 2023. Finding a solution that meets a set of constraints is the goal of constraint satisfaction problems (CSPs), a type of AI issue. Finding values for a group of variables that fulfill a set of restrictions or rules is the aim of constraint satisfaction ...

3. en.wikipedia.org › Constraint_satisfaction_problemConstraint satisfaction problem - Wikipedia

   en.wikipedia.org › Constraint_satisfaction_problem

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   Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods.

4. People also ask

   How do you solve a constraint satisfaction problem?

   • An evaluation is a solution if it is consistent and complete; such an evaluation is said to solve the constraint satisfaction problem. Constraint satisfaction problems on finite domains are typically solved using a form of search. The most used techniques are variants of backtracking, constraint propagation, and local search.

   Constraint satisfaction problem - Wikipedia

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   What is a constraint satisfaction problem?

   • Finding values for a group of variables that fulfill a set of restrictions or rules is the aim of constraint satisfaction problems. For tasks including resource allocation, planning, scheduling, and decision-making, CSPs are frequently employed in AI. Variables: The things that need to be determined are variables.

   Constraint Satisfaction Problems (CSP) in Artificial Intelligence

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   What is a constraint satisfaction problem (CSP)?

   • Constraint Satisfaction Problem (CSP) is defined by: X is a set of n variables X1, X2,..., Xn each defined by a finite domain D1, D2,...Dn of possible values. C is a set of constraints C1, C2,..., Cm. Each Ci involves a subset of the variables; specifies the allowable combinations of values for that subset.

   Constraint Satisfaction - Department of Computer Science

   www.cs.cornell.edu/courses/cs4700/2011fa/lectures/05_CSP.pdf

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   What is a constraint satisfaction problem in artificial intelligence?

   • A Constraint Satisfaction Problem in artificial intelligence involves a set of variables, each of which has a domain of possible values, and a set of constraints that define the allowable combinations of values for the variables. The goal is to find a value for each variable such that all the constraints are satisfied.

   Constraint Satisfaction Problem in AI - Scaler

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5. en.wikipedia.org › wiki › Constraint_satisfactionConstraint satisfaction - Wikipedia

   en.wikipedia.org › wiki › Constraint_satisfaction

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   In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. [1] A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in the feasible region .

6. www.scaler.com › topics › artificial-intelligenceConstraint Satisfaction Problem in AI - Scaler

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   Constraint Satisfaction Problem (CSP) is a fundamental topic in artificial intelligence (AI) that deals with solving problems by identifying constraints and finding solutions that satisfy those constraints. CSP has a wide range of applications, including scheduling, resource allocation, and automated reasoning.

7. web.stanford.edu › class › archiveConstraint Satisfaction Problems (CSPs) - Stanford University

   web.stanford.edu › class › archive

   Definition: Constraint Satisfaction Problem (CSP) A CSP is a factor graph where all factors are constraints: for all. The constraint is satisfied iff. Definition: Consistent Assignments. An assignment x if. (i. all constraints are satisfied.) Setup: Have E events and T time slots. Each event e must be put in exactly one time slot.

8. aima.cs.berkeley.edu › newchap055 CONSTRAINT SATISFACTION PROBLEMS - University of California ...

   aima.cs.berkeley.edu › newchap05

   CONSTRAINT SATISFACTION PROBLEM VARIABLES. CONSTRAINTS. DOMAIN. VALUES. ASSIGNMENT. CONSISTENT. OBJECTIVE FUNCTION. Formally speaking, a constraint satisfaction problem (or CSP) is defined by a set of vari-ables, X1; X2; : : : ; Xn, and a set of constraints, C1; C2; : : : ; Cm. Each variable Xi has a nonempty domain Di of possible values.

9. www.cs.cornell.edu › courses › cs4700Constraint Satisfaction - Department of Computer Science

   www.cs.cornell.edu › courses › cs4700

   Constraint Satisfaction Problem (CSP) is defined by: X is a set of n variables X1, X2,..., Xn each defined by a finite domain D1, D2,...Dn of possible values. C is a set of constraints C1, C2,..., Cm. Each Ci involves a subset of the variables; specifies the allowable combinations of values for that subset.