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https://github.com/dkendal/aruspex

A configurable constraint solver
https://github.com/dkendal/aruspex

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A configurable constraint solver

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README 

        
# Aruspex

Aruspex is a configurable [constraint

solver](https://en.wikipedia.org/wiki/Constraint_satisfaction_problem), written

purely in Elixir.



Aruspex does, or atleast has the capacity to, support multiple constraint problem

satisfaction strategies. Because of this property it is theoretically capable

of supporting various types of CSPs.



At the time of writing Aruspex ships with one strategy, simulated annealing,

which supports weighted CSPs.



**This readme refers to master, please check the readme for your release.**



## Example

Given a map of Australia, find some colouring of teritories, such that no adjacent territory has the same colour.



![](http://australia.pppst.com/Australia_map_regions.gif)



```elixir

import Aruspex.Server

use Aruspex.Constraint



{:ok, problem} = start_link



variables = [

  wa  = :western_australia,

  nt  = :nothern_territory,

  q   = :queensland,

  sa  = :south_australia,

  nsw = :new_south_wales,

  v   = :victoria,

  t   = :tasmania

]



domain = [:red, :green, :blue]



Enum.map variables, &(variable problem, &1, domain)



problem

|> set_search_strategy(Aruspex.Strategy.SimulatedAnnealing)

# adjacent territories cannot be the same colour

# The pin operator is used to reference a named variable in a constraint,

# check the section on variables below.

|> post(linear ^wa != ^nt)

|> post(linear ^wa != ^sa)

|> post(linear ^sa != ^nt)

|> post(linear ^sa != ^q)

|> post(linear ^sa != ^nsw)

|> post(linear ^sa != ^v)

|> post(linear ^nt != ^q)

|> post(linear ^q != ^nsw)

|> post(linear ^nsw != ^v)

|> find_solution

|> IO.inspect

# [ new_south_wales:    :blue,

#   nothern_territory:  :blue,

#   queensland:         :green,

#   south_australia:    :red,

#   tasmania:           :green,

#   victoria:           :green,

#   western_australia:  :green ]

```



For some more examples checkout [these.](test/support/examples/)



## Usage

Check the api exposed by `Aruspex.Server`



### Creating a new problem

Aruspex uses a `GenServer` under the hood, to create a new problem simply use

```elixir

{:ok, pid} = Aruspex.Server.start_link

```



### Defining a new variable

A literal is used to name a new variable, and a domain is specified for the

variable.  This literal will be used to reference the variable later when

defining constraints and will appear in the solution.

```elixir

@spec variable(pid, Literals, Enum.t) :: pid

^pid = Aruspex.Server.variable(pid, :x, 1..100)

```



### Defining a new constraint

Adding a new constraint is called *posting* a constraint. Posting a constraint

requires specifying the variables that participate in the constraint, as well

as a function the returns a *cost* when tested.



Strategies attempt to minimize

the cost of all constraints, where a total cost of 0 would be a perfect

solution.



#### all_diff/1

Constraints may be defined using built in constraints:



```elixir

pid

|> post(all_diff [:x, :y])

```



The `all_diff` constraint would impose a condition that all variables specified

must be unique.



#### linear/1

using the `linear/{1,2}` macro (only supports clauses that can be inlined -

only expressions that can appear in guard clauses):



```elixir

pid

|> post(linear ^:x == ^:y)

```



inside the body of the `linear/1` macro pinned literals indicate that the value

refers to a named variable which will be substituted in during compilation.

pinned variables may also be used to the same effect.



unpinned values will be used by value.



```elixir

some_var = :x

z = 1

pid

|> post(linear ^some_var == ^:y + z)

```



is equivalent to:



```elixir

pid

|> post(linear ^:x == ^:y + 1)

```



#### linear/2

In it's second form, the named variables may be defined explicitly, and matched

on.



```elixir

pid

|> post(linear [:x, :y],

               [{x1, _}, {_, y2}] when x1 == y2)

```



#### constraint/1

User defined constraints are also supported by using the constraint record

directly.



Strategies will test constraints by applying the values for `variables`, in

the order specified, to `function`.



`function` **must** have a type of `[Literals] -> number`.



```elixir

pid

|> post(constraint(

  variables: [:v, :w],

  function: fn ([v, w]) ->

    cond do

      v > 10 ->

        100

      w < 10 ->

        9999

      true ->

       0

    end

  end

))

```

## Roadmap

- [ ] configurable settings for s.a. strategy (run time, cooling strategy, etc.)

- [ ] configurable tolerance for what is an acceptable solution (default is only perfect solutions)

- [ ] allow strategies to return multiple soltuions with message box.

- [ ] allow multiple strategies to be employed, which will act as middlewear.

- [ ] user defined optimization tolerance

- [ ] implement more common constraints from [the global constraint catalog](http://www.emn.fr/z-info/sdemasse/gccat/sec5.html).

- [ ] add additional strategies