Julia Constraints

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Defining Variables and Exploring Domains ​

ConstraintDomains.jl stands as the standard way to define variables and explore domains within the Julia Constraints ecosystem. This package provides the infrastructure necessary for specifying both discrete and continuous domains. Explorations features are mainly related to the learning about constraints aspect and will be detailed in that chapter.

Variables and their domains can also be defined through MOI and JuMP syntaxes in their respective models.

Implementing the AbstractDomain Interface ​

At the foundation of ConstraintDomains.jl is the AbstractDomain type, an abstract supertype for all domain types. Implementations of AbstractDomain must provide methods for checking membership (∈), generating random elements (rand), and determining the domain's size or range (length). These functionalities are essential for defining the behavior and properties of variable domains within constraint models.

ConstraintDomains.AbstractDomain Type
julia
AbstractDomain

An abstract super type for any domain type. A domain type D <: AbstractDomain must implement the following methods to properly interface AbstractDomain.

  • Base.∈(val, ::D)

  • Base.rand(::D)

  • Base.length(::D) that is the number of elements in a discrete domain, and the distance between bounds or similar for a continuous domain

Additionally, if the domain is used in a dynamic context, it can extend

  • add!(::D, args)

  • delete!(::D, args)

where args depends on D's structure

source

Discrete Domains ​

Optimization in discrete spaces has been the core of Constraint Programming since its inception. We provide three kinds of discrete domains.

SetDomain ​

A SetDomain is simply a Set of unordered numerical values.

julia
using ConstraintDomains

d1 = domain([53.69, 89.2, 0.12])
d2 = domain([2//3, 89//123])
d3 = domain(4.3)
d4 = domain(1, 42, 3.14)
julia
using CBLS, JuMP

m = JuMP.Model(CBLS.Optimizer)

@variable(m, x1 in DiscreteSet([53.69, 89.2, 0.12]))
@variable(m, x2 in DiscreteSet([2//3, 89//123]))
@variable(m, x3 in DiscreteSet(4.3))
@variable(m, x4 in DiscreteSet([1, 42, 3.14]))
julia
using CBLS
import MathOptInterface as MOI

optimizer = CBLS.Optimizer()

v1 = MOI.add_variable(optimizer)
MOI.add_constraint(optimizer, v1, CBLS.DiscreteSet([53.69, 89.2, 0.12]))

v2 = MOI.add_variable(optimizer)
MOI.add_constraint(optimizer, v2, CBLS.DiscreteSet([2//3, 89//123]))

v3 = MOI.add_variable(optimizer)
MOI.add_constraint(optimizer, v3, CBLS.DiscreteSet(4.3))

v4 = MOI.add_variable(optimizer)
MOI.add_constraint(optimizer, v4, CBLS.DiscreteSet([1, 42, 3.14]))

RangeDomain ​

A range domain allows for minimal storage and more efficient operation on discrete sets defined as Range in Julia. It is not recommended for dynamic domains (it will be replaced with SetDomain as soon as a non-extremal element is removed).

julia
using ConstraintDomains

d1 = domain(1:5)
d2 = domain(0.4:0.1:1.3)
julia
## To be implemented
# using CBLS, JuMP

# m = JuMP.Model(CBLS.Optimizer)

# @variable(m, 1 ≤ x1 ≤ 5, Int) # Consecutive integers are interpreted as range
# @variable(m, x2 in RangeSet(0.4:0.1:1.3))
julia
## To be implemented
# using CBLS
# import MathOptInterface as MOI

# optimizer = CBLS.Optimizer()

# v1 = MOI.add_variable(optimizer)
# MOI.add_constraint(optimizer, v1, MOI.RangeSet(1:5))

# v2 = MOI.add_variable(optimizer)

# MOI.add_constraint(optimizer, v1, MOI.RangeSet(0.4:0.1:1.3))

Arbitrary Domains ​

As odd as it may sound, we provide a constructor for sets of elements making up arbitrary, possibly non-numerical, domains.

Until some practical examples are implemented, this structure will mainly be a placeholder with default behavior.

Continuous Domains ​

Numerous problems cannot be challenged without expressing at least part of their domains as continuous variables. In Julia Constraints we provide such domains as (set of) intervals.

julia
using ConstraintDomains, Intervals

d1 = domain(Interval{Open,Closed}(3.2, true), (42, false))
d2 = domain(3.2..42)
d3 = domain([3.2..42, 63.2..324.1])
julia
## see MOI.Interval
julia
## see MOI.Interval