Constraints.jl: Streamlining Constraint Definition and Integration in Julia

JC-API

using Constraints

concept(:all_different, [1,1,1,2]) # false
concept(:all_different, [1,9,3,2]) # true

XCSP

using Constraints

c = x -> Constraints.xcsp_all_different(
    list = x
)
@info c([1, 2, 3, 3]) # false
@info c([1, 2, 3, 4]) # true

JuMP

using CBLS, JuMP

model = Model(CBLS.Optimizer)
@variable(model, 1≤X[1:4]≤4, Int)
@variable(model, 0≤Y[1:4]≤2, Int)
@constraint(model, X in AllDifferent())
@constraint(model, Y in AllDifferent(; vals = [0]))
JuMP.optimize!(model)
@info "All Different" value.(X) value.(Y)

# Note that this example gives a solution for the all_different constraint.

MOI

# TODO: How to handle intention in JuMP/MOI

JC-API

using Constraints

concept(:all_equal, [1,1,1,2]) #false
concept(:all_equal, [1,1,1,1]) #true

XCSP

using Constraints

c = x -> Constraints.xcsp_all_equal(
    list = x
)

@info c([1, 1, 1, 1]) # false
@info c([1, 2, 3, 4]) # true

JuMP

using JuMP, CBLS

model = Model(CBLS.Optimizer)
@variable(model, 0≤X[1:4]≤4, Int)
@constraint(model, X in AllEqual())
JuMP.optimize!(model)
@info "All Equal" value.(X)

# Note that this example gives a solution for the all_equal constraint.

MOI

# TODO: How to handle intention in JuMP/MOI

JC-API

using Constraints

@info concept(:ordered, [1, 2, 3, 4, 4]; op=≤)
@info concept(:ordered, [1, 2, 3, 3, 5]; op=<)
@info concept(:increasing, [1,2,2,3])

XCSP

using Constraints

c = x -> Constraints.xcsp_ordered(
   	list = x,
	operator = ≥
)

@info c([1, 1, 1, 1])
@info c([9, 3, 6, 8])

JuMP

using CBLS, JuMP

model = Model(CBLS.Optimizer)
@variable(model, 1≤X[1:5]≤5, Int)
@variable(model, 1≤Y[1:5]≤5, Int)
@constraint(model, X in Ordered())
@constraint(model, Y in Ordered(; op = <))
JuMP.optimize!(model)
@info "Ordered" value.(X) value.(Y)

MOI

# TODO: How to handle intention in JuMP/MOI

Comparison-based Constraints

Constraints.xcsp_all_different Function

xcsp_all_different(list::Vector{Int})

Return true if all the values of list are different, false otherwise.

Arguments

• list::Vector{Int}: list of values to check.

Variants

• :all_different: Global constraint ensuring that the values in x are all different.

concept(:all_different, x; vals)
concept(:all_different)(x; vals)

Examples

c = concept(:all_different)

c([1, 2, 3, 4])
c([1, 2, 3, 1])
c([1, 0, 0, 4]; vals=[0])
c([1, 0, 0, 1]; vals=[0])

source

Constraints.xcsp_all_equal Function

xcsp_all_equal(list::Vector{Int}, val::Int)

Return true if all the values of list are equal to val, false otherwise.

Arguments

• list::Vector{Int}: list of values to check.

• val::Int: value to compare to.

Variants

• :all_equal: Global constraint ensuring that the values in x are all equal.

concept(:all_equal, x; val=nothing, pair_vars=zeros(x), op=+)
concept(:all_equal)(x; val=nothing, pair_vars=zeros(x), op=+)

Examples

c = concept(:all_equal)

c([0, 0, 0, 0])
c([1, 2, 3, 4])
c([3, 2, 1, 0]; pair_vars=[0, 1, 2, 3])
c([0, 1, 2, 3]; pair_vars=[0, 1, 2, 3])
c([1, 2, 3, 4]; op=/, val=1, pair_vars=[1, 2, 3, 4])
c([1, 2, 3, 4]; op=*, val=1, pair_vars=[1, 2, 3, 4])

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Constraints.xcsp_ordered Function

xcsp_ordered(list::Vector{Int}, operator, lengths)

Return true if all the values of list are in an increasing order, false otherwise.

Arguments

• list::Vector{Int}: list of values to check.

• operator: comparison operator to use.

• lengths: list of lengths to use. Defaults to nothing.

Variants

• :ordered: Global constraint ensuring that all the values of x are in a total order defined by a comparison operator.

concept(:ordered, x; op=≤, pair_vars=nothing)
concept(:ordered)(x; op=≤, pair_vars=nothing)

• :increasing: Global constraint ensuring that all the values of x are in an increasing order.

concept(:increasing, x; op=≤, pair_vars=nothing)
concept(:increasing)(x; op=≤, pair_vars=nothing)

• :decreasing: Global constraint ensuring that all the values of x are in a decreasing order.

concept(:decreasing, x; op=≥, pair_vars=nothing)
concept(:decreasing)(x; op=≥, pair_vars=nothing)

• :strictly_increasing: Global constraint ensuring that all the values of x are in a strictly increasing order.

concept(:strictly_increasing, x; op=<, pair_vars=nothing)
concept(:strictly_increasing)(x; op=<, pair_vars=nothing)

• :strictly_decreasing: Global constraint ensuring that all the values of x are in a strictly decreasing order.

concept(:strictly_decreasing, x; op=>, pair_vars=nothing)
concept(:strictly_decreasing)(x; op=>, pair_vars=nothing)

Examples

c = concept(:ordered)

c([1, 2, 3, 4, 4]; op=≤)
c([1, 2, 3, 4, 5]; op=<)
!c([1, 2, 3, 4, 3]; op=≤)
!c([1, 2, 3, 4, 3]; op=<)

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