Constraints.jl: Streamlining Constraint Definition and Integration in Julia

JC-API

using Constraints

@info concept(:cumulative, [1, 2, 3, 4, 5]; val = 1)
@info concept(:cumulative, [1, 2, 2, 4, 5]; val = 1)
@info concept(:cumulative, [1, 2, 3, 4, 5]; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = ≤, val = 5)
@info concept(:cumulative, [1, 2, 3, 4, 5]; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = <, val = 5)

XCSP

using Constraints

c = x -> Constraints.xcsp_cumulative(
	origins = x,
	lengths = [3, 2, 5, 4, 2],
	heights = [1, 2, 1, 1, 3],
	condition = (≤, 5)
)

@info c([1, 2, 3, 4, 5])
@info c([1, 1, 1, 2, 2])

JuMP

using CBLS, JuMP

model = Model(CBLS.Optimizer)
@variable(model, 1≤X[1:5]≤5, Int)
@variable(model, 1≤Y[1:5]≤5, Int)
@variable(model, 1≤Z[1:5]≤5, Int)
@constraint(model, X in Cumulative(; val = 1))
@constraint(model,
    Y in Cumulative(; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = ≤, val = 5))
@constraint(model,
    Z in Cumulative(; pair_vars = [3 2 5 4 2; 1 2 1 1 3], op = <, val = 5))
JuMP.optimize!(model)
@info "Cumulative" value.(X) value.(Y) value.(Z)

MOI

# TODO: How to handle intention in JuMP/MOI

JC-API

using Constraints

@info concept(:no_overlap, [1, 2, 3, 4, 5])
@info concept(:no_overlap, [1, 2, 3, 4, 1])
@info concept(:no_overlap, [1, 2, 4, 6, 3]; pair_vars = [1, 1, 1, 1, 1])
@info concept(:no_overlap, [1, 2, 4, 6, 3]; pair_vars = [1, 1, 1, 3, 1])
@info concept(:no_overlap, [1, 2, 4, 6, 3]; pair_vars = [1, 1, 3, 1, 1])

XCSP

using Constraints

c = x -> Constraints.xcsp_no_overlap(
	origins = x,
	lengths = [1, 4, 10],
	zero_ignored = true
)

@info c([1, 3, 10])
@info c([2, 1, 4, 3])

JuMP

using CBLS, JuMP

model = Model(CBLS.Optimizer)
@variable(model, 1≤X[1:5]≤5, Int)
@variable(model, 1≤Y[1:5]≤6, Int)
@variable(model, 1≤Z[1:12]≤12, Int)
@constraint(model, X in NoOverlap())
@constraint(model, Y in NoOverlap(; pair_vars = [1, 1, 1, 1, 1]))
@constraint(model,
    Z in NoOverlap(; pair_vars = [2, 4, 1, 4, 2, 3, 5, 1, 2, 3, 3, 2], dim = 3))
JuMP.optimize!(model)
@info "NoOverlap" value.(X) value.(Y) value.(Z)

MOI

# TODO: How to handle intention in JuMP/MOI

Packing and Scheduling Constraints

# Constraints.xcsp_cumulative — Function.

xcsp_cumulative(; origins, lengths, heights, condition)

Return true if the cumulative constraint is satisfied, false otherwise. The cumulative constraint is a global constraint used in constraint programming that is often used in scheduling problems. It ensures that for any point in time, the sum of the "heights" of tasks that are ongoing at that time does not exceed a certain limit.

Arguments

• origins::AbstractVector: list of origins of the tasks.

• lengths::AbstractVector: list of lengths of the tasks.

• heights::AbstractVector: list of heights of the tasks.

• condition::Tuple: condition to check.

Variants

• :cumulative: The cumulative constraint is a global constraint used in constraint programming that is often used in scheduling problems. It ensures that for any point in time, the sum of the "heights" of tasks that are ongoing at that time does not exceed a certain limit.

concept(:cumulative, x; pair_vars, op, val)
concept(:cumulative)(x; pair_vars, op, val)

Examples

c = concept(:cumulative)

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

source

# Constraints.xcsp_no_overlap — Function.

xcsp_no_overlap(; origins, lengths, zero_ignored)

Return true if the no_overlap constraint is satisfied, false otherwise. The no_overlap constraint is a global constraint used in constraint programming, often in scheduling problems. It ensures that tasks do not overlap in time, i.e., for any two tasks, either the first task finishes before the second task starts, or the second task finishes before the first task starts.

Arguments

• origins::AbstractVector: list of origins of the tasks.

• lengths::AbstractVector: list of lengths of the tasks.

• zero_ignored::Bool: whether to ignore zero-length tasks.

Variants

• :no_overlap: The no_overlap constraint is a global constraint used in constraint programming, often in scheduling problems. It ensures that tasks do not overlap in time, i.e., for any two tasks, either the first task finishes before the second task starts, or the second task finishes before the first task starts.

concept(:no_overlap, x; pair_vars, bool)
concept(:no_overlap)(x; pair_vars, bool)

• :no_overlap_no_zero: The no_overlap constraint is a global constraint used in constraint programming, often in scheduling problems. It ensures that tasks do not overlap in time, i.e., for any two tasks, either the first task finishes before the second task starts, or the second task finishes before the first task starts. This variant ignores zero-length tasks.

concept(:no_overlap_no_zero, x; pair_vars)
concept(:no_overlap_no_zero)(x; pair_vars)

• :no_overlap_with_zero: The no_overlap constraint is a global constraint used in constraint programming, often in scheduling problems. It ensures that tasks do not overlap in time, i.e., for any two tasks, either the first task finishes before the second task starts, or the second task finishes before the first task starts. This variant includes zero-length tasks.

concept(:no_overlap_with_zero, x; pair_vars)
concept(:no_overlap_with_zero)(x; pair_vars)

Examples

c = concept(:no_overlap)

c([1, 2, 3, 4, 5])
c([1, 2, 3, 4, 1])
c([1, 2, 4, 6, 3]; pair_vars = [1, 1, 1, 1, 1])
c([1, 2, 4, 6, 3]; pair_vars = [1, 1, 1, 3, 1])
c([1, 2, 4, 6, 3]; pair_vars = [1, 1, 3, 1, 1])
c([1, 1, 1, 3, 5, 2, 7, 7, 5, 12, 8, 7]; pair_vars = [2, 4, 1, 4 ,2 ,3, 5, 1, 2, 3, 3, 2], dim = 3)
c([1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4]; pair_vars = [2, 4, 1, 4 ,2 ,3, 5, 1, 2, 3, 3, 2], dim = 3)

source