DisjunctiveProgramming.jl

Generalized Disjunctive Programming extension to JuMP

Installation

using Pkg
Pkg.add("https://github.com/hdavid16/DisjunctiveProgramming.jl")

Disjunctions

Disjunctions can be applied to standard JuMP models with constraints of that are either GreaterThan, LessThan, or EqualTo. Reformulations on constraints that are Interval are not supported. The disjunctions can be reformulated via the Big-M method or the Convex Hull as described here. The user may provide an M object that represents the BigM value(s). The M object can be a Number that is applied to all constraints in the disjuncts, or a Vector/Tuple of values that are used for each of the disjuncts.

For the Convex Hull Reformulation, the perspective function proposed in Furman, et al. [2020] is used.

Example

The example below is from the Northwestern University Process Optimization Open Textbook.

To perform the Big-M reformulation, :BMR is passed to the reformulation keyword argument. If nothing is passed to the keyword argument M, tight Big-M values will be inferred from the variable bounds using IntervalArithmetic.jl. If x is not bounded, Big-M values must be provided for either the whole system (e.g., M = 10) or for each of the constraint arrays in the example (e.g., M = ((10,10),(10,10))).

To perform the Convex-Hull reformulation, reformulation = :CHR. Variables must have bounds for the reformulation to work.

using JuMP
using DisjunctiveProgramming

m = Model()
@variable(m, 0<=x[1:2]<=10)

@constraint(m, con1[i=1:2], x[i] <= [3,4][i])
@constraint(m, con2[i=1:2], zeros(2)[i] <= x[i])
@constraint(m, con3[i=1:2], [5,4][i] <= x[i])
@constraint(m, con4[i=1:2], x[i] <= [9,6][i])

@disjunction(m,(con1,con2),(con3,con4), reformulation=:BMR)

┌ Warning: No M value passed for con1[1] : x[1] <= 3.0. M = 7.0 was inferred from the variable bounds.
┌ Warning: No M value passed for con1[2] : x[2] <= 4.0. M = 6.0 was inferred from the variable bounds.
┌ Warning: No M value passed for con2[1] : -x[1] <= 0.0. M = 0.0 was inferred from the variable bounds.
┌ Warning: No M value passed for con2[2] : -x[2] <= 0.0. M = 0.0 was inferred from the variable bounds.
┌ Warning: No M value passed for con3[1] : -x[1] <= -5.0. M = 5.0 was inferred from
the variable bounds.
┌ Warning: No M value passed for con3[2] : -x[2] <= -4.0. M = 4.0 was inferred from
the variable bounds.
┌ Warning: No M value passed for con4[1] : x[1] <= 9.0. M = 1.0 was inferred from the variable bounds.
┌ Warning: No M value passed for con4[2] : x[2] <= 6.0. M = 4.0 was inferred from the variable bounds.