DisjunctiveProgramming.jl: Generalized Disjunctive Programming Models and Algorithms for JuMP

Abstract

We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer Programs (MIPs) that can be solved with the various MIP solvers supported by JuMP. To do so, logical propositions are converted to Conjunctive Normal Form (CNF) and reformulated into equivalent algebraic constraints. Disjunctions are reformulated into mixed-integer constraints via the reformulation technique specified by the user (Big-M or Hull reformulations). The package supports reformulations for disjunctions containing linear, quadratic, and nonlinear constraints.