MultiobjectiveAlgorithms.Jl: a Julia package for solving multiobjective optimization problems

Abstract

We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multiobjective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements 10 different solution algorithms that all rely on an iterative scalarization of the problem from a multiobjective optimization problem to a sequence of single-objective subproblems. As part of this work, we extended JuMP to support vector-valued objective functions. Because it is based on JuMP, MultiObjectiveAlgorithms.jl can use a wide variety of commercial and open-source solvers to solve the single-objective subproblems, and it supports problem classes including linear, integer, conic, semidefinite, and general nonlinear.