MultiObjectiveAlgorithms.jl: A Julia Package for Solving Multiobjective Optimization Problems

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.

History: Accepted by Ted Ralphs, Area Editor for Software Tools.

Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1449) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2025.1449). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/.