The prototype version of the MOP solver, named vOptSolver, is under development. It is a free open source MOLP/MOMIP/MOCO/MOIP solver available under the MIT licence. It can be used as an open box for the scientific community, as well as a black box for the practitionners, through a collection of API.

The version 0.0.1 implemented in C/C++ languages and runs under the operating systems linux has been released in July 2016.  It integrates the following methods and algorithms:

  • a parametric bi-objective simplex algorithm
  • the bi-objective linear assigment algorithm [1,4]
  • the bi- and three- objective 01 unidimensional knapsack algorithm [2]
  • the bi-objective discrete uncapacited facility location algorithm [3]

The version 0.0.2 has been released as open source in June 2017. It is now implemented in Julia language and integrates algorithms implemented in Julia/C/C++ languages. Based on JuMP, vOptSolver provides a modeling language supporting the following classes of multi-objective optimization problems: MOLP, MOMILP, MOCO, MOIP.

The last version of vOptSolver is downloadable here: (homepage of vOptSolver) (repository of vOptSpecific) (repository of vOptGeneric)

Follow the video (in French) presented during the GDR RO tutorial talk at ROADEF’2018 conference:

Algorithmes de branch-and-bound multiobjectif et vOptSolver
by Xavier Gandibleux and Anthony Przybylski

References of the algorithms integrated:

[1] A. Przybylski, X. Gandibleux, M. Ehrgott: Two phase algorithms for the bi-objective assignment problem. European Journal of Operational Research, Volume 185, Issue 2, Pages 509-533, 2008.

[2] J. Jorge: Nouvelles propositions pour la résolution exacte du sac à dos multi-objectif unidimensionnel en variables binaires. PhD Thesis, Université de Nantes, 2010.

[3] X. Gandibleux, A. Przybylski , S. Bourougaa, A. Derrien, A. Grimault: Computing the Efficient Frontier for the 0/1 Biobjective Uncapacitated Facility Location Problem CORS/MOPGP’2012 (10th international conference on Multiple Objective Programming and Goal Programming). June 11-13, 2012, Niagara Falls, Canada.

[4] X. Gandibleux, H. Morita, N. Katoh.  A population-based algorithm for solving linear assignment problems with two objectives. Computers & Operations Research. In Press, Available online, 2016.