Solver of multiobjective linear optimization problems: description and documents
vOptSolver is an ecosystem for modeling and solving multiobjective linear optimization problems (MOMIP, MOLP, MOIP, MOCO). It integrates several exact algorithms for computing the set of non-dominated points, and the corresponding complete set of efficient solutions, for structured and non-structured optimization problems with at least two objectives.
It is composed of the two julia packages vOptGeneric and vOptSpecific, and hosts vOPtLib, a library of numerical instances:
03-Sep-2022: Instances and parser for uncapacitated facility location problems added
12-Mar-2022: vOptGeneric is compliant with JuMP 0.23.0 and MOI 1.1.0
25-Jan-2022: Parser for set partitionning problems added
24-Jul-2021: vOptSpecific updated, and new examples added
21-Jul-2021: Examples for vOptGeneric updated and new examples added
15-Jun-2019: Testing the version of vOptGeneric compliant with JuMP 0.19
22-Apr-2019: Preparing an update of the documentation
31-Oct-2018: vOptSpecific and vOptGeneric are compliant with Julia v1.x
01-Jul-2018: Preparing the switch to Julia 0.7 and to the new version of JuMP
01-Sep-2017: Algorithms added to vOptGeneric and vOptSpecific, documentation and examples are coming.
20-Jul-2017: Examples presented in conferences (MCDM'2017; IFORS'2017) are online (folder examples)
26-Jun-2017: Source codes of vOptGeneric and vOptSpecific for v0.0.2 are online
17-Jun-2017: Moved from GitLab to GitHub
03-Jun-2017: The next release (v0.0.2) is scheduled for June 2017
All bugs, feature requests, pull requests, feedback, etc., are welcome.
Prof. Dr. Xavier Gandibleux, University of Nantes - France (contact)
By alphabetical order:
In brief, every contributions aiming to share our efforts, our algorithms, our productions around this open source software are welcome.
vOptSolver is distributed under the MIT License.
Xavier Gandibleux, Gauthier Soleilhac, Anthony Przybylski. vOptSolver: an ecosystem for multi-objective linear optimization. JuliaCon 2021. July 28-30, 2021. Online and everywhere. Abstract.
Xavier Gandibleux, Gauthier Soleilhac, Anthony Przybylski, Flavien Lucas, Stefan Ruzika, Pascal Halffmann. vOptSolver, a “get and run” solver of multiobjective linear optimization problems built on Julia and JuMP. MCDM2017: 24th International Conference on Multiple Criteria Decision Making. July 10-14, 2017. Ottawa (Canada).
Xavier Gandibleux, Gauthier Soleilhac, Anthony Przybylski, Stefan Ruzika. vOptSolver: an open source software environment for multiobjective mathematical optimization. IFORS2017: 21st Conference of the International Federation of Operational Research Societies. July 17-21, 2017. Quebec City (Canada).
The development of vOptSolver started in the ANR/DFG-14-CE35-0034-01 research project vOpt (2015-2019) (link) involving Université de Nantes (France) and University of Koblenz-Landau/University of Kaiserslautern (Germany).
The solving algorithms included compute exact solution(s) corresponding to Y_{lex}, Y_{SN}, or Y_{N}.
Refer to the instructions provided for
NB: the available documentation is obsolete (written for Julia v0.6.4; new documentation compliant with v1.x is coming).
Old documentation:
Examples of problems ready to be solved:
[Haimes1971] Y.V. Haimes, L.S. Lasdon, D.A. Wismer: On a bicriterion formation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man and Cybernetics, Volume SMC-1, Issue 3, Pages 296-297, July 1971.
[Aneja1979] Y. P. Aneja and K. P. K. Nair: Bicriteria Transportation Problem. Management Science, 25:1, 73-78 1979.
[Wassenhove1980] L. N. Van Wassenhove, L. F. Gelders: Solving a bicriterion scheduling problem. European Journal of Operational Research, Volume 4, Issue 1, Pages 42-48, 1980.
[Chalmet1986] L.G. Chalmet, L. Lemonidis, D.J. Elzinga: An algorithm for the bi-criterion integer programming problem. European Journal of Operational Research, Volume 25, Issue 2, Pages 292-300, 1986.
[Gandibleux2006] X. Gandibleux, F. Beugnies, S. Randriamasy:
Martins’ algorithm revisited for multi-objective shortest path problems with a MaxMin cost function.
4OR: A Quarterly Journal of Operations Research, Springer Verlag, 4 (1), pp.47-59, 2006.
[Przybylski2008] 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.
[Jorge2010] J. Jorge: Nouvelles propositions pour la résolution exacte du sac à dos multi-objectif unidimensionnel en variables binaires. PhD Thesis (in French), Université de Nantes - France, 2010.
[Gandibleux2012] 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.
[Vincent2013] Th. Vincent: Caractérisation des solutions efficaces et algorithmes d’énumération exacts pour l’optimisation multiobjectif en variables mixtes binaires. PhD Thesis (in French), Université de Nantes - France, 2013.
[Delmee2017] Q. Delmée, X. Gandibleux, A. Przybylski: Résolution exacte du problème de localisation de services bi-objectif sans contrainte de capacité en variables mixtes. ROADEF2017 (18ème édition du congrès annuel de la Société Française de Recherche Opérationnelle et d’Aide à la Décision). 22-24 février 2017, Metz, France.
[Dumez2017] D. Dumez, X. Gandibleux, I. Rusu. Datastructures for Filtering and Storing Non-Dominated Points. MOPGP’2017: 12th International Conference on Multiple Objective Programming and Goal Programming. 30-31 October 2017, Metz, France.
Terms and acronyms used