to enumerate all (or some of the) nondominated points; or
to optimize a linear function over the set of efficient solutions (to an arbitrary optimality gap); or
to compute the Nadir point; or
to compute an arbitrary component of the Nadir point.
Please kindly cite the following article if you are using this package:
Boland, N., Charkhgard, H., Savelsbergh, M. (2016) ``A New Method for Optimizing a Linear Function over the Efficient Set of a Multiobjective Integer Program". European Journal of Operational Research, available online.
Some standard instances for bi-objective pure-or-mixed integer programming
Please kindly cite the following articles if you are using these instances:
Boland, N., Charkhgard, H., Savelsbergh, M. (2015) ``A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: The Triangle Splitting Method". INFORMS Journal on Computing, 27(4):597-618.
Boland, N., Charkhgard, H., Savelsbergh, M. (2015) ``A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method". INFORMS Journal on Computing, 27(4):735-754.
Also, to access the C++ source code of the balanced box method, please contact me directly.
A feasibility pump based heuristic algorithm and some instances for multi-objective mixed integer linear programming
Pal, A., Charkhgard, H.``A Feasibility Pump and Local Search Based Heuristic
for Bi-objective Pure Integer Linear Programming". To appear in INFORMS Journal On Computing.
The Triangle Splitting Method: An algorithm for generating the nondominated frontier of bi-objective mixed integer linear programs
DOWNLOAD the code for bi-objective mixed 0-1 linear programs.
DOWNLOAD the code for bi-objective mixed (general) integer linear programs.
The code generates three files including Summary.txt, ResultsBeforePostProcessing.txt and ResultsAfterPostProcessing.txt.
Summary.txt provides some general information such as the solution time and so on.
ResultsBeforePostProcessing.txt is more accurate and one may use this file. ResultsAfterPostProcessing.txt is just an approximation (or simplified version) of ResultsBeforePostProcessing.txt
Each row in ResultsBeforePostProcessing.txt has three columns and shows a NonDominated Point (NDP).
For instance, consider row i in ResultsBeforePostProcessing.txt. The first column shows the first objective value of NDP i.
The second column shows the second objective value of NDP i.
The third column can take either 0 or 1 value. If it is one then it shows that the NDP i is connected to NDP i+1.
This means that all points in the line segment between NDP i and NDP i+1 are part of the nondominated frontier.
Please kindly cite the following articles if you are using this package:
Boland, N., Charkhgard, H., Savelsbergh, M. (2015) ``A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: The Triangle Splitting Method". INFORMS Journal on Computing, 27(4):597-618.
Boland, N., Charkhgard, H., Savelsbergh, M. (2015) ``A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method". INFORMS Journal on Computing, 27(4):735-754.
A C++ package for optimizing a linear function over the set of efficient solutions of bi-objective mixed integer linear programs
Please kindly cite the following article if you are using this package:
Sierra-Altamiranda, A., Charkhgard, H.. ``A New Exact Algorithm to Optimize a Linear Function Over the Set of Efficient Solutions for Bi-objective Mixed Integer Linear Programming", http://www.optimization-online.org/DB_HTML/2017/10/6262.html.
A C++ package for solving a class of mixed integer linear maximum multiplicative programs
Please kindly cite the following article if you are using this package:
Ghasemi Saghand, P., Charkhgard, H., Kwon, C. ``A Branch-and-Bound Algorithm for a Class of Mixed Integer Linear Maximum Multiplicative Programs: A Multi-objective Optimization Approach", http://www.optimization-online.org/DB_FILE/2018/04/6562.pdf.
MSEA.jl: A Multi-Stage Exact Algorithm for Bi-objective Pure Integer Linear Programming in Julia
Please kindly cite the following article if you are using this package:
Sierra-Altamiranda, A., Charkhgard, H.. ``OOES.jl: A julia package for optimizing a linear function over the set of efficient solutions for bi-objective mixed integer linear programming", http://www.optimization-online.org/DB_FILE/2018/04/6596.pdf.