AdEnA - Advanced Enclosure Algorithm
AdEnA is a software to solve multi-objective optimization problems (MOP). In particular, it is able to solve multi-objective convex optimization problems (MOCP) as well as multi-objective mixed-integer quadratic optimization problems (MOMIQP). The software is based on the ideas and algorithms from [1].
The implementation is realized as MATLAB code. It is publicly available on GitHub using the MIT Licence.
- Gabriele Eichfelder, Leo Warnow, Advancements in the computation of enclosures for multi-objective optimization problems, European Journal of Operational Research, 310(1), 315-327, 2023.
ASMO - A Solver for Multiobjective Optimization
ASMO is a solver for solving multiobjective optimization problems (MOP). It is based on ideas and algorithms from [1] and [2] using scalarization approaches.
This implementation is realized entirely as MATLAB code. It is licenced under the GNU Lesser General Public Licence and free to use.
You can read more about its features and download the files on GitHub.
- Gabriele Eichfelder, An Adaptive Scalarization Method in Multi-Objective Optimization, SIAM Journal on Optimization, Volume 19, Issue 4, 1694-1718, 2009.
- Gabriele Eichfelder, Adaptive Scalarization Methods in Multiobjective Optimization. Springer, 242 p., ISBN: 978-3-540-79157-7, 2008.
BB-MOQIP- A Branch-and-Bound method for Multiobjective Convex Quadratic Integer Problems
BB-MOQIP is a solver for mutliobjective convex quadratic integer problems presented in the paper De Santis, M., Eichfelder, G., A Decision Space Algorithm for Multiobjective Convex Quadratic Integer Optimization, OptimizationOnline, 2020.
This implementation is realized as MATLAB code. It is published on GitHub and licenced under the GNU Lesser General Public Licence and free to use.
HyPaD - Hybrid Patch Decomposition Algorithm
HyPaD is a solver for multi-objective mixed-integer convex optimization problems (MOMICP). It is based on the results and algorithms presented in [1].
This implementation is realized as MATLAB code. It is publicly available on GitHub and licenced under the MIT Licence.
- Gabriele Eichfelder and Leo Warnow, A hybrid patch decomposition approach to compute an enclosure for multi-objective mixed-integer convex optimization problems, Mathematical Methods of Operations Research, 2023.
MOBO - Multiobjective Bilevel Optimization Solver
MOBO is a solver for continuous multiobjective bilevel optimization problems based on the algorithm published in G. Eichfelder, Multiobjective bilevel optimization, Mathematical Programming 123(2), 419-449, 2010. It is licenced under the GNU Lesser General Public Licence, can be found on GitHub and is free to use.
MOMIBB - Multiobjective Mixed-Integer Branch-and-Bound Algorithm
MOMIBB is a solver for multi-objective mixed-integer optimization problems (MOMIP). It is based on the results and algorithms from [1]. In particular, MOMIBB is able to solve multi-objective mixed-integer nonconvex optimization problems.
This implementation is realized as MATLAB code. It is publicly available on GitHub under the MIT Licence.
- Gabriele Eichfelder, Oliver Stein, Leo Warnow, A solver for multiobjective mixed-integer convex and nonconvex optimization, Journal of Optimization Theory and Applications, 2023.
MOMIX - A Solver for Multiobjective Mixed Integer Convex Optimization
MOMIX is a solver for Multiobjective Mixed Integer Convex Optimization. It is a branch-and-bound method based on the use of properly defined lower bounds, constructed by convex relaxations and by linear outer approximations of the image set in an adaptive way. The algorithm guarantee correctness in terms of detecting both the efficient and the nondominated set of multiobjective mixed integer convex problems according to a prescribed precision. This implementation is realized as MATLAB code. It is published on GitHub and licenced under the GNU Lesser General Public Licence and free to use.
The implementation is based on the paper M. De Santis, G. Eichfelder, J. Niebling, S. Rocktäschel, Solving Multiobjective Mixed Integer Convex Optimization Problems, SIAM Journal on Optimization, 30(4), 3122-3145, 2020. See also OptimizationOnline
Spherical Branch And Bound Algorithms
This Github project includes an R package containing a branch and bound algorithm for computing Fréchet-p-means on the circle and the 2-sphere. Moreover, it provides a wrapper to easily extend these algorithms also to spheres of higher dimension. The repository is supplementary to the paper Eichfelder, G., Hotz, T., Wieditz, J., An algorithm for computing Fréchet means on the sphere, 2019, and was implemented by Johannes Wieditz.