The main idea of this question is to have a list of exact methods applied to solve (Multi-objective optimization problem) MOPs. I am interested in the problem, number of objectives, how it behaves with more objectives and large instances.
As far i have found Multi-objective branch and bound based on dominance, and some parallel B&B.
Please visit the following site. It is a good book. Though the name is "...evolutionary algorithms", the first and chapter describes the analytical methods to solve multiobjective problems. The book may be useful to you.
https://books.google.co.in/books/about/Multi_Objective_Optimization_Using_Evolu.html?id=OSTn4GSy2uQC&redir_esc=y
Exact solution of Multi-Objective Optimization problems is not a new research area, but recently, it has attracted more attention. The main focus has been on solving Multi-Objective Mixed Integer Programming (MOMIP). Most research has been concentrated on the simplest problem, i.e. Bi-Objective Mixed Integer Programming (BIMIP).
There are two methodologically different approaches to BIMIP/MOMIP's:
- Objective Space methods, where Single-Objective MIP solves are applied:
- the epsilon-constraint method
- the two-phase method (UlunguTeghem.pdf)
- and a number of other related methods.
- Decision Space methods, i.e. where modified Branch & Bound methods are modified to cater to two or more criteria:
- Mavrotas & Diakoulaki (MavrotasDiakoulaki.pdf)
- Vincent Et. Al (VincentSeippRuzikaPrzbylskiGandibleux.pdf
- Belotti Et. Al. (BelottiSoyluWiecek.pdf)
- Stidsen Et. Al. (StidsenAndersenRyther.pdf)
Which approach is the best is hard to say, more research is needed.
Please see the paper entitled "Barzilai and Borwein’s method for multiobjective optimization problems" from the following link:
https://www.researchgate.net/publication/283621966_Barzilai_and_Borwein%27s_method_for_multiobjective_optimization_problems
Article Barzilai and Borwein’s method for multiobjective optimization problems
See the recent report of Albertas Gimbutas (2014): LIPSCHITZ OPTIMIZATION FOR MULTI-OBJECTIVE PROBLEMS. There is also a paper written recently by A. Zilinskas.
Hi,
I found it, here
Visualization of a statistical approximation of the Pareto front
November 2015 · Applied Mathematics and Computation 11/2015; 271:694-700. DOI:10.1016/j.amc.2015.09.052
Antanas Žilinskas
Jose Carlos: Si tu entiendes por metodos exactos aquellos que no son heuristicos, entonces los metodos clasicos te permiten encontrar elementos del frente de Pareto.
Consulta los capitulos 2 y 3 del libro "Multiobjective optimizatiion using evolutionary algorithms de Kalyanmoy Deb Wiley .Ahi veras las condiciones de Kuhn Tucker para problemas multiobjetivo y algunos resultados que te permiten la busqueda de forma analitica( no algoritmica) de puntos del frente de Pareto.Ese libro es el mas claro para el estudio de optimizacion clasica y heuristica.Espero te sirva el comentario.Te envio mi tesis doctoral. Ahi puedes ver lo que te comento y algunos ejercicios resueltos de forma clasica para la obtencion de los puntos de Pareto en forma exacta.
Here is a link to a survey of tools:
http://www.lionhrtpub.com/orms/surveys/das/das.html
K-PPM is another exact method to solve multi-objective combinatorial optimization problems
http://www.sciencedirect.com/science/article/pii/S0377221708010709
Hello, after having values of all objective functions, you classify the solutions according to the "pareto rank". Of course, Best solutions that belong to the first rank.
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