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Leveldiagrams for multiobjective decision making

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A tool to draw Leveldiagrams for Pareto Set/Front, allowingsome basics graphics manipulations.



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This toolbox draws Leveldiagrams for Pareto Set and its associated Front, and allows some basics graphics manipulations (coloring plot according preferences, axis manipulation and point selections) to help in decision making. Details about Leveldiagrams and some examples supplied in this toolbox are described in:
[1] X. Blasco, J.M. Herrero, J. Sanchis, M. Martínez. A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences 178 (2008) 3908–3924. doi:10.1016/j.ins.2008.06.010
Short video with example usage:
For advance features comparing Pareto Fronts:

Level diagram have been used in:

[2] E. Zio, R. Bazzo. Multiobjective optimization of the inspection intervals of a nuclear safety system: A clustering-based framework for reducing the Pareto Front. Annals of Nuclear Energy 37 (2010) 798–812. doi:10.1016/j.anucene.2010.02.020

[3] E. Zio, R. Bazzo. A clustering procedure for reducing the number of representative solutions in the Pareto Front of multiobjective optimization problems. European Journal of Operational Research
Volume 210, Issue 3, 1 May 2011, pages 624-634.

[4] E. Zio, R. Bazzo. Level Diagrams analysis of Pareto Front for multiobjective system redundancy allocation. Reliability Engineering and System Safety, volume 96 (2011), pages 569–580. doi:10.1016/j.ress.2010.12.016

[5] A. Hajiloo, N. Nariman-zadeh, Ali Moeini, Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties. Mechatronics (ISSN 0957-4158). Online 11 May 2012. doi:10.1016/j.mechatronics.2012.04.003.

[6] A.T.D. Perera, R.A. Attalage, K.K.C.K. Perera, V.P.C. Dassanayake. A hybrid tool to combine multi-objective optimization and multi-criterion decision making in designing standalone hybrid energy systems. Applied Energy, Vol 107 (2013), pages 412–425.

[7] S. Pourzeynali, S. Salimi, H. Eimani Kalesar. Robust multi-objective optimization design of TMD control device to reduce tall building responses against earthquake excitations using genetic algorithms. Scientia Iranica Transaction A. (2013).

[8] H. Li and H. Ding, "Modeling and multi-objective design optimization of quasi-continuous high magnetic field systems," Progress In Electromagnetics Research, Vol. 139, 353-372, 2013.

[9] Porto, Miguel; Correia, Otilia; Beja, Pedro. “Optimization of Landscape Services under Uncoordinated Management by Multiple Landowners.” PLOS ONE, 9 (1). JAN 17 2014

[10] An automated approach towards detecting complex behaviours in deep brain oscillations
Mace, M; Yousif, N; Naushahi, M; Abdullah-Al-Mamun, K; Wang, SY; Nandi, D; Vaidyanathan, R

Comments and Ratings (3)


amal (view profile)

Thank you a lot. it is very helpful

Xavier Blasco

Xavier Blasco (view profile)

The required inputs for our toolbox are a Pareto Set and a Pareto front; you will need to define two different matrix, with:

1) As many columns as dimensions (decision variables / design objectives)
2) As many rows as different solutions.

Please, do not hesitate to make any further questions.


Iman (view profile)

Dear Xavier,
I am quite new to the concept but the thing that made me to work on your file is looking for a Decision Making way of Pareto results.My question is in regard with Objectives and variables.Do we need to define Objectives and design variables for this program or the only required input of this program is results produced in my optimization?



Added a link with a short screencast with an example.


Update of multidisciplinary works that use Level diagrams


Updating of references to articles that use Level Diagrams


Adding another article that uses LD


Bugs fixed. classbypreference5 function and data for example corrected. Mistakes of documentation corrected.


Adding another article that uses LD.


Adding another article that uses LD


A reference to an article the uses Level diagram is added.


A reference to an article that uses Level diagram has been added.


New tag and changes in license

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