Structural and Multidisciplinary Optimization

, Volume 60, Issue 4, pp 1455–1473 | Cite as

Many-objective differential evolution optimization based on reference points: NSDE-R

  • Sohail R. ReddyEmail author
  • George S. Dulikravich


Design methodologies of today require the solution of several many-objective optimization problems. The last two decades have seen a surge in several algorithms capable of solving multi-objective optimization problems. It was only in the past 5 years that new algorithms capable of coping with a large number of objectives have been introduced. This work presents a new differential evolution algorithm (NSDE-R) capable of efficiently solving many-objective optimization problems. The algorithms make use of reference points evenly distributed through the objective function space to preserve diversity and aid in multi-criteria-decision-making. The proposed NSDE-R was applied to test problems from the DTLZ and WFG suite, having three to 15 objectives. Two mutation donor operators were investigated for their ability to converge to the analytical Pareto front while maintaining diversity. The ability of NSDE-R to converge to a user-specified region of the Pareto front is also investigated. The proposed NSDE-R algorithm has shown to have a higher rate of convergence and better convergence to the analytical Pareto front.


Evolutionary computation Differential evolution Many-objective optimization Non-dominated sorting NSDE-R Reference points 



The first author gratefully acknowledges the financial support from Florida International University in the form of an FIU Presidential Fellowship and FIU Dissertation Year Fellowship. The authors are grateful for the research funding provided by the grant NSF CBET-1642253 monitored by Dr. Jose Lage, U.S. Army for the equipment grant W911NF-16-1-0494, and NASA grant NNX17AJ96A via TAMU.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Materials Engineering and Multidisciplinary Analysis, Inverse Design, Robust Optimization and Control - MAIDROC LaboratoryFlorida International UniversityMiamiUSA

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