Cite Us

If you have used our framework for research purposes, you can cite pymoo:

    author={J. {Blank} and K. {Deb}},
    journal={IEEE Access},
    title={pymoo: Multi-Objective Optimization in Python},

All references of this online documentation are listed below. The corresponding BibTex is available as well.


Annibale Panichella. An adaptive evolutionary algorithm based on non-euclidean geometry for many-objective optimization. In Proceedings of the Genetic and Evolutionary Computation Conference, GECCO ‘19, 595–603. New York, NY, USA, 2019. Association for Computing Machinery. URL:, doi:10.1145/3321707.3321839.


Ke Li, Renzhi Chen, Guangtao Fu, and Xin Yao. Two-Archive Evolutionary Algorithm for Constrained Multiobjective Optimization. IEEE Transactions on Evolutionary Computation, 23(2):303–315, April 2019. doi:10.1109/TEVC.2018.2855411.


Qingfu Zhang and Hui Li. A multi-objective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, Accepted, 2007.


K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm: nsga-II. Trans. Evol. Comp, 6(2):182–197, April 2002. URL:, doi:10.1109/4235.996017.


Kalyanmoy Deb and Himanshu Jain. An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 18(4):577–601, 2014. doi:10.1109/TEVC.2013.2281535.


H. Jain and K. Deb. An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part II: handling constraints and extending to an adaptive approach. IEEE Transactions on Evolutionary Computation, 18(4):602–622, Aug 2014.


Julian Blank, Kalyanmoy Deb, and Proteek Chandan Roy. Investigating the normalization procedure of nsga-iii. In Kalyanmoy Deb, Erik Goodman, Carlos A. Coello Coello, Kathrin Klamroth, Kaisa Miettinen, Sanaz Mostaghim, and Patrick Reed, editors, Evolutionary Multi-Criterion Optimization, 229–240. Cham, 2019. Springer International Publishing.


Kalyanmoy Deb and J. Sundar. Reference point based multi-objective optimization using evolutionary algorithms. In Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, GECCO ‘06, 635–642. New York, NY, USA, 2006. ACM. URL:, doi:10.1145/1143997.1144112.


Y. Vesikar, K. Deb, and J. Blank. Reference point based NSGA-III for preferred solutions. In 2018 IEEE Symposium Series on Computational Intelligence (SSCI), 1587–1594. Nov 2018. doi:10.1109/SSCI.2018.8628819.


H. Seada and K. Deb. A unified evolutionary optimization procedure for single, multiple, and many objectives. IEEE Transactions on Evolutionary Computation, 20(3):358–369, June 2016. doi:10.1109/TEVC.2015.2459718.


Nikolaus Hansen, Youhei Akimoto, and Petr Baudis. CMA-ES/pycma on Github. Zenodo, DOI:10.5281/zenodo.2559634, February 2019. URL:, doi:10.5281/zenodo.2559634.


Nikolaus Hansen and Andreas Ostermeier. Completely derandomized self-adaptation in evolution strategies. Evol. Comput., 9(2):159–195, June 2001. URL:, doi:10.1162/106365601750190398.


Nikolaus Hansen. The CMA Evolution Strategy: A Comparing Review, pages 75–102. Springer Berlin Heidelberg, Berlin, Heidelberg, 2006. URL:, doi:10.1007/3-540-32494-1_4.


Kenneth Price, Rainer M. Storn, and Jouni A. Lampinen. Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series). Springer-Verlag, Berlin, Heidelberg, 2005. ISBN 3540209506.


T.P. Runarsson and Xin Yao. Search biases in constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 35(2):233–243, 2005. doi:10.1109/TSMCC.2004.841906.


J. A. Nelder and R. Mead. A simplex method for function minimization. Computer Journal, 7:308–313, 1965.

Robert Hooke and T. A. Jeeves. “ direct search’’ solution of numerical and statistical problems. J. ACM, 8(2):212–229, April 1961. URL:, doi:10.1145/321062.321069.


J. Kennedy and R. Eberhart. Particle swarm optimization. In Proceedings of ICNN’95 - International Conference on Neural Networks, volume 4, 1942–1948 vol.4. 1995.


Z. Zhan, J. Zhang, Y. Li, and H. S. Chung. Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(6):1362–1381, 2009.


T.P. Runarsson and Xin Yao. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation, 4(3):284–294, 2000. doi:10.1109/4235.873238.


Kalyanmoy Deb and Deb Kalyanmoy. Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Inc., New York, NY, USA, 2001. ISBN 047187339X.


J. Blank and K. Deb. A running performance metric and termination criterion for evaluating evolutionary multi- and many-objective optimization algorithms. In 2020 IEEE Congress on Evolutionary Computation (CEC), volume, 1–8. 2020. doi:10.1109/CEC48606.2020.9185546.


L. Rachmawati and D. Srinivasan. Multiobjective evolutionary algorithm with controllable focus on the knees of the pareto front. IEEE Transactions on Evolutionary Computation, 13(4):810–824, Aug 2009. doi:10.1109/TEVC.2009.2017515.


Andrzej P Wierzbicki. The use of reference objectives in multiobjective optimization. In Multiple criteria decision making theory and application, pages 468–486. Springer, 1980.


Andrzej P. Wierzbicki. A mathematical basis for satisficing decision making. Mathematical Modelling, 3(5):391 – 405, 1982. Special IIASA Issue. URL:, doi:


David A. Van Veldhuizen and David A. Van Veldhuizen. Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Technical Report, Evolutionary Computation, 1999.


Hisao Ishibuchi, Hiroyuki Masuda, Yuki Tanigaki, and Yusuke Nojima. Modified distance calculation in generational distance and inverted generational distance. In António Gaspar-Cunha, Carlos Henggeler Antunes, and Carlos Coello Coello, editors, Evolutionary Multi-Criterion Optimization, 110–125. Cham, 2015. Springer International Publishing.


Carlos A. Coello Coello and Margarita Reyes Sierra. A study of the parallelization of a coevolutionary multi-objective evolutionary algorithm. In Raúl Monroy, Gustavo Arroyo-Figueroa, Luis Enrique Sucar, and Humberto Sossa, editors, MICAI 2004: Advances in Artificial Intelligence, 688–697. Berlin, Heidelberg, 2004. Springer Berlin Heidelberg.


Carlos M. Fonseca, Luís Paquete, and Manuel López-Ibáñez. An improved dimension sweep algorithm for the hypervolume indicator. In Proceedings of the 2006 Congress on Evolutionary Computation (CEC 2006), pages 1157–1163. IEEE Press, Piscataway, NJ, July 2006. doi:10.1109/CEC.2006.1688440.


Kalyanmoy Deb and Mohamed Abouhawwash. An optimality theory-based proximity measure for set-based multiobjective optimization. IEEE Trans. Evolutionary Computation, 20(4):515–528, 2016. URL:, doi:10.1109/TEVC.2015.2483590.


Kalyanmoy Deb, Mohamed Abouhawwash, and Haitham Seada. A computationally fast convergence measure and implementation for single-, multiple-, and many-objective optimization. IEEE Trans. Emerging Topics in Comput. Intellig., 1(4):280–293, 2017. URL:, doi:10.1109/TETCI.2017.2719707.


Indraneel Das and J. E. Dennis. Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J. on Optimization, 8(3):631–657, March 1998. URL:, doi:10.1137/S1052623496307510.


J. Blank, K. Deb, Y. Dhebar, S. Bandaru, and H. Seada. Generating well-spaced points on a unit simplex for evolutionary many-objective optimization. IEEE Transactions on Evolutionary Computation, 25(1):48–60, 2021. doi:10.1109/TEVC.2020.2992387.


D.P. Hardin and E.B. Saff. Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds. Advances in Mathematics, 193(1):174 – 204, 2005. doi:


Kalyanmoy Deb, Karthik Sindhya, and Tatsuya Okabe. Self-adaptive simulated binary crossover for real-parameter optimization. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, GECCO ‘07, 1187–1194. New York, NY, USA, 2007. ACM. URL:, doi:10.1145/1276958.1277190.


Zhun Fan, Wenji Li, Xinye Cai, Hui Li, Caimin Wei, Qingfu Zhang, Kalyanmoy Deb, and Erik Goodman. Difficulty Adjustable and Scalable Constrained Multiobjective Test Problem Toolkit. Evolutionary Computation, pages 1–40, May 2019. doi:10.1162/evco_a_00259.


Cyril Picard and Jürg Schiffmann. Realistic Constrained Multi-Objective Optimization Benchmark Problems from Design. IEEE Transactions on Evolutionary Computation, pages 1–1, 2020. doi:10.1109/TEVC.2020.3020046.


Zhongwei Ma and Yong Wang. Evolutionary Constrained Multiobjective Optimization: Test Suite Construction and Performance Comparisons. IEEE Transactions on Evolutionary Computation, 23(6):972–986, December 2019. doi:10.1109/TEVC.2019.2896967.


To Thanh Binh and Ulrich Korn. Mobes: a multiobjective evolution strategy for constrained optimization problems. In IN PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON GENETIC ALGORITHMS (MENDEL97, 176–182. 1997.


Kalyanmoy Deb and Santosh Tiwari. Omni-optimizer: a generic evolutionary algorithm for single and multi-objective optimization. European Journal of Operational Research, 185(3):1062 – 1087, 2008. URL:, doi:


Günter Rudolph, Boris Naujoks, and Mike Preuss. Capabilities of emoa to detect and preserve equivalent pareto subsets. In Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization, EMO’07, 36–50. Berlin, Heidelberg, 2007. Springer-Verlag.


Kalyanmoy Deb and Aravind Srinivasan. Innovization: innovating design principles through optimization. In Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, GECCO ‘06, 1629–1636. New York, NY, USA, 2006. ACM. URL:, doi:10.1145/1143997.1144266.


Eckart Zitzler, Kalyanmoy Deb, and Lothar Thiele. Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation, 8(2):173–195, 2000. doi:10.1162/106365600568202.


H. H. Rosenbrock. An automatic method for finding the greatest or least value of a function. The Computer Journal, 3(3):175–184, mar 1960. URL:, doi:10.1093/comjnl/3.3.175.


J. Blank and K. Deb. pymoo: multi-objective optimization in python. IEEE Access, 8():89497–89509, 2020. doi:10.1109/ACCESS.2020.2990567.