Abstract
Evolutionary Algorithms are search and optimisation methods based on the principles of natural evolution and genetics that attempt to approximate the optimal solution of a problem. Instead of only one, they evolve a population of potential solutions to the problem, using operators like mutation, crossover and selection.
In this work, we present a new crossover operator, in the context of Multiobjective Evolutionary Algorithms, which makes use of the concept of Pareto optimality. After that it is compared to four common crossover operators. The results obtained are very promising.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alberto I, Mateo PM (2008) Using Pareto optimality for defining the mutation operator step size. Technical report. In: Prepublicaciones del seminario matemático García Galdeano, University of Zaragoza, 8, pp 1–19
Casella G, Berger RL (2002) Statistical inference, 2nd edn. Duxbury advanced series. Duxbury, Pacific Grove
CEC (2007) Special session and competition on performance assessment of multi-objective optimization algorithms. Available in web page http://www3.ntu.edu.sg/home/epnsugan/. Accessed August 2008
Coello CA (2005) Recent trends in evolutionary multiobjective optimization. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization: theoretical advances and applications. Springer, London, pp 7–32
Coello CA (2008) EMOO repository (online). Available in http://delta.cs.cinvestav.mx/~ccoello/EMOO/. Accessed September 2008
Coello CA, Lamont GB, Van Veldhuizen DA (2007) Evolutionary algorithms for solving multi-objective problems, 2nd edn. Springer, Berlin
Deb K (2001) Multi-objective optimization using evolutionary algorithms, 2nd edn. Wiley, Chichester
Deb K, Agrawal S (1995) Simulated binary crossover for continuous search space. Complex Syst 9(2):115–148
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197
Deb K, Thiele L, Laumanns M, Zitzler E (2002) Scalable multi-objective optimization test problems. In: Congress on evolutionary computation CEC’2002, vol 1. IEEE Press, Piscataway, pp 825–830
Eiben AE, Smith JE (2007) Introduction to evolutionary computing, 2nd edn. Springer, Berlin
Eshelman LJK, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Whitley LD (ed) Foundations of genetic algorithms II. Morgan Kaufmann, Los Altos, pp 187–202
Fonseca CM, Fleming PJ (1993) Genetic algorithms for multi-objective optimization: formulation, discussion and generalization. In: Forrest S (ed) Genetic algorithms: proceedings of the fifth international conference. Morgan Kaufmann, San Mateo, pp 416–423
Fonseca CM, Paquete L, Lopez-Ibanez M (2006a) An improved dimension-sweep algorithm for the hypervolume indicator. In: Congress on evolutionary computation CEC’2006. IEEE Press, Vancouver, pp 1157–1163
Fonseca CM, Paquete L, Lopez-Ibanez M (2006b) Computation of the hypervolume indicator, codes available in web page http://sbe.napier.ac.uk/~manuel/hypervolume. Accessed August 2008
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison–Wesley, Reading
Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12(4):265–319
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Huang VL, Qin AK, Deb K, Zitzler E, Suganthan PN, Liang JJ, Preuss M, Huband S (2007) Problem definitions for performance assessment on multiobjective optimization algorithms. Technical report CEC-TR2007, Nanyang Technological University, Singapore
Huband S, Hingston P, Barone L, While L (2007) A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans Evol Comput 10(5):477–506
Mezura-Montes E, Reyes-Sierra M, Coello CA (2008) Multi-objective optimization using differential evolution: a survey of the state-of-the-art. In: Chakraborty UK (ed) Advances in differential evolution. Springer, Berlin, pp 173–196
Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs, 3rd edn. Springer, Berlin
Schaffer JD (1984) Multiple objective optimization with vector evaluated genetic algorithms. Ph.D. thesis, Vanderbilt University, Nashville, Tennessee
Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Grefenstette JJ (ed) Genetic algorithms and their applications, proceedings of the first international conference on genetic. Lawrence Erlbaum, Hillsdale, pp 93–100
Storn R, Price K (1995) Differential evolution—a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report TR-95-12, International Computer Science, Berkeley, California, pp 1–12
Wright AH (1991) Genetic algorithms for real parameter optimization. In: Rawlins GJE (ed) Foundations of genetic algorithms. Morgan Kaufmann, San Mateo, pp 205–218
Zitzler E (1999) Evolutionary algorithms for multiobjective optimization: methods and applications. Ph.D. thesis, dissertation ETH no 13398, Swiss Federal Institute of Technology (ETH), Zürich, Switzerland
Zitzler E, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans Evol Comput 3(4):257–271
Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195
Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. Technical report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institue of Technology (ETH), Zurich, Switzerland, pp 1–21
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Alberto, I., Mateo, P.M. A crossover operator that uses Pareto optimality in its definition. TOP 19, 67–92 (2011). https://doi.org/10.1007/s11750-009-0082-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11750-009-0082-7