Abstract
This paper provides a new proposal that aims to solve multi-objective optimization problems (MOP s ) using quantum evolutionary paradigm. Three main features characterize the proposed framework. In one hand, it exploits the states superposition quantum concept to derive a probabilistic representation encoding the vector of the decision variables for a given MOP. The advantage of this representation is its ability to encode the entire population of potential solutions within a single chromosome instead of considering only a gene pool of individuals as proposed in classical evolutionary algorithms. In the other hand, specific quantum operators are defined in order to reward good solutions while maintaining diversity. Finally, an evolutionary dynamics is applied on these quantum based elements to allow stochastic guided exploration of the search space. Experimental results show not only the viability of the method but also its ability to achieve good approximation of the Pareto Front when applied on the multi-objective knapsack problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Collette, Y., Siarry, P.: Optimisation multi-objectifs, Eyrolles edn. (2002)
Van Veldhuizen, D.A., Lamont, G.B.: Multi-objective evolutionary algorithms: Analyzing the state of the art. Evolutionary computation 8(2), 125–147 (2000)
Schaffer, J.D.: Multi-objectiveoptimization with vector evaluated genetic algorithms. In: Genetic Algorithms and their Applications: Proc. of the First International Conference on Genetic Algorithms, pp. 93–100. Lawrence Erlbaum, Hillsdale (1985)
Horn, J., Nafptiolis, N., Goldberg, D.: A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In: First IEEE Conference on evolutionary Computation, IEEE World Congress on computational Intelligence, New Jersey, vol. 1, pp. 82–88 (1994)
Srinivas, N., Deb, K.: Multi-objective optimization using nondominated sorting in genetic algorithms 2(3), 221–248 (1994)
Deb, K., Agrawal, S., Pratapand, A., Meyarivan, T.: A Fast and Elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary computation 6(2) (April 2002)
Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2:Improving the Performance of the Strength Pareto evolutionary Algorithm, Technical Report 103, Computer Engineering and Communication Networks lab(Tik), Swiss Federal Institute of Technology(ETH) Zurith, Gloriastrasse 35, CH-8092 Zurith (May 2001)
Coello Coello, C.A., Toscano Publido, G.: Multi-objective optimization using a micro-genetic algorithm. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 247–282. Morgan Kaufman, San Fransisco (2001)
Coello Coello, C.A., Cortes, N.C.: Solving multi-objective optimization problems using artificial immune system. Genetic Programming and Evolvable Machines 6, 163–190 (2005)
Han, K.H., Kim, J.H.: Quantum inspired evolutionary algorithms with a new termination criterion, He gate and two phase scheme. IEEE Transactions on Evolutionary Computation 8, 156–169 (2004)
Han, K.H., Kim, J.H.: Genetic quantum algorithm and its application to combinatorial optimization problem. In: Proc. Congr. Evolutionary Computation, La Jolla, CA, vol. 2, pp. 1354–1360 (2000)
Williams, C.P., Clearwater, S.H.: Explorations in quantum computing. Springer, Berlin (1998)
Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: Proc. 35th Annu. Symp. Foundations Computer Science, Sante Fe, NM, pp. 124–134 (1994)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proc. 28th ACM Symp. Theory Computing, pp. 212–219 (1996)
Narayanan, A., Moore, M.: Quantum-inspired genetic algorithms. In: Proc. IEEE Int. Conf. Evolutionary Computation, pp. 61–66 (1996)
Zitzler, E., Laumanns, M.: Problems and Test Data for Multiobjective Optimizers, http://www.tik.ee.ethz.ch/~zitzler/testdata.html
International Society on Multiple Criteria Decision Making. MCDM Numerical Instances Library, http://www.univ-valencienne.fr/ROAD/MCDM
Coello Coello, C.A., Van Veldhuilzen, D.A., Lamot, G.B.: Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, New York (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Meshoul, S., Mahdi, K., Batouche, M. (2005). A Quantum Inspired Evolutionary Framework for Multi-objective Optimization. In: Bento, C., Cardoso, A., Dias, G. (eds) Progress in Artificial Intelligence. EPIA 2005. Lecture Notes in Computer Science(), vol 3808. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11595014_19
Download citation
DOI: https://doi.org/10.1007/11595014_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30737-2
Online ISBN: 978-3-540-31646-6
eBook Packages: Computer ScienceComputer Science (R0)