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Multiobjective Optimization Grover Adaptive Search

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Recent Advances in Computational Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 795))

Abstract

Quantum computing is a fast evolving subject with a promise of highly efficient solutions to difficult and complex problems in science and engineering. With the advent of large-scale quantum computation, a lot of effort is invested in finding new applications of quantum algorithms. In this article, we propose an algorithm based on Grover’s adaptative search for multiobjective optimization problems where access to the objective functions is given via two different quantum oracles. The proposed algorithm, considering both types of oracles, are compared against NSGA-II, a highly cited multiobjective optimization evolutionary algorithm. Experimental evidence suggests that the quantum optimization method proposed in this work is at least as effective as NSGA-II in average, considering an equal number of executions.

M. Villagra is supported by CONACYT research grant PINV15-208.

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Notes

  1. 1.

    http://math.nist.gov/quantum/zoo/

References

  1. von Lücken, C., Barán, B., Brizuela, C.: A survey on multi-objective evolutionary algorithms for many-objective problems. Comput. Optim. Appl. 58(3), 707–756 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Barán, B., Villagra, M.: Multiobjective optimization in a quantum adiabatic computer. Electron. Notes Theor. Comput. Sci. 329, 27–38 (2016)

    Article  MathSciNet  Google Scholar 

  3. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of 35th Annual Symposium on Foundations of Computer Science (FOCS), pp. 124–134 (1994)

    Google Scholar 

  4. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on Theory of computing (STOC), pp. 212–219 (1996)

    Google Scholar 

  5. McGeoch, C.C.: Adiabatic Quantum Computation and Quantum Annealing. Synthesis Lectures on Quantum Computing. Morgan & Claypool (2014)

    Google Scholar 

  6. Farhi, E., Goldstone, J., Gutman, S., Sipser, M.: Quantum Computation by Adiabatic Evolution (2000). arXiv:quant-ph/0001106

  7. Baritompa, W.P., Bulger, D.W., Wood, G.R.: Grover’s quantum algorithm applied to global optimization. SIAM J. Optim. 15(4), 1170–1184 (2005)

    Article  MathSciNet  Google Scholar 

  8. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  9. Fogel, G., Barán, B., Villagra, M.: Comparison of two types of quantum oracles based on Grovers adaptative search algorithm for multiobjective optimization problems. In: Proceedings of the 10th International Workshop on Computational Optimization, Federated Conference in Computer Science and Information Systems (FedCSIS), ACSIS 11, pp. 421–428, Prague, Czech Republic, 3–6 Sept 2017

    Google Scholar 

  10. Dürr, C., Høyer, P.: A quantum algorithm for finding the minimum (1996). arXiv:quant-ph/9607014

  11. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge university press (2010)

    Google Scholar 

  12. Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J Comput 26(5), 1510–1523 (1997)

    Article  MathSciNet  Google Scholar 

  13. Born, M., Vladimir Fock, F.: Beweis des adiabatensatzes. Z. für Phys. 51(3–4), 165–180 (1926)

    Google Scholar 

  14. Lipton, R.J., Regan, K.W.: Quantum Algorithms via Linear Algebra. MIT Press (2014)

    Google Scholar 

  15. Chase, N., Rademacher, M., Goodman, E., Averill, R., Sidhu, R.: A benchmark study of multi-objective optimization methods. BMK-3021, Rev 6 (2009)

    Google Scholar 

  16. Riquelme, N., Baran, B., von Lücken, C.: Performance metrics in multi-objective optimization. In: Proceedings of the 41st Latin American Computing Conference (CLEI) (2015)

    Google Scholar 

  17. Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Universidad Nacional de Asunción, NIDTEC, Campus Universitario, San Lorenzo, C.P.2619, Paraguay

    Benjamín Barán & Marcos Villagra

Authors
  1. Benjamín Barán
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  2. Marcos Villagra
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Corresponding author

Correspondence to Marcos Villagra .

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Editors and Affiliations

  1. Department of Parallel Algorithms, Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

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Barán, B., Villagra, M. (2019). Multiobjective Optimization Grover Adaptive Search. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 795. Springer, Cham. https://doi.org/10.1007/978-3-319-99648-6_11

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