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Using modifications to Grover's Search algorithm for quantum global optimization

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  • Liu, Yipeng
  • Koehler, Gary J.

Abstract

We study the problem of finding a global optimal solution to discrete optimization problems using a heuristic based on quantum computing methods. (Knowledge of quantum computing ideas is not necessary to read this paper.) We focus on a successful quantum computing method introduced by Baritompa, Bulger, and Wood, that we refer to as the BBW algorithm, and develop two modifications. First, we modify the BBW algorithm to achieve a dramatic speedup that lets us extend the known BBW static schedule from 33 to 43 points, thereby increasing its applicability. We further modify it by converting it from a static method to a dynamic one. Experimental results show the value of this latter modification.

Suggested Citation

  • Liu, Yipeng & Koehler, Gary J., 2010. "Using modifications to Grover's Search algorithm for quantum global optimization," European Journal of Operational Research, Elsevier, vol. 207(2), pages 620-632, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:620-632
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    References listed on IDEAS

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    1. Vasek Chvátal, 1980. "Hard Knapsack Problems," Operations Research, INFORMS, vol. 28(6), pages 1402-1411, December.
    2. Ghosh, Diptesh & Chakravarti, Nilotpal & Sierksma, Gerard, 2006. "Sensitivity analysis of a greedy heuristic for knapsack problems," European Journal of Operational Research, Elsevier, vol. 169(1), pages 340-350, February.
    3. Zelda Zabinsky & David Bulger & Charoenchai Khompatraporn, 2010. "Stopping and restarting strategy for stochastic sequential search in global optimization," Journal of Global Optimization, Springer, vol. 46(2), pages 273-286, February.
    4. Andonov, R. & Poirriez, V. & Rajopadhye, S., 2000. "Unbounded knapsack problem: Dynamic programming revisited," European Journal of Operational Research, Elsevier, vol. 123(2), pages 394-407, June.
    5. Balev, Stefan & Yanev, Nicola & Freville, Arnaud & Andonov, Rumen, 2008. "A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 63-76, April.
    6. Derpich, Ivan & Vera, Jorge R., 2006. "Improving the efficiency of the Branch and Bound algorithm for integer programming based on "flatness" information," European Journal of Operational Research, Elsevier, vol. 174(1), pages 92-101, October.
    7. Chia‐Shin Chung & Ming S. Hung & Walter O. Rom, 1988. "A hard knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 85-98, February.
    8. D. Bulger & W. P. Baritompa & G. R. Wood, 2003. "Implementing Pure Adaptive Search with Grover's Quantum Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 517-529, March.
    9. Kohli, Rajeev & Krishnamurti, Ramesh & Mirchandani, Prakash, 2004. "Average performance of greedy heuristics for the integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 154(1), pages 36-45, April.
    10. Billionnet, Alain & Soutif, Eric, 2004. "An exact method based on Lagrangian decomposition for the 0-1 quadratic knapsack problem," European Journal of Operational Research, Elsevier, vol. 157(3), pages 565-575, September.
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    Cited by:

    1. Pedro Lara & Renato Portugal & Carlile Lavor, 2014. "A new hybrid classical-quantum algorithm for continuous global optimization problems," Journal of Global Optimization, Springer, vol. 60(2), pages 317-331, October.
    2. Yipeng Liu & Gary Koehler, 2012. "A hybrid method for quantum global optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 607-626, March.

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