Abstract
Approximate dynamic programming (ADP) was developed for solving large-scale optimization problems, and function approximation is an important method in the dynamic programming scheme. Continuous quadratic programming relaxation (CQPR) and the integral parts of the solutions to CQPR are two intuitionistic heuristics as function approximations in ADP for solving quadratic knapsack problems (QKPs). We propose a rule of ordering variables to sort the first variable to be solved in ADP, and develop a heuristic which adaptively fixes the variables according to the solution to CQPR of convex QKPs based the rule. By using the rule and heuristics, we propose a sorted ADP heuristic scheme for QKPs.
Supported by Program for New Century Excellent Talents in University of China (Grant No.: NCET-04-0570), NSFC (Grant No.: 70571073) and the Specialized Research Fund for the Doctoral Programme of Higher Education (Grant No.: 20050358002).
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References
Hua, Z.S., Banerjee, P.: Aggregate Line Capacity Design for PWB Assembly Systems. Int. J. Prod. Res. 38, 2417–2441 (2000)
Ferreira, C.E., Martin, A., De, S.C., Weismantel, R., Wolsey, L.: Formulations and Valid Inequalities for the Node Capacitated Graph Partitioning Problem. Math. Program. 74, 247–267 (1996)
Hammer, P.L., Rader, D.J.: Efficient Methods for Solving Quadratic 0-1 Knapsack Problems. Infor 35, 170–182 (1997)
Cooper, L., Cooper, M.W.: Introduction to Dynamic Programming. Pergamon Press, Elmsford (1981)
Zhang, B., Hua, Z.S.: An Improved Lemke Algorithm for Convex Quadratic Programming with Equality Constraints. Journal of University of Science and Technology of China 34, 668–677 (2004)
Hua, Z.S., Zhang, B., Liang, L.: An Approximate Dynamic Programming Approach to Convex Quadratic Knapsack Problems. Comput. Oper. Res., 660–673 (2006)
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© 2006 Springer-Verlag Berlin Heidelberg
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Zhang, B., Hua, Z. (2006). Heuristics to Convex Quadratic Knapsack Problems in Sorted ADP. In: Huang, DS., Li, K., Irwin, G.W. (eds) Intelligent Computing. ICIC 2006. Lecture Notes in Computer Science, vol 4113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816157_109
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DOI: https://doi.org/10.1007/11816157_109
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37271-4
Online ISBN: 978-3-540-37273-8
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