Abstract
We consider a well-known NP-hard server load balancing problem. We study the computational complexity of finding approximate solutions with guaranteed accuracy estimate. We show that this problem is Log-APX-hard with respect to PTAS reductions. To solve the problem, we develop an approximate method based on the ideas of genetic local search. We show results of computational experiments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kochetov, Yu.A. and Kochetova, N.A., Server Load Balancing Problem, Vestn. Novosib. Gos. Univ., Ser. Inform. Tekhnol., 2013, vol. 11, no. 4, pp. 71–76.
Davydov, I.A., Kononova, P.A., and Kochetov, Yu.A., Local Search with Exponential Neighborhood for the Server Load Balancing Problem, Diskret. Anal. Issled. Oper., 2014, vol. 21, no. 6, pp. 21–34.
Kochetov, Yu., Panin, A., and Plyasunov, A., Genetic Local Search for the Servers Load Balancing Problem, Supplement. Proc. 9th Int. Conf. Discret. Optim. Oper. Res. Sci. School (DOOR 2016), 2016, pp. 453–463.
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., and Protasi, M., Complexity and Approximation: Combinatorial Optimization Problems and Their Aproximability Properties, Berlin: Springer-Verlag, 1999.
Bazgan, C., Escoffer, B., and Paschos, V.Th., Completeness in Standard and Differential Approximation Classes: Poly-(D)APX-and (D)PTAS-completeness, Theor. Comput. Sci., 2005, vol. 339, pp. 272–292.
Crescenzi, P., Kann, V., Silvestri, R., and Trevisan, L., Structure in Approximation Classes, SIAM J. Comput., 1999, vol. 28, no. 5, pp. 1759–1782.
Crescenzi, P. and Trevisan, L., On Approximation Scheme Preserving Reducibility and Its Application, Proc. 14th Conf. on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, vol. 880, 1994, Berlin: Springer-Verlag, pp. 330–341.
Garey, M.R. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NPCompleteness, San Francisco: Freeman, 1979. Translation under the title Vychislitel’nye mashiny i trudnoreshaemye zadachi, Moscow: Mir, 1982.
Escoffier, B. and Paschos, V.Th., Completeness in Approximation Classes beyond APX, Theor. Comput. Sci., 2006, vol. 359, pp. 369–377.
Talbi, E-G., Metaheuristics: From Design to Implementation, Berlin: Wiley, 2009.
Alekseeva, E.V. and Kochetov, Yu.A., Genetic Local Search for the p-Median Problem with Client Preferences, Diskret. Anal. Issled. Oper., Ser. 2, 2007, vol. 14, no. 1, pp. 3–31.
Kochetov, Yu.A. and Plyasunov, A.V., Genetic Local Search for the Graph Partitioning Problem into Shares of Bounded Cardinality, Zh. Vychisl. Mat. Mat. Fiz., 2012, vol. 52, no. 1, pp. 164–176.
Dolgui, A., Eremeev, A., Kolokolov, A., and Sigaev, V., A Genetic Algorithm for the Allocation of Buffer Storage Capacities in a Production Line with Unreliable Machines, J. Math. Modell. Alg., 2002, vol. 1, no. 2, pp. 89–104.
Panin, A.A., Pashchenko, M.G., and Plyasunov, A.V., Bilevel Competitive Facility Location and Pricing Problems, Autom. Remote Control, 2014, vol. 75, no. 4, pp. 715–727.
Kochetov, Yu., Panin, A., and Plyasunov, A., Comparison of Metaheuristics for the Bilevel Facility Location and Mill Pricing Problem, J. App. Ind. Math., 2015, vol. 9, no. 3, pp. 392–401.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.A. Kochetov, A.A. Panin, A.V. Plyasunov, 2017, published in Avtomatika i Telemekhanika, 2017, No. 3, pp. 51–62.
Rights and permissions
About this article
Cite this article
Kochetov, Y.A., Panin, A.A. & Plyasunov, A.V. Genetic local search and hardness of approximation for the server load balancing problem. Autom Remote Control 78, 425–434 (2017). https://doi.org/10.1134/S0005117917030043
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117917030043