Abstract
Column generation is a basic tool for the solution of large-scale mathematical programming problems. We present a class of column generation algorithms in which the columns are generated by derivative free algorithms, like population-based algorithms. This class can be viewed as a framework to define hybridization of free derivative algorithms. This framework has been illustrated in this article using the Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms, combining them with the Nelder-Mead (NM) method. Finally a set of computational experiments has been carried out to illustrate the potential of this framework.
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References
García, R., Marín, A., Patriksson, M.: Column generation algorithms for nonlinear optimization, I: Convergence analysis. Optimization 52(2), 171–200 (2003)
Von Hohenbalken, B.: Simplicial decomposition in nonlinear programming algorithms. Mathematical Programming 13(1), 49–68 (1977)
Ventura, J.A., Hearn, D.W.: Restricted simplicial decomposition for convex constrained problems. Mathematical Programming 59, 71–85 (1993)
Frank, M., Wolfe, P.: An algorithm for quadratic programming. Naval Research Logistics Quarterly, 95–110 (1956)
Hearn, D.W., Lawphongpanich, S., Ventura, J.A.: Restricted simplicial decomposition: Computation and extensions. Mathematical Programming Study 31, 99–118 (1987)
García-Ródenas, R., Marín, A., Patriksson, M.: Column generation algorithms for nonlinear optimization, II: Numerical investigations. Computers and Operations Research 38(3), 591–604 (2011)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)
Bohachevsky, I.O., Johnson, M.E., Myron, L.S.: Generalized Simulated Annealing for Function Optimization. Technometrics 28(3) (1986)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings IEEE of the International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)
Kennedy, J.F., Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann Publishers (2001)
Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. Journal of the Association for Computing Machinery, 212–229 (1961)
Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the nelder-mead simplex method in low dimensions. SIAM Journal on Optimization 9(1), 112–147 (1999)
Laarhoven, P., Aarts, E.: Simulated annealing: Theory and Applications, 3rd edn. Kluwer Academic Publishers, Dordrecht (1987)
Poli, R.: Analysis of the publications on the applications of particle swarm optimisation. Journal of Artificial Evolution and Applications, 1–10 (2008)
Angulo, E., Castillo, E., García-Ródenas, R., Sánchez-Vizcaíno, J.: Determining Highway Corridors. Journal of Transportation Engineering 138(5), 557–570 (2012)
Fan, S.-K.S., Zahara, E.: A hybrid simplex search and particle swarm optimization for unconstrained optimization. European Journal of Operational Research, 527–548 (2006)
Functions definition, http://bit.ly/UQlMTB (last access: January 15th, 2013)
Espinosa-Aranda, J.L., García-Ródenas, R.: A discrete event-based simulation model for real-time traffic management in railways. Journal of Intelligent Transportation Systems 16(2), 94–107 (2012)
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Espinosa-Aranda, J.L., Garcia-Rodenas, R., Angulo, E. (2013). A Framework for Derivative Free Algorithm Hybridization. In: Tomassini, M., Antonioni, A., Daolio, F., Buesser, P. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2013. Lecture Notes in Computer Science, vol 7824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37213-1_9
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DOI: https://doi.org/10.1007/978-3-642-37213-1_9
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