zbMATH — the first resource for mathematics

Designing a superstructure for parametric search for optimal search spaces in non-trivial optimization problems. (English) Zbl 1021.90027
Summary: We design a super genetic hybrid algorithm (SupprGHA), an integrated optimization system for simultaneous parametric search and nonlinear optimization. The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimization process. The family of parameter vectors evolves through ordinary genetic operators aimed at producing the best possible parametrization for the underlying optimization problem. In comparison to traditional genetic algorithms, the integrated superstructure involves a twofold ordering of the population of parameter vectors. The first sorting key is provided by the objective function of the optimization problem at issue. The second key is given by the total mesh time absorbed by the parametric setting. In consequence, SuperGHA is geared at solving an optimization problem, using the best feasible parametrization in terms of optimality and time absorbance. The algorithm combines features from classical nonlinear optimization methodology and evolutionary computation utilizing a powerful accelerator technique. The constrained problem can be cast into multiple representations, supporting the integration of different mathematical programming environments. We show by extensive Monte Carlo simulations that SuperGHA extracts suitable parameter vectors for fast solution of complicated nonlinear programming problems.

90B40 Search theory
65C05 Monte Carlo methods
Full Text: DOI
[1] DOI: 10.1007/BF01298458 · Zbl 0840.90028 · doi:10.1007/BF01298458
[2] Dorsey, R.E. and Mayer, W.J. (1995), ”Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability and other Irregular Features”, Journal of Business and Economic Statistics, 13, pp. 53–66.
[3] DOI: 10.1007/s001680050082 · doi:10.1007/s001680050082
[4] DOI: 10.1111/j.1540-5915.1977.tb01074.x · doi:10.1111/j.1540-5915.1977.tb01074.x
[5] Glover, F. (1997), ”A Template for Scatter Search and Path Relinking”, in, Lecture Notes in Computer Science, Hao, J.K. , Lutton, E. , Ronald, E. , Schoenauer, M. , Snyers, D. (Eds), pp. 1–50.
[6] DOI: 10.1016/0098-1354(96)00031-2 · doi:10.1016/0098-1354(96)00031-2
[7] DOI: 10.1177/003754979406200405 · doi:10.1177/003754979406200405
[8] DOI: 10.1007/BF01411373 · doi:10.1007/BF01411373
[9] DOI: 10.1007/BF00127077 · Zbl 0853.68157 · doi:10.1007/BF00127077
[10] DOI: 10.1007/BFb0120949 · Zbl 0477.90069 · doi:10.1007/BFb0120949
[11] DOI: 10.1007/BF00436583 · Zbl 0759.90004 · doi:10.1007/BF00436583
[12] DOI: 10.1023/A:1008621308348 · Zbl 0954.90033 · doi:10.1023/A:1008621308348
[13] DOI: 10.1016/S0305-0548(98)00035-5 · Zbl 0933.90048 · doi:10.1016/S0305-0548(98)00035-5
[14] DOI: 10.1016/S0305-0548(99)00034-9 · Zbl 0947.65046 · doi:10.1016/S0305-0548(99)00034-9
[15] DOI: 10.1016/S0165-0114(98)00057-8 · Zbl 0970.68567 · doi:10.1016/S0165-0114(98)00057-8
[16] Potter, M.A. and De Jong, K.A. (1995), ”Evolving Neural Networks with Collaborative Species”, in, Proceedings of the 1995 Summer Computer Simulation Conference, July 24–26, Ottawa, Ontario, Canada.
[17] Smith, A.E. and Tate, D.M. (1993), ”Genetic Optimization Using a Penalty Function”, in, Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 499–505.
[18] DOI: 10.1016/0098-1354(94)E0006-9 · doi:10.1016/0098-1354(94)E0006-9
[19] DOI: 10.1016/S0098-1354(97)00000-8 · doi:10.1016/S0098-1354(97)00000-8
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.