EVOLUTIONARY ALGORITHMS FOR SOLVING QUASI GEOMETRIC PROGRAMMING PROBLEMS

R. Toscano, P. Lyonnet

2010

Abstract

In this paper we introduce an extension of standard geometric programming (GP) problems which we call quasi geometric programming (QGP) problems. The consideration of this particular kind of nonlinear and possibly non smooth optimization problem is motivated by the fact that many engineering problems can be formulated as a QGP. However, solving a QGP remains a difficult task due to its intrinsic non-convex nature. This is why we investigate the possibility of using evolutionary algorithms (EA) for solving a QGP problem. The main idea developed in this paper is to combine evolutionary algorithms with interior point method for efficiently solving QGP problems. An interesting feature of the proposed approach is that it does not need to develop specific program solver and works well with any existing EA and available solver able to solve conventional GP. Some considerations on the robustness issue are also presented. Numerical experiments are used to validate the proposed method.

References

  1. Back, T. and Schwefel., H. P. (1993). An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1(1):1-23.
  2. Boyd, S., Kim, S.-J., Vandenberghe, L., and Hassibi., A. (2007). A tutorial on geometric programming. Optimization and Engineering, 8(1):67-127.
  3. Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press.
  4. Cagnina, L. C., Esquivel, S. C., and Coello., C. A. C. (2008). Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica, 32(3):319-326.
  5. Chipperfield, A., Fleming, P., Pohlheim, H., and Fonseca, C. (1995). Genetic Algorithm TOOLBOX For Use with MATLAB.
  6. Grant, M. and Boyd, S. (2010). CVX: Matlab Software for Disciplined Convex Programming, version 1.21. http://cvxr.com/cvx.
  7. He, Q. and Wang., L. (2007). An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engineering Application of Artificial Intelligence, 20(1):89-99.
  8. Michalewicz, Z. and Schoenauer., M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1):1-32.
  9. Qu, S. J., Zhang, K. C., and Ji., Y. (2007). A new global optimization algorithm for signomial geometric programming via lagrangian relaxation. Applied Mathematics and Computation, 184(2):886-894.
  10. Rockafellar, R. T. (1993). Lagrange multipliers and optimality. SIAM Review, 35:183-238.
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Paper Citation


in Harvard Style

Toscano R. and Lyonnet P. (2010). EVOLUTIONARY ALGORITHMS FOR SOLVING QUASI GEOMETRIC PROGRAMMING PROBLEMS . In Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010) ISBN 978-989-8425-31-7, pages 163-169. DOI: 10.5220/0003071901630169


in Bibtex Style

@conference{icec10,
author={R. Toscano and P. Lyonnet},
title={EVOLUTIONARY ALGORITHMS FOR SOLVING QUASI GEOMETRIC PROGRAMMING PROBLEMS},
booktitle={Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)},
year={2010},
pages={163-169},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003071901630169},
isbn={978-989-8425-31-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)
TI - EVOLUTIONARY ALGORITHMS FOR SOLVING QUASI GEOMETRIC PROGRAMMING PROBLEMS
SN - 978-989-8425-31-7
AU - Toscano R.
AU - Lyonnet P.
PY - 2010
SP - 163
EP - 169
DO - 10.5220/0003071901630169