Artificial immune system for solving generalized geometric problems: a preliminary results

  • Authors:
  • Jui-Yu Wu;Yun-Kung Chung

  • Affiliations:
  • Yuan Ze University, Chung-Li, Taiwan R.O.C.;Yuan Ze University, Chung-Li, Taiwan R.O.C.

  • Venue:
  • GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
  • Year:
  • 2005

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Abstract

Generalized geometric programming (GGP) is an optimization method in which the objective function and constraints are nonconvex functions. Thus, a GGP problem includes multiple local optima in its solution space. When using conventional nonlinear programming methods to solve a GGP problem, local optimum may be found, or the procedure may be mathematically tedious. To find the global optimum of a GGP problem, a bio-immune-based approach is considered. This study presents an artificial immune system (AIS) including: an operator to control the number of antigen-specific antibodies based on an idiotypic network hypothesis; an editing operator of receptor with a Cauchy distributed random number, and a bone marrow operator used to generate diverse antibodies. The AIS method was tested with a set of published GGP problems, and their solutions were compared with the known global GGP solutions. The testing results show that the proposed approach potentially converges to the global solutions.