## Artificial Immune System for Solving Generalized Geometric Problems: A Preliminary Results

### BibTeX

@MISC{Wu_artificialimmune,

author = {Jui-yu Wu and Yun-kung Chung},

title = {Artificial Immune System for Solving Generalized Geometric Problems: A Preliminary Results},

year = {}

}

### OpenURL

### 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 bioimmune-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.

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Citation Context ... value, while other Abs undergo receptor editing. The operators of somatic hypermutation and receptor editing are described below. (1) Somatic hypermutation This study uses multi-non-uniform mutation =-=[17]-=- as the somatic hypermutation operator, which can be expressed as follows: where ⎧ u xn + ( xn − xn ) A( G), if U ( 0, 1) < 0. 5 ⎪ ˆ l x n = ⎨xn − ( xn + xn ) A( G), if U ( 0, 1) ≥ 0. 5 (12) ⎪ x , oth... |

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Citation Context ...σ = ± 1, σ = ± 1, t = 1, 2, K, T , a = real number mt mt m m (stand for exponentiation here), m = 0, 1, K, M Traditionally, two approaches in solving GGP problems are general: posynomial condensation =-=[14]-=- and pseudo-duality [15]. Posynomial condensation condenses the multiple polynomial terms of GGP to a posynomial with a single term and obtains optimal solution by iteratively calculating a sequence o... |