## Non-stationary problem optimization using the primal-dual genetic algorithm (2003)

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Venue: | Proc. of the 2003 Congr. on Evol. Comput |

Citations: | 42 - 27 self |

### BibTeX

@INPROCEEDINGS{Yang03non-stationaryproblem,

author = {Shengxiang Yang},

title = {Non-stationary problem optimization using the primal-dual genetic algorithm},

booktitle = {Proc. of the 2003 Congr. on Evol. Comput},

year = {2003},

pages = {2246--2253}

}

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### Abstract

Abstract- Genetic algorithms (GAS) have been widely used for stationary optimization problems where the fitness landscape does not change during the computation. However, the environments of real world problems may change over time, which puts forward serious challenge to traditional GAS. In this paper, we introduce the application of a new variation of GA called the Primal-Dual Genetic Algorithm (PDGA) for problem optimization in non-stationary environments. Inspired by the complementarity and dominance mechanisms in nature, PDGA operates on a pair of chromosomes that are primal-dual to each other in the sense of maximum distance in genotype in a given distance space. This paper investigates an important aspect of PDGA, its adaptability to dynamic environments. A set of dynamic problems are generated from a set of stationary benchmark problems using a dynamic problem generating technique proposed in this paper. Experimental study over these dynamic problems suggests that PDGA can solve complex dynamic problems more efficiently than traditional GA and a peer GA, the Dual Genetic Algorithm. The experimental results show that PDGA has strong viability and robustness in dynamic environments. 1

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Citation Context ...100 bits will be used for this study. And the unique optimum solution has a fitness of 100. 2. Royal Road Function: This function is the same as Mitchell, Forrest and Holland’s Royal Road function R1 =-=[MFH92]-=-. It is defined on a sixtyfour bit string consisting of eight contiguous building blocks (BBs) of eight hits, each of which contributes ti = 8 (i = 1, ..., 8) to the total fitness if all of the eight ... |

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Citation Context ...Road function are now of order-8 instead of orderI as in the One-Max problem. The increased size of basic BBs makes it much harder for the GAS to search them and also enhances the “hi1chhiking”effect =-=[FM93]-=-. Hitchhiking seriously decreases the diversity of those loci corresponding to BBs not found at the last generation of the stationary period. And the fitness landscape changing mode destroys almost al... |

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Citation Context ...for a continuous adaptation to the changing landscape. To improve GA's performance in dynamic environments, researchers have applied the diploidy and dominance mechanisms that broadly exist in nature =-=[GS87]-=-, [NW95]. In nature, most organisms have a diploid genotype, i.e., a set of double-stranded chroinosomes. When the double-stranded chromosomes are exposed to the environment of the organism, dominance... |

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(Show Context)
Citation Context ...ntinuous adaptation to the changing landscape. To improve GA's performance in dynamic environments, researchers have applied the diploidy and dominance mechanisms that broadly exist in nature [GS87], =-=[NW95]-=-. In nature, most organisms have a diploid genotype, i.e., a set of double-stranded chroinosomes. When the double-stranded chromosomes are exposed to the environment of the organism, dominance mechani... |

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Citation Context ...y environments, since the additional information stored in the genotype provides a latent source ofdiisersin in the population and allows the population to respond more quickly to the fitness changes =-=[LHR98]-=-. Inspired by the complementarity and dominance mechanisms in nature a new genetic.algorithm called primal-dual genetic algorithm (PDGA) has been proposed [Yang03]. Withh PDGA. each chromosome is defi... |

5 | PDGA: the Primal-Dual Genetic Algorithm
- Yang
- 2003
(Show Context)
Citation Context ...d more quickly to the fitness changes [LHR98]. Inspired by the complementarity and dominance mechanisms in nature a new genetic.algorithm called primal-dual genetic algorithm (PDGA) has been proposed =-=[Yang03]-=-. Withh PDGA. each chromosome is definid a dual chromosome that is of maximum distance in genotype to it in a given distance space, e.g., the Hamming distance space. During the running of PDGA before ... |

1 |
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Citation Context ...tion t, we can select nd(t) least fit primal chromosomes from P'(t) for dual evaluations. Now what is left is how to decide the value ofnd(t). Both Holland's [Holland751 and Stephens and Waelhroeck's =-=[SW99]-=- schema theorems indicate that schemas or strings with less than average fitness or average effective fitness receive an exponentially decreasing number of trials over time. Let ninf (t) denote the ac... |

1 |
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Citation Context ...a fixed crossover probability p, = 0.6, bit mutation with mutation probability p, = 0.001, and fitness proportionate selection with the Stochastic Universal Sampling (SUS) (Baker871 and elitist model =-=[DeJong75]-=-. The population size N was set to 128 for all the GAS. PDGA-specific parameters were set as follows: for the deterministic selection scheme a = p = 0.5 and n, = 1; for the adaptive selection scheme a... |

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