【摘要】：基因表達(dá)式編程(gene expression programming,GEP)解空間模型理論對算法性能的改進(jìn)有現(xiàn)實(shí)指導(dǎo)意義。公開文獻(xiàn)對GEP解空間模型的研究較少,鮮見針對GEP表現(xiàn)型的理論研究。基于此,提出一種基于表現(xiàn)型的GEP解空間模型。首先,通過定義GEP染色體表現(xiàn)型高度,給出單基因染色體和多基因染色體表現(xiàn)型高度確定上界的定理及證明,利用GEP算法自身函數(shù)發(fā)現(xiàn)的能力,探索出操作符集最小目數(shù)為1或2的GEP染色體表現(xiàn)型高度上界計(jì)算的通項(xiàng)公式,以保證GEP表現(xiàn)型解空間模型的確定有界性與可計(jì)算性。其次,以GEP表現(xiàn)型高度的確定上界定理為基礎(chǔ),構(gòu)建基于表現(xiàn)型的GEP解空間模型,總結(jié)GEP表現(xiàn)型解空間模型的性質(zhì)和定理。通過進(jìn)一步定義GEP表現(xiàn)型的完全解空間概念,對最優(yōu)解在GEP表現(xiàn)型解空間和完全解空間中的分布特征進(jìn)行探索研究,獲知在完全解空間中最優(yōu)解隨子空間序號的增長呈大比例增加的分布特征�；诒憩F(xiàn)型空間模型知識,提出限制GEP種群搜索空間的基本思想與控制策略,利用模型知識合理地解釋公開文獻(xiàn)中多種GEP改進(jìn)算法的有效性。
[Abstract]:The theory of solving space model of gene expression programming (gene expression programming,GEP) has practical significance to improve the performance of the algorithm. There are few studies on GEP solution space model in the open literature, and few theoretical studies on GEP phenotype. Based on this, a representation-based GEP solution space model is proposed. First of all, by defining the height of GEP chromosome phenotype, the theorem and proof of determining the upper bound of the height of single gene chromosome and polygene chromosome phenotype are given, and the ability of GEP algorithm to discover its own function is given. In order to ensure the boundedness and computability of the GEP phenotype solution space model, a general term formula for calculating the upper bound of the height of the GEP chromosome phenotype with the minimum number of mesh 1 or 2 of the operator set is explored. Secondly, based on the upper bound theorem of GEP representation height, the GEP solution space model based on representation type is constructed, and the properties and theorems of GEP representation solution space model are summarized. By further defining the concept of complete solution space of GEP representation type, the distribution characteristics of optimal solution in GEP representation solution space and complete solution space are studied. It is found that the growth of the ordinal number of the optimal solution subspace in the complete solution space is increased in large proportion. Based on the knowledge of representation space model, this paper puts forward the basic idea and control strategy of restricting the search space of GEP population, and reasonably explains the effectiveness of various improved GEP algorithms in open literature by using model knowledge.
【作者單位】： 黔南民族師范學(xué)院計(jì)算機(jī)與信息學(xué)院;廣州大學(xué)計(jì)算機(jī)科學(xué)與教育軟件學(xué)院;武漢大學(xué)軟件工程國家重點(diǎn)實(shí)驗(yàn)室;
【基金】：國家自然科學(xué)基金資助項(xiàng)目(61170199) 貴州省科技廳聯(lián)合基金項(xiàng)目資助(20157727;2013GZ12215)
【分類號】：Q811.4

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