In Search of Optimal Linkage Trees

Linkage-learning Evolutionary Algorithms (EAs) use linkage learning to construct a linkage model, which is exploited to solve problems efficiently by taking into account important linkages, i.e. dependencies between problem variables, during variation. It has been shown that when this linkage model is aligned correctly with the structure of the problem, these EAs are capable of solving problems efficiently by performing variation based on this linkage model [2]. The Linkage Tree Genetic Algorithm (LTGA) uses a Linkage Tree (LT) as a linkage model to identify the problem's structure hierarchically, enabling it to solve various problems very efficiently. Understanding the reasons for LTGA's excellent performance is highly valuable as LTGA is also able to efficiently solve problems for which a tree-like linkage model seems inappropriate. This brings us to ask what in fact makes a linkage model ideal for LTGA to be used

Efficient and Accurate Construction of Genetic Linkage Maps from the Minimum Spanning Tree of a Graph

Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap

Exploiting linkage information and problem-specific knowledge in evolutionary distribution network expansion planning

This article tackles the Distribution Network Expansion Planning (DNEP) problem that has to be solved by distribution network operators to decide which, where, and/or when enhancements to electricity networks should be introd uced to satisfy the future power demands. Because of many real-world details involved, the structure of the problem is not exploited easily using mathematical programming techniques, for which reason we consider solving this problem with evolutionary algorithms (EAs). We compare three types of EAs for optimizing expansion plans : the classic genetic algorithm (GA), the estimation-of-distribution algorith m (EDA), and the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA). Not fully k nowing the structure of the problem, we study the effect of linkage learning through the use of three linkage models: univariate, marginal product, and linkage tree. We furthermore experiment with the impact of incorporating different levels of proble m-specific knowledge in the variation operators. Experiments show that the use of problem-specific variation operators is far more important for the classic GA to find high-quality solutions. In all EAs, the marginal product model and its linkage learning pro cedure have difficulty in capturing and exploiting the DNEP problem structure. GOMEA, especially when combined with the linkage tree structure, is found to have the most robust performance by far

Statistical Modeling of Epistasis and Linkage Decay using Logic Regression

Logic regression has been recognized as a tool that can identify and model non-additive genetic interactions using Boolean logic groups. Logic regression, TASSEL-GLM and SAS-GLM were compared for analytical precision using a previously characterized model system to identify the best genetic model explaining epistatic interaction for vernalization-sensitivity in barley. A genetic model containing two molecular markers identified in vernalization response in barley was selected using logic regression while both TASSEL-GLM and SAS-GLM included spurious associations in their models. The results also suggest the logic regression can be used to identify dominant/recessive relationships between epistatic alleles through its use of conjugate operators

Statistical Modeling of Epistasis and Linkage Decay using Logic Regression

Logic regression has been recognized as a tool that can identify and model non-additive genetic interactions using Boolean logic groups. Logic regression, TASSEL-GLM and SAS-GLM were compared for analytical precision using a previously characterized model system to identify the best genetic model explaining epistatic interaction of vernalization-sensitivity in barley. A genetic model containing two molecular markers identified in vernalization response in barley was selected using logic regression while both TASSEL-GLM and SAS-GLM included spurious associations in their models. The results also suggest the logic regression can be used to identify dominant/recessive relationships between epistatic alleles through its use of conjugate
operators