ETEA: A euclidean minimum spanning tree-Based evolutionary algorithm for multiobjective optimization

© the Massachusetts Institute of TechnologyAbstract The Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in the space, where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based Evolutionary Algorithm (ETEA) to solve multiobjective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically in ETEA, four strategies are introduced: 1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; 2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; 3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; 4) Three diversity indicators-the minimum edge, degree, and ETCD-with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom under Grant EP/K001310/1, and the National Natural Science Foundation of China under Grant 61070088

Overlapping Multi-hop Clustering for Wireless Sensor Networks

Clustering is a standard approach for achieving efficient and scalable performance in wireless sensor networks. Traditionally, clustering algorithms aim at generating a number of disjoint clusters that satisfy some criteria. In this paper, we formulate a novel clustering problem that aims at generating overlapping multi-hop clusters. Overlapping clusters are useful in many sensor network applications, including inter-cluster routing, node localization, and time synchronization protocols. We also propose a randomized, distributed multi-hop clustering algorithm (KOCA) for solving the overlapping clustering problem. KOCA aims at generating connected overlapping clusters that cover the entire sensor network with a specific average overlapping degree. Through analysis and simulation experiments we show how to select the different values of the parameters to achieve the clustering process objectives. Moreover, the results show that KOCA produces approximately equal-sized clusters, which allows distributing the load evenly over different clusters. In addition, KOCA is scalable; the clustering formation terminates in a constant time regardless of the network size

Steiner Distance in Product Networks

For a connected graph $G$ of order at least $2$ and $S\subseteq V(G)$, the \emph{Steiner distance} $d_G(S)$ among the vertices of $S$ is the minimum size among all connected subgraphs whose vertex sets contain $S$. Let $n$ and $k$ be two integers with $2\leq k\leq n$. Then the \emph{Steiner $k$-eccentricity $e_k(v)$} of a vertex $v$ of $G$ is defined by $e_k(v)=\max \{d_G(S)\,|\,S\subseteq V(G), \ |S|=k, \ and \ v\in S\}$. Furthermore, the \emph{Steiner $k$-diameter} of $G$ is $sdiam_k(G)=\max \{e_k(v)\,|\, v\in V(G)\}$. In this paper, we investigate the Steiner distance and Steiner $k$-diameter of Cartesian and lexicographical product graphs. Also, we study the Steiner $k$-diameter of some networks.Comment: 29 pages, 4 figure

Linear kernels for outbranching problems in sparse digraphs

In the $k$-Leaf Out-Branching and $k$-Internal Out-Branching problems we are given a directed graph $D$ with a designated root $r$ and a nonnegative integer $k$. The question is to determine the existence of an outbranching rooted at $r$ that has at least $k$ leaves, or at least $k$ internal vertices, respectively. Both these problems were intensively studied from the points of view of parameterized complexity and kernelization, and in particular for both of them kernels with $O(k^2)$ vertices are known on general graphs. In this work we show that $k$-Leaf Out-Branching admits a kernel with $O(k)$ vertices on $\mathcal{H}$-minor-free graphs, for any fixed family of graphs $\mathcal{H}$, whereas $k$-Internal Out-Branching admits a kernel with $O(k)$ vertices on any graph class of bounded expansion.Comment: Extended abstract accepted for IPEC'15, 27 page

Use of easy measurable phenotypic traits as a complementary approach to evaluate the population structure and diversity in a high heterozygous panel of tetraploid clones and cultivars

Diversity in crops is fundamental for plant breeding efforts. An accurate assessment of genetic diversity, using molecular markers, such as single nucleotide polymorphism (SNP), must be able to reveal the structure of the population under study. A characterization of population structure using easy measurable phenotypic traits could be a preliminary and low-cost approach to elucidate the genetic structure of a population. A potato population of 183 genotypes was evaluated using 4859 high-quality SNPs and 19 phenotypic traits commonly recorded in potato breeding programs. A Bayesian approach, Minimum Spanning Tree (MST) and diversity estimator, as well as multivariate analysis based on phenotypic traits, were adopted to assess the population structure. Results: Analysis based on molecular markers showed groups linked to the phylogenetic relationship among the germplasm as well as the link with the breeding program that provided the material. Diversity estimators consistently structured the population according to a priori group estimation. The phenotypic traits only discriminated main groups with contrasting characteristics, as different subspecies, ploidy level or membership in a breeding program, but were not able to discriminate within groups. A joint molecular and phenotypic characterization analysis discriminated groups based on phenotypic classification, taxonomic category, provenance source of genotypes and genetic background. Conclusions: This paper shows the significant level of diversity existing in a parental population of potato as well as the putative phylogenetic relationships among the genotypes. The use of easily measurable phenotypic traits among highly contrasting genotypes could be a reasonable approach to estimate population structure in the initial phases of a potato breeding program.Fil: Tagliotti, Martin Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires Sur. Estación Experimental Agropecuaria Balcarce; ArgentinaFil: Deperi, Sofía Irene. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires Sur. Estación Experimental Agropecuaria Balcarce; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Bedogni, María Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires Sur. Estación Experimental Agropecuaria Balcarce; ArgentinaFil: Zhang, Ruofang. Inner Mongolia University; ChileFil: Manrique Carpintero, Norma C.. Michigan State University; Estados UnidosFil: Coombs, Joseph. Michigan State University; Estados UnidosFil: Douches, David. Michigan State University; Estados UnidosFil: Huarte, Marcelo Atilio. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Buenos Aires Sur. Estación Experimental Agropecuaria Balcarce; Argentin

Parameterized Complexity Analysis of Randomized Search Heuristics

This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running time of algorithms solving combinatorial problems in finer detail than traditional approaches from classical complexity theory. We outline the main results and proof techniques for a collection of randomized search heuristics tasked to solve NP-hard combinatorial optimization problems such as finding a minimum vertex cover in a graph, finding a maximum leaf spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of Evolutionary Computation: Recent Developments in Discrete Optimization", edited by Benjamin Doerr and Frank Neumann, published by Springe