Variations on Memetic Algorithms for Graph Coloring Problems

11 pages, 8 figures, 3 tables, 2 algorithmsInternational audienceGraph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing. Those hybrid algorithms use a powerful local search inside a population-based algorithm.This paper presents a new memetic algorithm based on one of the most effective algorithms: the Hybrid Evolutionary Algorithm HEA from Galinier and Hao (1999).The proposed algorithm, denoted HEAD - for HEA in Duet - works with a population of only two individuals.Moreover, a new way of managing diversity is brought by HEAD.These two main differences greatly improve the results, both in terms of solution quality and computational time.HEAD has produced several good results for the popular DIMACS benchmark graphs, such as 222-colorings for , 81-colorings for and even 47-colorings for and 82-colorings for

Algebraic and Computer-based Methods in the Undirected Degree/diameter Problem - a Brief Survey

This paper discusses the most popular algebraic techniques and computational methods that have been used to construct large graphs with given degree and diameter

Data Mining Using the Crossing Minimization Paradigm

Our ability and capacity to generate, record and store multi-dimensional, apparently unstructured data is increasing rapidly, while the cost of data storage is going down. The data recorded is not perfect, as noise gets introduced in it from different sources. Some of the basic forms of noise are incorrect recording of values and missing values. The formal study of discovering useful hidden information in the data is called Data Mining. Because of the size, and complexity of the problem, practical data mining problems are best attempted using automatic means. Data Mining can be categorized into two types i.e. supervised learning or classification and unsupervised learning or clustering. Clustering only the records in a database (or data matrix) gives a global view of the data and is called one-way clustering. For a detailed analysis or a local view, biclustering or co-clustering or two-way clustering is required involving the simultaneous clustering of the records and the attributes. In this dissertation, a novel fast and white noise tolerant data mining solution is proposed based on the Crossing Minimization (CM) paradigm; the solution works for one-way as well as two-way clustering for discovering overlapping biclusters. For decades the CM paradigm has traditionally been used for graph drawing and VLSI (Very Large Scale Integration) circuit design for reducing wire length and congestion. The utility of the proposed technique is demonstrated by comparing it with other biclustering techniques using simulated noisy, as well as real data from Agriculture, Biology and other domains. Two other interesting and hard problems also addressed in this dissertation are (i) the Minimum Attribute Subset Selection (MASS) problem and (ii) Bandwidth Minimization (BWM) problem of sparse matrices. The proposed CM technique is demonstrated to provide very convincing results while attempting to solve the said problems using real public domain data. Pakistan is the fourth largest supplier of cotton in the world. An apparent anomaly has been observed during 1989-97 between cotton yield and pesticide consumption in Pakistan showing unexpected periods of negative correlation. By applying the indigenous CM technique for one-way clustering to real Agro-Met data (2001-2002), a possible explanation of the anomaly has been presented in this thesis

AccuSyn: Using Simulated Annealing to Declutter Genome Visualizations

We apply Simulated Annealing, a well-known metaheuristic for obtaining near-optimal solutions to optimization problems, to discover conserved synteny relations (similar features) in genomes. The analysis of synteny gives biologists insights into the evolutionary history of species and the functional relationships between genes. However, as even simple organisms have huge numbers of genomic features, syntenic plots initially present an enormous clutter of connections, making the structure difficult to understand. We address this problem by using Simulated Annealing to minimize link crossings. Our interactive web-based synteny browser, AccuSyn, visualizes syntenic relations with circular plots of chromosomes and draws links between similar blocks of genes. It also brings together a huge amount of genomic data by integrating an adjacent view and additional tracks, to visualize the details of the blocks and accompanying genomic data, respectively. Our work shows multiple ways to manually declutter a synteny plot and then thoroughly explains how we integrated Simulated Annealing, along with human interventions as a human-in-the-loop approach, to achieve an accurate representation of conserved synteny relations for any genome. The goal of AccuSyn was to make a fairly complete tool combining ideas from four major areas: genetics, information visualization, heuristic search, and human-in-the-loop. Our results contribute to a better understanding of synteny plots and show the potential that decluttering algorithms have for syntenic analysis, adding more clues for evolutionary development. At this writing, AccuSyn is already actively used in the research being done at the University of Saskatchewan and has already produced a visualization of the recently-sequenced Wheat genome