Research in metaheuristics for combinatorial optimization problems has lately experienced a noteworthy shift towards the hybridization of metaheuristics with other techniques for optimization. At the same time, the focus of research has changed from being rather algorithm-oriented to being more problem-oriented.\ud Nowadays the focus is on solving the problem at hand in the best way possible, rather than\ud promoting a certain metaheuristic. This has led to an enormously fruitful cross-fertilization of different areas of optimization. This cross-fertilization is documented by a multitude of powerful hybrid algorithms that were obtained by combining components from several different optimization techniques. Hereby, hybridization is not restricted to the combination of different metaheuristics but includes, for example, the combination of exact algorithms and metaheuristics. In this work we provide a survey of some of the most important lines of hybridization. The literature review is accompanied by the presentation of illustrative examples.Peer ReviewedPostprint (published version

The fundamental design choices in an evolutionary algorithm are its representation of candidate solutions and the operators that will act on that representation. We propose representing spanning trees in evolutionary algorithms for network design problems directly as sets of their edges, and we describe initialization, recombination, and mutation operators for this representation. The operators offer locality, heritability, and computational efficiency. Initialization and recombination depend on an underlying random spanning tree algorithm; three choices for this algorithm, based on the minimum spanning tree algorithms of Prim and Kruskal and on random walks, respectively, are examined analytically and empirically. We demonstrate the usefulness of the edge-set encoding in an evolutionary algorithm for the NP-hard degree-constrained minimum spanning tree problem. The algorithm's operators are easily extended to generate only feasible spanning trees and to incorporate local, problem-specific heuristics. Comparisons of this algorithm to others that encode candidate spanning trees via the Blob Code, with network random keys, and as strings of weights indicate the superiority of the edge-set encoding, particularly on larger instances.

SummaryCytosine methylation is a hallmark of epigenetic information in the DNA of many fungi, vertebrates and plants. The technique of bisulphite genomic sequencing reveals the methylation state of every individual cytosine in a sequence, and thereby provides high-resolution data on epigenetic diversity; however, the manual evaluation and documentation of large amounts of data is laborious and error-prone. While some software is available for facilitating the analysis of mammalian DNA methylation, which is found nearly exclusively at CG sites, there is no software optimally suited for data from DNA with significant non-CG methylation. We describe CyMATE (Cytosine Methylation Analysis Tool for Everyone) for in silico analysis of DNA sequences after bisulphite conversion of plant DNA, in which methylation is more divergent with respect to sequence context and biological relevance. From aligned sequences, CyMATE includes and distinguishes methylation at CG, CHG and CHH (where H = A, C or T), and can extract both quantitative and qualitative data regarding general and pattern-specific methylation per sequence and per position, i.e. data for individual sites in a sequence and the epigenetic divergence within a sample. In addition, it can provide graphical output from alignments in either an overview or a 'zoom-in' view as pdf files. Detailed information, including a quality control of the sequencing data, is provided in text format. We applied CyMATE to the analysis of DNA methylation at transcriptionally silenced promoters in diploid and polyploid Arabidopsis and found significant hypermethylation, high stability of the methylated state independent of chromosome number, and non-redundant patterns of m C distribution. CyMATE is freely available for non-commercial use at http://www.gmi.oeaw.ac.at/CyMATE.

International audienceWe present a general framework for solving a real-world multi-modal home-healthcare scheduling (MHS) problem from a major Austrian home-healthcare provider. The goal of MHS is to assign home-care staff to customers and determine efficient multimodal tours while considering staff and customer satisfaction. Our approach is designed to be as problem-independent as possible, such that the resulting methods can be easily adapted to MHS setups of other home-healthcare providers. We chose a two-stage approach: in the first stage, we generate initial solutions either via constraint programming techniques or by a random procedure. During the second stage, the initial solutions are (iteratively) improved by applying one of four metaheuristics: variable neighborhood search, a memetic algorithm, scatter search and a simulated annealing hyper-heuristic. An extensive computational comparison shows that the approach is capable of solving real-world instances in reasonable time and produces valid solutions within only a few seconds

Abstract. In this survey we discuss different state-of-the-art approaches of combining exact algorithms and metaheuristics to solve combinatorial optimization problems. Some of these hybrids mainly aim at providing optimal solutions in shorter time, while others primarily focus on getting better heuristic solutions. The two main categories in which we divide the approaches are collaborative versus integrative combinations. We further classify the different techniques in a hierarchical way. Altogether, the surveyed work on combinations of exact algorithms and metaheuristics documents the usefulness and strong potential of this research direction.