The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

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Metaheuristics in combinatorial optimization: Overview and conceptual comparison

“Exploration and exploitation are the two cornerstones of problem solving by search.” For more than a decade, Eiben and Schippers' advocacy for balancing between these two antagonistic cornerstones still greatly influences the research directions of evolutionary algorithms (EAs) [1998]. This article revisits nearly 100 existing works and surveys how such works have answered the advocacy. The article introduces a fresh treatment that classifies and discusses existing work within three rational aspects: (1) what and how EA components contribute to exploration and exploitation; (2) when and how exploration and exploitation are controlled; and (3) how balance between exploration and exploitation is achieved. With a more comprehensive and systematic understanding of exploration and exploitation, more research in this direction may be motivated and refined.

Exploration and exploitation in evolutionary algorithms: A survey

Hybrid metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. A wide variety of hybrid approaches have been proposed in the literature. In this paper, a taxonomy of hybrid metaheuristics is presented in an attempt to provide a common terminology and classification mechanisms. The taxonomy, while presented in terms of metaheuristics, is also applicable to most types of heuristics and exact optimization algorithms.

As an illustration of the usefulness of the taxonomy an annoted bibliography is given which classifies a large number of hybrid approaches according to the taxonomy.

A Taxonomy of Hybrid Metaheuristics

This paper contains a modern vision of the parallelization techniques used for evolutionary algorithms (EAs). The work is motivated by two fundamental facts: 1) the different families of EAs have naturally converged in the last decade while parallel EAs (PEAs) are still lack of unified studies; and 2) there is a large number of improvements in these algorithms and in their parallelization that raise the need for a comprehensive survey. We stress the differences between the EA model and its parallel implementation throughout the paper. We discuss the advantages and drawbacks of PEAs. Also, successful applications are mentioned and open problems are identified. We propose potential solutions to these problems and classify the different ways in which recent results in theory and practice are helping to solve them. Finally, we provide a highly structured background relating to PEAs in order to make researchers aware of the benefits of decentralizing and parallelizing an EA.

/pdf/parallelism-and-evolutionary-algorithms-hitdkwys5k.pdf

Parallelism and evolutionary algorithms

Every search algorithm needs to address the exploration and exploitation of a search space. Exploration is the process of visiting entirely new regions of a search space, whilst exploitation is the process of visiting those regions of a search space within the neighborhood of previously visited points. In order to be successful a search algorithm needs to establish a good ratio between exploration and exploitation. In this respect Evolutionary Algorithms (EAs) [De Jong 2002; Eiben and Smith 2008], such as Genetic Algorithms (GAs) [Michalewicz 1996; Goldberg 2008], Evolutionary Strategies (ES) [Back 1996], Evolutionary Programming (EP) [Fogel 1999], and Genetic Programming (GP) [Koza 1992], to name the more well-known instances, are no exception. Herrera and Lozano [1996] emphasized this by saying “The genetic algorithm behaviour is determined by the exploitation and exploration relationship kept throughout the run.” Many researchers believe that EAs are effective because of their good ratio between exploration and exploitation. Michalewicz [1996] stated that “Genetic Algorithms are a

A Exploration and Exploitation in Evolutionary Algorithms: A Survey

Graph Coloring Problems

Edge dominating set and colorings on graphs with fixed clique-width

https://www.gerad.ca/~alainh/Framework.pdf

A framework for the description of evolutionary algorithms

In a graph G a matching is a set of edges in which no two edges have a common endpoint. An induced matching is a matching in which no two edges are linked by an edge of G. The maximum induced matching (abbreviated MIM) problem is to find the maximum size of an induced matching for a given graph G. This problem is known to be NP-hard even on bipartite graphs or on planar graphs. We present a polynomial time algorithm which given a graph G either finds a maximum induced matching in G, or claims that the size of a maximum induced matching in G is strictly less than the size of a maximum matching in G. We show that the MIM problem is NP-hard on line-graphs, claw-free graphs, chair-free graphs, Hamiltonian graphs and r-regular graphs for r \geq 5. On the other hand, we present polynomial time algorithms for the MIM problem on (P5,Dm)-free graphs, on (bull, chair)-free graphs and on line-graphs of Hamiltonian graphs.

Finding Maximum Induced Matchings in Subclasses of Claw-Free and P5-Free Graphs, and in Graphs with Matching and Induced Matching of Equal Maximum Size

https://hal.archives-ouvertes.fr/hal-00346551/document

Daniel Kobler

Papers

Graph Coloring Problems

Edge dominating set and colorings on graphs with fixed clique-width

A framework for the description of evolutionary algorithms

Finding Maximum Induced Matchings in Subclasses of Claw-Free and P5-Free Graphs, and in Graphs with Matching and Induced Matching of Equal Maximum Size

Parallel Island-Based Genetic Algorithm for Radio Network Design