A Brief Survey on Hybrid Metaheuristics

The combination of components from different algorithms is currently one of the most successful trends in optimization. The hybridization of metaheuristics such as ant colony optimization, evolutionary algorithms, and variable neighborhood search with techniques from operations research and artificial intelligence plays hereby an important role. The resulting hybrid algorithms are generally labelled hybrid metaheuristics. The rising of this new research field was due to the fact that the focus of research in optimization has shifted from an algorithm-oriented point of view to a problem-oriented point of view. In this brief survey on hybrid metaheuristics we provide an overview on some of the most interesting and representative developments

A set-based particle swarm optimization method

The representation used in Particle Swarm Optimization (PSO) is an n-dimensional vector. If you want to apply the PSO method, you have to encode your problem as fix-sized vector. But many problem domains have solutions of unknown sizes as for instance in data clustering where you often don't know the number of clusters in advance. In this paper a set-based PSO is proposed which replaces the position and velocity vectors by position and velocity sets realizing this way a PSO with variable length representation. All operations of the PSO update equations are redefined in an appropriate manner. Additionally, an operator reducing set bloating effects is introduced. The presented approach is applied to well-known data clustering problems and performs better as other algorithms on them

An Evolutionary Algorithm with Solution Archive for the Generalized Minimum Spanning Tree Problem

We consider the recently proposed concept of enhancing an evolutionary algorithm (EA) with a complete solution archive. It stores evaluated solutions during the optimiza-tion in order to detect duplicates and to efficiently transform them into yet unconsidered solutions. For this approach we introduce the so-called bounding extension in order to identify and prune branches in the trie-based archive which only contain inferior solutions. This extension enables the EA to concentrate the search on promising areas of the so-lution space. Similarly to the classical branch-and-bound technique, bounds are obtained via primal and dual heuris-tics. As an application we consider the generalized min-imum spanning tree problem where we are given a graph with nodes partitioned into clusters and exactly one node from each cluster must be connected in the cheapest way. As the EA uses operators based on two dual representa-tions, we exploit two corresponding tries that complement each other. Test results on TSPlib instances document the strength of this concept and that it can compete with the leading metaheuristics for this problem in the literature

Fixed parameter evolutionary algorithms and maximum leaf spanning trees: a matter of mutation

Evolutionary algorithms have been shown to be very successful for a wide range of NP-hard combinatorial optimization problems. We investigate the NP-hard problem of computing a spanning tree that has a maximal number of leaves by evolutionary algorithms in the context of fixed parameter tractability (FPT) where the maximum number of leaves is the parameter under consideration. Our results show that simple evolutionary algorithms working with an edge-set encoding are confronted with local optima whose size of the inferior neighborhood grows with the value of an optimal solution. Investigating two common mutation operators, we show that an operator related to spanning tree problems leads to an FPT running time in contrast to a general mutation operator that does not have this property.Stefan Kratsch, Per Kristian Lehre, Frank Neumann and Pietro Simone Olivet