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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… (More)

- Günther R. Raidl
- 2000

The representation of candidate solutions and the variation operators are fundamental design choices in an evolutionary algorithm (EA). This paper proposes a novel representation technique and suitable variation operators for the degree-constrained minimum spanning tree problem. For a weighted, undirected graph G(V, E), this problem seeks to identify the… (More)

Given a connected, weighted, undirected graph <i>G</i> and a bound <i>D</i>, the bounded-diameter minimum spanning tree problem seeks a spanning tree on <i>G</i> of lowest weight in which no path between two vertices contains more than <i>D</i> edges. This problem is NP-hard for 4 < <i>D</i> < <i>n</i> - 1, where n is the number of vertices in… (More)

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… (More)

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. Nowadays the focus is on solving the problem… (More)

In this work we extend a VNS for the periodic vehicle routing problem with time windows (PVRPTW) to a multiple VNS (mVNS) where several VNS instances are applied cooperatively in an intertwined way. The mVNS adaptively allocates VNS instances to promising areas of the search space. Further, an intertwined collaborative cooperation with a generic ILP solver… (More)

Our main aim is to provide guidelines and practical help for the design of appropriate representations and operators for evolutionary algorithms (EAs). For this purpose, we propose techniques to obtain a better understanding of various effects in the interplay of the representation and the operators. We study six different representations and associated… (More)

- Günther R. Raidl
- 1998

— This paper presents an improved hybrid Genetic Algorithm (GA) for solving the Multiconstrained 0–1 Knapsack Problem (MKP). Based on the solution of the LP-relaxed MKP, an efficient pre-optimization of the initial population is suggested. Furthermore, the GA uses sophisticated repair and local improvement operators which are applied to each newly generated… (More)

We consider the problem of finding two-dimensional cutting patterns for glass sheets in order to produce rectangular elements requested by customers. The number of needed sheets, and therefore the waste, is to be minimized. The cutting facility requires three-staged guil-lotineable cutting patterns, and in addition, a plan for loading produced elements on… (More)