Results 1  10
of
17
Greedy Heuristics and an Evolutionary Algorithm for the BoundedDiameter Minimum Spanning Tree Problem
 Proceedings of the 2003 ACM Symposium on Applied Computing
, 2003
"... bound D, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NPhard for 4 1, where n is the number of vertices in G. An existing greedy heuristic for the problem, called ..."
Abstract

Cited by 35 (13 self)
 Add to MetaCart
bound D, the boundeddiameter minimum spanning tree problem seeks a spanning tree on G of lowest weight in which no path between two vertices contains more than D edges. This problem is NPhard for 4 1, where n is the number of vertices in G. An existing greedy heuristic for the problem, called OTTC, is based on Prim's algorithm. OTTC usually yields poor results on instances in which the triangle inequality approximately holds; it always uses the lowestweight edges that it can, but such edges do not in general connect the interior nodes of lowweight boundeddiameter trees. A new randomized greedy heuristic builds a boundeddiameter spanning tree from its center vertex or vertices. It chooses each next vertex at random but attaches the vertex with the lowestweight eligible edge. This algorithm is faster than OTTC and yields substantially better solutions on Euclidean instances. An evolutionary algorithm encodes spanning trees as lists of their edges, augmented with their center vertices. It applies operators that maintain the diameter bound and always generate valid o#spring trees. These operators are e#cient, so the algorithm scales well to larger problem instances. On 25 Euclidean instances of up to 1 000 vertices, the EA improved substantially on solutions found by the randomized greedy heuristic.
Redundant representations in evolutionary computation
 EVOLUTIONARY COMPUTATION
, 2003
"... This paper investigates how the use of redundant representations influences the performance of genetic and evolutionary algorithms. Representations are redundant if the number of genotypes exceeds the number of phenotypes. A distinction is made between synonymously and nonsynonymously redundant ..."
Abstract

Cited by 25 (2 self)
 Add to MetaCart
This paper investigates how the use of redundant representations influences the performance of genetic and evolutionary algorithms. Representations are redundant if the number of genotypes exceeds the number of phenotypes. A distinction is made between synonymously and nonsynonymously redundant representations. Representation are synonymously redundant if the genotypes that represent the same phenotype are very similar to each other. Nonsynonymously redundant representations do not allow genetic operators to work properly and result in a lower performance of evolutionary search. When using synonymously redundant representations, the performance of selectorecombinative genetic algorithms (GAs) depends on the modification of the initial supply. Theoretical models are developed that show the necessary population size to solve a problem and the number of generations goes with O(2 /r), where k r is the order of redundancy and r is the number of genotypic building blocks (BB) that represent the optimal phenotypic BB. Therefore, uniformly redundant representations do not change the behavior of GAs. Only by increasing r, which means overrepresenting the optimal solution, does GA performance increase. Therefore, nonuniformly redundant representations can only be used advantageously if apriori information exists regarding the optimal solution. The validity of the proposed theoretical concepts is illustrated for the binary trivial voting mapping and the realvalued linkbiased encoding. The empirical investigations show that the developed population sizing and time to convergence models allow an accurate prediction of the empirical results.
EdgeSets: An Effective Evolutionary Coding of Spanning Trees
, 2002
"... 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 d ..."
Abstract

Cited by 14 (7 self)
 Add to MetaCart
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
Initialization is Robust in Evolutionary Algorithms that Encode Spanning Trees as Sets of Edges
 in Proceedings of the 2002 ACM Symposium on Applied Computing
, 2002
"... Evolutionary algorithms (EAs) that search spaces of spanning trees can encode candidate trees as sets of edges. In this case, edgesets for an EA's initial population should represent spanning trees chosen with uniform probabilities on the graph that underlies the target problem instance. The genera ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
Evolutionary algorithms (EAs) that search spaces of spanning trees can encode candidate trees as sets of edges. In this case, edgesets for an EA's initial population should represent spanning trees chosen with uniform probabilities on the graph that underlies the target problem instance. The generation of random spanning trees is not as simple as it might appear. Mechanisms based on Prim's and Kruskal's minimum spanning tree algorithms are not uniform, and uniform mechanisms are slow, not guaranteed to terminate, or require that the underlying graph be complete.
On the Optimal Communication Spanning Tree Problem
, 2003
"... This paper presents an investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem finds a spanning tree that connects all nodes and satisfies their communication requirements for a minimum total cost. The paper compares the properties of randomly ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
This paper presents an investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem finds a spanning tree that connects all nodes and satisfies their communication requirements for a minimum total cost. The paper compares the properties of randomly created solutions to the best solutions that are found using an evolutionary algorithm framework. The results show that on average the distance between the optimal solution and the minimum spanning tree (MST) that is calculated according to the distance weights is significantly smaller than the distance between a randomly created solution and the MST. This means, optimal solutions for the OCST problem are biased towards the MST defined on the distance weights alone. Consequently, the performance of optimization methods for the OCST problem can be increased if the search is biased towards MSTlike solutions.
Some novel locality results for the Blob Code spanning tree representation
 In Proceedings of the 9th Genetic and Evolutionary Computation Conference (GECCO 2007
, 2007
"... The Blob Code is a bijective tree code that represents each tree on n labelled vertices as a string of n − 2 vertex labels. In recent years, several researchers have deployed the Blob Code as a GA representation, and have reported promising results across a range of treebased optimization problems. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
The Blob Code is a bijective tree code that represents each tree on n labelled vertices as a string of n − 2 vertex labels. In recent years, several researchers have deployed the Blob Code as a GA representation, and have reported promising results across a range of treebased optimization problems. In this paper, we exploit a recently discovered lineartime decoding algorithm for the Blob Code to develop some novel locality results, extending previous work by Julstrom. Let Δ be the random variable representing the number of tree edges that are changed by a random singleelement string mutation. Under the Blob Code, we demonstrate that pessimal mutations (i.e., mutations for which Δ = n−1) can arise for any n>4. However, as n grows, the probability of perfect mutation P (Δ = 1) approaches one, following a powerlaw relationship, and E(Δ) approaches two. These results show that the locality of the Blob Code is high, but not as high as that of Dandelionlike codes. We also show that the choice of mutation position places restrictions on the range of Δ, and therefore influences the distribution of Δ. In particular, mutating the kth element of a Blob string alters at most n − k tree edges.
On the Locality of Representations
, 2003
"... It is well known that using highlocality representations is important for efficient evolutionary search. This paper discusses in detail how the locality of a representation influences the difficulty of a problem when using mutationbased search approaches. The results show that highlocality repres ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
It is well known that using highlocality representations is important for efficient evolutionary search. This paper discusses in detail how the locality of a representation influences the difficulty of a problem when using mutationbased search approaches. The results show that highlocality representations do not change problem difficulty. In contrast, lowlocality representations randomize the search process and make problems that are easy for mutationbased search more difficult and difficult problems more easy. Although lowlocality representations increase the performance of local search on difficult, deceptive problems this is not relevant for realworld problems as we assume that most problems in the realworld are easy for mutationbased search.
Codings and operators in two genetic algorithms for the leafconstrained minimum spanning tree problem
 International Journal of Applied Mathematics and Computer Science
, 2004
"... The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solution ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
The features of an evolutionary algorithm that most determine its performance are the coding by which its chromosomes represent candidate solutions to its target problem and the operators that act on that coding. Also, when a problem involves constraints, a coding that represents only valid solutions and operators that preserve that validity represent a smaller search space and result in a more effective search. Two genetic algorithms for the leafconstrained minimum spanning tree problem illustrate these observations. Given a connected, weighted, undirected graph G with n vertices and a bound ℓ, this problem seeks a spanning tree on G with at least ℓ leaves and minimum weight among all such trees. A greedy heuristic for the problem begins with an unconstrained minimum spanning tree on G, then economically turns interior vertices into leaves until their number reaches ℓ. One genetic algorithm encodes candidate trees with Prüfer strings decoded via the Blob Code. The second GA uses strings of length n−ℓ that specify trees ’ interior vertices. Both GAs apply operators that generate only valid chromosomes. The latter represents and searches a much smaller space. In tests on 65 instances of the problem, both Euclidean and with weights chosen randomly, the BlobCoded GA cannot compete with the greedy heuristic, but the subsetcoded GA consistently identifies leafconstrained spanning trees of lower weight than the greedy heuristic does, particularly on the random instances.
On the Debate Concerning Evolutionary Search Using Prüfer Numbers
 In Rothlauf, F. (Ed.), Representations and Operators for Network Problems (ROPNET 2001
, 2001
"... This paper sheds some light on the debate concerning evolutionary search using Priifer numbers, and explains some of the controversial results. Previous work has shown that Priifer numbers have low locality. Furthermore, it has been shown elsewhere that the locality of the Priifer number depends ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This paper sheds some light on the debate concerning evolutionary search using Priifer numbers, and explains some of the controversial results. Previous work has shown that Priifer numbers have low locality. Furthermore, it has been shown elsewhere that the locality of the Priifer number depends on the structure of the encoded tree. The locality of a Priifer number is high if it encodes a star network, and low elsewhere. The paper illustrates that when applying mutation as well as recombinationbased genetic search to the onemax tree problem, which allows to choose the structure of the optimal solution a priori, that both types of evolutionary search fail if the optimal solution is not starlike.
Lineartime algorithms for encoding trees as sequences of node labels
, 2007
"... In this paper we present O(n)time algorithms for encoding/decoding nnode labeled trees as sequences of n − 2 node labels. All known encodings of this type are covered, including Prüferlike codes and the three codes proposed by Picciotto the happy, blob, and dandelion codes. The algorithms for Pi ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In this paper we present O(n)time algorithms for encoding/decoding nnode labeled trees as sequences of n − 2 node labels. All known encodings of this type are covered, including Prüferlike codes and the three codes proposed by Picciotto the happy, blob, and dandelion codes. The algorithms for Picciotto’s codes are of special significance as previous publications describe suboptimal approaches requiring O(n log n) or even O(n 2) time.