5,113 research outputs found
Variable neighbourhood search for the minimum labelling Steiner tree problem
We present a study on heuristic solution approaches to the minimum labelling Steiner
tree problem, an NP-hard graph problem related to the minimum labelling spanning tree
problem. Given an undirected labelled connected graph, the aim is to find a spanning
tree covering a given subset of nodes of the graph, whose edges have the smallest number
of distinct labels. Such a model may be used to represent many real world problems in
telecommunications and multimodal transportation networks. Several metaheuristics are
proposed and evaluated. The approaches are compared to the widely adopted Pilot Method
and it is shown that the Variable Neighbourhood Search metaheuristic is the most effective
approach to the problem, obtaining high quality solutions in short computational running
times
A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem
The 0-1 knapsack problem is a well-known combinatorial optimisation problem.
Approximation algorithms have been designed for solving it and they return
provably good solutions within polynomial time. On the other hand, genetic
algorithms are well suited for solving the knapsack problem and they find
reasonably good solutions quickly. A naturally arising question is whether
genetic algorithms are able to find solutions as good as approximation
algorithms do. This paper presents a novel multi-objective optimisation genetic
algorithm for solving the 0-1 knapsack problem. Experiment results show that
the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy
genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm
Developing Efficient Metaheuristics for Communication Network Problems by using Problem-specific Knowledge
Metaheuristics, such as evolutionary algorithms or simulated annealing, are widely applicable heuristic optimization strategies that have shown encouraging results for a large number of difficult optimization problems. To show high performance, metaheuristics need to be adapted to the properties of the problem at hand. This paper illustrates how efficient metaheuristics can be developed for communication network problems by utilizing problem-specific knowledge for the design of a high-quality problem representation. The minimum communication spanning tree (MCST) problem finds a communication spanning tree that connects all nodes and satisfies their communication requirements for a minimum total cost. An investigation into the properties of the problem reveals that optimum solutions are similar to the minimum spanning tree (MST). Consequently, a problem-specific representation, the link biased (LB) encoding, is developed, which represents trees as a list of floats. The LB encoding makes use of the knowledge that optimum solutions are similar to the MST, and encodes trees that are similar to the MST with a higher probability. Experimental results for different types of metaheuristics show that metaheuristics using the LB-encoding efficiently solve existing MCST problem instances from the literature, as well as randomly generated MCST problems of different sizes and types
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
On the application of estimation of distribution algorithms to multi-marker tagging SNP selection
This paper presents an algorithm for the automatic selection of a
minimal subset of tagging single nucleotide polymorphisms (SNPs) using an estimation of distribution algorithm (EDA). The EDA stochastically searches the constrained space of possible feasible solutions and takes
advantage of the underlying topological structure defined by the SNP correlations to model the problem interactions. The algorithm is evaluated
across the HapMap reference panel data sets. The introduced algorithm
is effective for the identification of minimal multi-marker SNP sets, which
considerably reduce the dimension of the tagging SNP set in comparison
with single-marker sets. New reduced tagging sets are obtained for all the
HapMap SNP regions considered. We also show that the information extracted from the interaction graph representing the correlations between
the SNPs can help to improve the efficiency of the optimization algorithm.
keywords: SNPs, tagging SNP selection, multi-marker selection, estimation of distribution algorithms, HapMap
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