A Solution Merging Heuristic for the Steiner Problem in Graphs Using Tree Decompositions

Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of treewidth sufficiently small to make these al- gorithms fast enough for practical use. Consequently, tree decomposition based algorithms have limited applicability to large scale optimization. However, by first reducing the input graph so that a small width tree decomposition can be found, we can harness the power of tree decomposi- tion based techniques in a heuristic algorithm, usable on graphs of much larger treewidth than would be tractable to solve exactly. We propose a solution merging heuristic to the Steiner Tree Problem that applies this idea. Standard local search heuristics provide a natural way to generate subgraphs with lower treewidth than the original instance, and subse- quently we extract an improved solution by solving the instance induced by this subgraph. As such the fixed parameter tractable algorithm be- comes an efficient tool for our solution merging heuristic. For a large class of sparse benchmark instances the algorithm is able to find small width tree decompositions on the union of generated solutions. Subsequently it can often improve on the generated solutions fast

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

The development and application of metaheuristics for problems in graph theory: A computational study

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.It is known that graph theoretic models have extensive application to real-life discrete optimization problems. Many of these models are NP-hard and, as a result, exact methods may be impractical for large scale problem instances. Consequently, there is a great interest in developing e±cient approximate methods that yield near-optimal solutions in acceptable computational times. A class of such methods, known as metaheuristics, have been proposed with success. This thesis considers some recently proposed NP-hard combinatorial optimization problems formulated on graphs. In particular, the min- imum labelling spanning tree problem, the minimum labelling Steiner tree problem, and the minimum quartet tree cost problem, are inves- tigated. Several metaheuristics are proposed for each problem, from classical approximation algorithms to novel approaches. A compre- hensive computational investigation in which the proposed methods are compared with other algorithms recommended in the literature is reported. The results show that the proposed metaheuristics outper- form the algorithms recommended in the literature, obtaining optimal or near-optimal solutions in short computational running times. In addition, a thorough analysis of the implementation of these methods provide insights for the implementation of metaheuristic strategies for other graph theoretic problems

Bi-velocity discrete particle swarm optimization and its application to multicast routing problem in communication networks

This paper proposes a novel bi-velocity discrete particle swarm optimization (BVDPSO) approach and extends its application to the NP-complete multicast routing problem (MRP). The main contribution is the extension of PSO from continuous domain to the binary or discrete domain. Firstly, a novel bi-velocity strategy is developed to represent possibilities of each dimension being 1 and 0. This strategy is suitable to describe the binary characteristic of the MRP where 1 stands for a node being selected to construct the multicast tree while 0 stands for being otherwise. Secondly, BVDPSO updates the velocity and position according to the learning mechanism of the original PSO in continuous domain. This maintains the fast convergence speed and global search ability of the original PSO. Experiments are comprehensively conducted on all of the 58 instances with small, medium, and large scales in the OR-library (Operation Research Library). The results confirm that BVDPSO can obtain optimal or near-optimal solutions rapidly as it only needs to generate a few multicast trees. BVDPSO outperforms not only several state-of-the-art and recent heuristic algorithms for the MRP problems, but also algorithms based on GA, ACO, and PSO

Particle swarm optimization for the Steiner tree in graph and delay-constrained multicast routing problems

This paper presents the first investigation on applying a particle swarm optimization (PSO) algorithm to both the Steiner tree problem and the delay constrained multicast routing problem. Steiner tree problems, being the underlining models of many applications, have received significant research attention within the meta-heuristics community. The literature on the application of meta-heuristics to multicast routing problems is less extensive but includes several promising approaches. Many interesting research issues still remain to be investigated, for example, the inclusion of different constraints, such as delay bounds, when finding multicast trees with minimum cost. In this paper, we develop a novel PSO algorithm based on the jumping PSO (JPSO) algorithm recently developed by Moreno-Perez et al. (Proc. of the 7th Metaheuristics International Conference, 2007), and also propose two novel local search heuristics within our JPSO framework. A path replacement operator has been used in particle moves to improve the positions of the particle with regard to the structure of the tree. We test the performance of our JPSO algorithm, and the effect of the integrated local search heuristics by an extensive set of experiments on multicast routing benchmark problems and Steiner tree problems from the OR library. The experimental results show the superior performance of the proposed JPSO algorithm over a number of other state-of-the-art approaches

Internet of Things in urban waste collection

Nowadays, the waste collection management has an important role in urban areas. This paper faces this issue and proposes the application of a metaheuristic for the optimization of a weekly schedule and routing of the waste collection activities in an urban area. Differently to several contributions in literature, fixed periodic routes are not imposed. The results significantly improve the performance of the company involved, both in terms of resources used and costs saving

Benchmarking a wide spectrum of metaheuristic techniques for the radio network design problem

The radio network design (RND) is an NP-hard optimization problem which consists of the maximization of the coverage of a given area while minimizing the base station deployment. Solving RND problems efficiently is relevant to many fields of application and has a direct impact in the engineering, telecommunication, scientific, and industrial areas. Numerous works can be found in the literature dealing with the RND problem, although they all suffer from the same shortfall: a noncomparable efficiency. Therefore, the aim of this paper is twofold: first, to offer a reliable RND comparison base reference in order to cover a wide algorithmic spectrum, and, second, to offer a comprehensible insight into accurate comparisons of efficiency, reliability, and swiftness of the different techniques applied to solve the RND problem. In order to achieve the first aim we propose a canonical RND problem formulation driven by two main directives: technology independence and a normalized comparison criterion. Following this, we have included an exhaustive behavior comparison between 14 different techniques. Finally, this paper indicates algorithmic trends and different patterns that can be observed through this analysis.Publicad