A multi-start biased-randomized algorithm for the capacitated dispersion problem

The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study.Peer ReviewedPostprint (published version

Polynomially solvable cases of the bipartite traveling salesman problem

Given two sets, R and B, consisting of n cities each, in the bipartite traveling salesman problem one looks for the shortest way of visiting alternately the cities of R and B, returning to the city of origin. This problem is known to be NP-hard for arbitrary sets R and B. In this paper we provide an O(n6) algorithm to solve the bipartite traveling salesman problem if the quadrangle property holds. In particular, this algorithm can be applied to solve in O(n6) time the bipartite traveling salesman problem in the following cases: S=R¿B is a convex point set in the plane, S=R¿B is the set of vertices of a simple polygon and V=R¿B is the set of vertices of a circular graph. For this last case, we also describe another algorithm which runs in O(n2) time

An Adaptive Perturbation-Based Heuristic: An Application to the Continuous p-Centre Problem

A self-adaptive heuristic that incorporates a variable level of perturbation, a novel local search and a learning mechanism is proposed to solve the p-centre problem in the continuous space. Empirical results, using several large TSP-Lib data sets, some with over 1300 customers with various values of p, show that our proposed heuristic is both effective and efficient. This perturbation metaheuristic compares favourably against the optimal method on small size instances. For larger instances the algorithm outperforms both a multi-start heuristic and a discrete-based optimal approach while performing well against a recent powerful VNS approach. This is a self-adaptive method that can easily be adopted to tackle other combinatorial/global optimisation problems. For benchmarking purposes, the medium size instances with nodes are solved optimally for the first time, though requiring a large amount of computational time. As a by-product of this research, we also report for the first time the optimal solution of the vertex p-centre problem for these TSP-Lib data sets

Topology Control and Pointing in Free Space Optical Networks

Free space optical (FSO) communication provides functionalities that are different from fiber optic networks and omnidirectional RF wireless communications in that FSO is optical wireless (no infrastructure installation cost involving fibers) and is highly directional (no frequency interference). Moreover, its high-speed data transmission capability is an attractive solution to the first or last mile problem to bridge to current fiber optic network and is a preferable alternative to the low data rate directional point-to-point RF communications for inter-building wireless local area networks. FSO networking depends critically on pointing, acquisition and tracking techniques for rapidly and precisely establishing and maintaining optical wireless links between network nodes (physical reconfiguration), and uses topology reconfiguration algorithms for optimizing network performance in terms of network cost and congestion (logical reconfiguration). The physical and logical reconfiguration process is called Topology Control and can allow FSO networks to offer quality of service by quickly responding to various traffic demands of network users and by efficiently managing network connectivity. The overall objective of this thesis research is to develop a methodology for self-organized pointing along with the associated autonomous and precise pointing technique as well as heuristic optimization methods for Topology Control in bi-connected FSO ring networks, in which each network node has two FSO transceivers. This research provides a unique, autonomous, and precise pointing method using GPS and local angular sensors, which is applicable to both mobile and static nodes in FSO networking and directional point-to-point RF communications with precise tracking. Through medium (264 meter) and short (40 meter) range pointing experiments using an outdoor testbed on the University of Maryland campus in College Park, sub-milliradian pointing accuracy is presented. In addition, this research develops fast and accurate heuristic methods for autonomous logical reconfiguration of bi-connected ring network topologies as well as a formal optimality gap measure tested on an extensive set of problems. The heuristics are polynomial time algorithms for a congestion minimization problem at the network layer and for a multiobjective stochastic optimization of network cost and congestion at both the physical and network layers

Adaptive Heuristic Methods for the Continuous p-Centre Location Problems

This research studies the p-centre problem in the continuous space. This problem is particularly useful in locating emergency facilities, such as fire-fighting stations, police stations and hospitals where it is aimed to minimise the worst-case response time. This problem can be divided into a single facility minmax location problem (1-centre) and multi-facility minmax location problem (p-centre). The solution of the 1-centre location problem can be found optimally in polynomial time by using the well known Elzinga-Hearn algorithm for both the weighted and the unweighted case. The objective of the p-centre problem is to locate p facilities (p>1) so as to minimise the radius of the largest circle. However, in this case, we cannot always guarantee optimality as the problem is known to be NP hard. The aim of the research is to develop and analyse powerful meta-heuristics including the hybridisation of exact methods and heuristics to solve this global optimisation problem. To our knowledge this is the first study that meta-heuristics are developed for this problem. In addition larger instances previously used in the literature are tested .This is achieved by designing an efficient variable neighbourhood search, adapting a powerful perturbation method and extending a newly developed reformulation local search. Large instances are used to evaluate our approaches with promising results

Novel Split-Based Approaches to Computing Phylogenetic Diversity and Planar Split Networks

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