23 research outputs found
Application of the volume algorithm to the approximate and exact solving of the asymmetric
Neste artigo apresentamos resultados computacionais obtidos com o algoritmo volumétrico, uma variante do método do subgradiente, na resolução da relaxação linear que decorre da formulação estendida de fluxo desagregado
para o problema do Caixeiro Viajante Assimétrico. As experiências computacionais foram realizadas numa
selecção de instâncias da TSPLib e num conjunto de instâncias geradas aleatoriamente de acordo com o
Dimacs Implementation Challenge. Também experimentámos a aplicação de heurísticas durante a execução do algoritmo volumétrico. As experiências computacionais mostram sucesso moderado com instâncias de média dimensão.In this paper we present computational results with the volume algorithm, a variant
of the subgradient method, when solving the linear relaxation that stems from the extended
disaggregated °ow formulation of the Asymmetric Travelling Salesman Problems. Computational
experiments were performed on a selection of instances from the TSPLib and some randomly
generated instances according to the Dimacs Implementation Challenge. We have also tried ATSP
heuristics within the volume algorithm. Computational experiments show moderated success on
medium-scale instances.Fundação para a Ciência e Tecnologia - Projecto POCTI/MAT/14243/199
Path Planning Algorithms for Multiple Heterogeneous Vehicles
Unmanned aerial vehicles (UAVs) are becoming increasingly popular for surveillance
in civil and military applications. Vehicles built for this purpose vary in their
sensing capabilities, speed and maneuverability. It is therefore natural to assume
that a team of UAVs given the mission of visiting a set of targets would include
vehicles with differing capabilities. This paper addresses the problem of assigning
each vehicle a sequence of targets to visit such that the mission is completed with
the least "cost" possible given that the team of vehicles is heterogeneous. In order
to simplify the problem the capabilities of each vehicle are modeled as cost to travel
from one target to another. In other words, if a vehicle is particularly suited to visit
a certain target, the cost for that vehicle to visit that target is low compared to
the other vehicles in the team. After applying this simplification, the problem can be
posed as an instance of the combinatorial problem called the Heterogeneous Travelling
Salesman Problem (HTSP). This paper presents a transformation of a Heterogenous,
Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single,
Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available
for the single salesman problem can be used to solve the HMDMTSP. To show the
effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic
was applied to the transformed ATSP. Computational results show that good quality
solutions can be obtained for the HMDMTSP relatively fast.
Additional complications to the sequencing problem come in the form of precedence
constraints which prescribe a partial order in which nodes must be visited. In this context the sequencing problem was studied seperately using the Linear Program
(LP) relaxation of a Mixed Integer Linear Program (MILP) formulation of the
combinatorial problem known as the "Precedence Constrained Asymmetric Travelling
Salesman Problem" (PCATSP)
New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints
Given an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flow-based and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flow-based and hop-indexed formulations can be solved in about 2 days. © 2010 Elsevier Ltd. All rights reserved
New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller-Tucker-Zemlin constraints
Given an undirected network with positive edge costs and a natural number p, the Hop-Constrained Minimum Spanning Tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, we develop new formulations for HMST. The formulations are based on Miller-Tucker-Zemlin (MTZ) subtour elimination constraints, MTZ-based liftings in the literature offered for HMST, and a new set of topology-enforcing constraints. We also compare the proposed models with the MTZ-based models in the literature with respect to linear programming relaxation bounds and solution times. The results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to MTZ constraints, some of which are based on well-known, strong liftings of Desrochers and Laporte (1991). © 2011 Elsevier B.V. All rights reserved