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Distance-constrained vehicle routing problem: exact and approximate solution (mathematical programming)
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The asymmetric distance-constrained vehicle routing problem (ADVRP) looks at finding vehicle tours to connect all customers with a depot, such that the total distance is minimised; each customer is visited once by one vehicle; every tour starts and ends at a depot; and the travelled distance by each vehicle is less than or equal to the given maximum value. We present three basic results in this thesis. In the first one, we present a general flow-based formulation to ADVRP. It is suitable for symmetric and asymmetric instances. It has been compared with the adapted Bus School Routing formulation and appears to solve the
ADVRP faster. Comparisons are performed on random test instances with up to 200 customers. We reach a conclusion that our general formulation outperforms the adapted one. Moreover, it finds the optimal solution for small test instances quickly. For large instances, there is a high probability that an optimal solution can be found or at least improve upon the value of the best feasible solution found so far, compared to the other formulation which stops because of the time condition. This formulation is more general than Kara formulation since it does not require the distance matrix to satisfy the triangle inequality. The second result improves and modifies an old branch-and-bound method suggested by Laporte et al. in 1987. It is based on reformulating a distance-constrained vehicle routing
problem into a travelling salesman problem and uses the assignment problem as a lower
bounding procedure. In addition, its algorithm uses the best-first strategy and new branching rules. Since this method was fast but memory consuming, it would stop before optimality is proven. Therefore, we introduce randomness in choosing the node of the search tree in case we have more than one choice (usually we choose the smallest objective function). If an optimal solution is not found, then restart is required due to memory issues, so we restart our procedure. In that way, we get a multistart branch and bound method. Computational
experiments show that we are able to exactly solve large test instances with up to 1000
customers. As far as we know, those instances are much larger than instances considered for other VRP models and exact solution approaches from recent literature. So, despite its simplicity, this proposed algorithm is capable of solving the largest instances ever solved in literature. Moreover, this approach is general and may be used in solving other types of
vehicle routing problems. In the third result, we use VNS as a heuristic to find the best feasible solution for groups
of instances. We wanted to determine how far the difference is between the best feasible
solution obtained by VNS and the value of optimal solution in order to use the output
of VNS as an initial feasible solution (upper bound procedure) to improve our multistart method. Unfortunately, based on the search strategy (best first search), using a heuristic to find an initial feasible solution is not useful. The reason for this is because the branch and
bound is able to find the first feasible solution quickly. In other words, in our method using a good initial feasible solution as an upper bound will not increase the speed of the search. However, this would be different for the depth first search. However, we found a big gap between VNS feasible solution and an optimal solution, so VNS can not be used alone unless for large test instances when other exact methods are not able to find any feasible solution because of memory or stopping conditions
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
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