Applications of Biased Randomization and Simheuristic Algorithms to Arc Routing and Facility Location Problems

Most metaheuristics contain a randomness component, which is usually based on uniform randomization –i.e., the use of the Uniform probability distribution to make random choices. However, the Multi-start biased Randomization of classical Heuristics with Adaptive local search framework (MIRHA, Gonzalez-Martin et al., 2014a; Juan et al. ,2014a) proposes the use of biased (non-uniform) randomization for the design of alternative metaheuristics-i.e., the use of skewed probability distributions such as the Geometric or Triangular ones. In some scenarios, this non-biased randomization has shown to provide faster convergence to near-optimal solutions. The MIRHA framework also includes a local search step for improving the incumbent solutions generated during the multi-start process. It also allows the addition of tailored local search components, like cache (memory) or splitting (divide-and-conquer) techniques, that allow the generation of competitive (near-optimal) solutions. The algorithms designed using the MIRHA framework allows to obtain 'high-quality' solutions to realistic problems in reasonable computing times. Moreover, they tend to use a reduced number of parameters, which makes them simple to implement and configure in most practical applications. This framework has successfully been applied in many routing and scheduling problems. One of the main goals of this thesis is to develop new algorithms, based in the aforementioned framework, for solving some combinatorial optimization problems that can be of interest in the telecommunication industry (Figure 1). One of the current issues in the telecommunication sector is that of planning of telecommunication networks. For instance, finding the best placements of base station on a mobile network, the placement of optical fiber networks or selecting the servers which could provide a given service with the lowest network latency, are examples of these problems. Two known families of combinatorial optimization problems that can be used for modeling the aforementioned problems are the Facility Location Problems (FLP) and the Arc Routing Problems (ARP). In this thesis we will propose new algorithms based on the MIRHA framework for problems belonging to these two families. The FLP is a location problem where the goal is to find the best placement of some facilities which minimizes the costs of providing a service to a set of customers. ii The ARP is similar to the well-known Vehicle Routing Problem (VRP), but its nature makes it also a good candidate for modeling certain real-life telecommunication problems. While the VRP has been extensively studied in the literature-mainly because of its applications to logistics and transportation-, there …