Bi-criteria network optimization: problems and algorithms

Several approaches, exact and heuristics, have been designed in order to generate the Pareto frontier for multi-objective combinatorial optimization problems. Although several classes of standard optimization models have been studied in their multi- objective version, there still exists a big gap between the solution techniques and the complexity of the mathematical models that derive from the most recent real world applications. In this thesis such aspect is highlighted with reference to a specific application field, the telecommunication sector, where several emerging optimization problems are characterized by a multi-objective nature. The study of some of these problems, analyzed and solved in the thesis, has been the starting point for an assessment of the state of the art in multicriteria optimization with particular focus on multi-objective integer linear programming. A general two-phase approach for bi-criteria integer network flow problems has been proposed and applied to the bi-objective integer minimum cost flow and the bi-objective minimum spanning tree problem. For both of them the two-phase approach has been designed and tested to generate a complete set of efficient solutions. This procedure, with appropriate changes according to the specific problem, could be applied on other bi-objective integer network flow problems. In this perspective, this work can be seen as a first attempt in the direction of closing the gap between the complex models associated with the most recent real world applications and the methodologies to deal with multi-objective programming. The thesis is structured in the following way: Chapter 1 reports some preliminary concepts on graph and networks and a short overview of the main network flow problems; in Chapter 2 some emerging optimization problems are described, mathematically formalized and solved, underling their multi-objective nature. Chapter 3 presents the state of the art on multicriteria optimization. Chapter 4 describes the general idea of the solution algorithm proposed in this work for bi-objective integer network flow problems. Chapter 5 is focused on the bi-objective integer minimum cost flow problem and on the adaptation of the procedure proposed in Chapter 4 on such a problem. Analogously, Chapter 6 describes the application of the same approach on the bi-objective minimum spanning tree problem. Summing up, the general scheme appears to adapt very well to both problems and can be easily implemented. For the bi-objective integer minimum cost flow problem, the numerical tests performed on a selection of test instances, taken from the literature, permit to verify that the algorithm finds a complete set of efficient solutions. For the bi-objective minimum spanning tree problem, we solved a numerical example using two alternative methods for the first phase, confirming the practicability of the approach

Two-phase strategies for the bi-objective minimum spanning tree problem

This paper presents a new two-phase algorithm for the bi-objective minimum spanning tree (BMST) prob-lem. In the first phase, it computes the extreme supported efficient solutions resorting to both mathematicalprogramming and algorithmic approaches, while the second phase is devoted to obtaining the remaining ef-ficient solutions (non-extreme supported and non-supported). This latter phase is based on a new recursiveprocedure capable of generating all the spanning trees of a connected graph through edge interchanges basedon increasing evaluation of non-zero reduced costs of associated weighted linear programs. Such a procedureexploits a common property of a wider class of problems to which the minimum spanning tree (MST) prob-lem belongs, that is the spanning tree structure of its basic feasible solutions. Computational experimentsare conducted on different families of graphs and with different types of cost. These results show that thisnew two-phase algorithm is correct, very easy to implement and it allows one to extract conclusions on thedifficulty of finding the entire set of Pareto solutions of the BMST problem depending on the graph topologyand the possible correlation of the edge cost

Minimum Cost Design of Cellular Networks in Rural Areas with UAVs, Optical Rings, Solar Panels and Batteries

Bringing the cellular connectivity in rural zones is a big challenge, due to the large installation costs that are incurred when a legacy cellular network based on fixed Base Stations (BSs) is deployed. To tackle this aspect, we consider an alternative architecture composed of UAV-based BSs to provide cellular coverage, ground sites to connect the UAVs with the rest of the network, Solar Panels (SPs) and batteries to recharge the UAVs and to power the ground sites, and a ring of optical fiber links to connect the installed sites. We then target the minimization of the installation costs for the considered UAV-based cellular architecture, by taking into account the constraints of UAVs coverage, SPs energy consumption, levels of the batteries and the deployment of the optical ring. After providing the problem formulation, we derive an innovative methodology to ensure that a single ring of installed optical fibers is deployed. Moreover, we propose a new algorithm, called DIARIZE, to practically tackle the problem. Our results, obtained over a set of representative rural scenarios, show that DIARIZE performs very close to the optimal solution, and in general outperforms a reference design based on fixed BSs

A new approach for train calendar description generation

This paper describes a new method of generating text starting from a calendar, automatically and in a representation clear to customers. We focus in particular on railway applications. Railway undertakings are trying to improve their communication with commuters, employees and travelers, especially for the frequent occurrences of path modifications implying scattered calendars and not intelligible descriptions appearing in various outputs such as websites, mobile applications, timetable boards, train transport diagrams and books. We propose two alternative approaches for this challenging task. The first one combines a customized set covering problem formulation with a parallel vector generation algorithm. The second one integrates the vector generation problem in the set covering problem into a more complex mathematical model. Our aim is to verify that with a mathematical programming approach it is possible to improve the quality of outcomes in terms of intelligibility. We used a commercial mip solver (CPLEX 12.4) to solve the two models, while we designed a specific parallel algorithm for the vector generation problem in the first approach. The new solutions were tested on several real timetables and compared with the tools used so far

Mathematical Models for On-Line Train Calendars Generation

In this paper we present a new model for train calendars textual generation, that is a method for auto- matically generating a text to customers in a concise and clear way with a service calendar represented by a boolean vector as its input. This problem arises in the transportation field, in particular in railway services. A new mathematical model which guarantees the optimality of solutions and good computa- tional performances is described and tested on several real railway timetables, always obtaining optimal solutions. Moreover, it is extensively compared with existing models showing a significant reduction of computational times that makes it applicable in practical context