Mapping virtual networks onto substrate networks

Network virtualization is a promising technique for building the Internet of the future since it enables the low cost introduction of new features into network elements. An open issue in such virtualization is how to effect an efficient mapping of virtual network elements onto those of the existing physical network, also called the substrate network. Mapping is an NP-hard problem and existing solutions ignore various real network characteristics in order to solve the problem in a reasonable time frame. This paper introduces new algorithms to solve this problem based on 0–1 integer linear programming, algorithms based on a whole new set of network parameters not taken into account by previous proposals. Approximative algorithms proposed here allow the mapping of virtual networks on large network substrates. Simulation experiments give evidence of the efficiency of the proposed algorithms.

Structural analysis of combinatorial optimization problem characteristics and their resolution using hybrid approaches

Many combinatorial problems coming from the real world may not have a clear and well defined structure, typically being dirtied by side constraints, or being composed of two or more sub-problems, usually not disjoint. Such problems are not suitable to be solved with pure approaches based on a single programming paradigm, because a paradigm that can effectively face a problem characteristic may behave inefficiently when facing other characteristics. In these cases, modelling the problem using different programming techniques, trying to ”take the best” from each technique, can produce solvers that largely dominate pure approaches. We demonstrate the effectiveness of hybridization and we discuss about different hybridization techniques by analyzing two classes of problems with particular structures, exploiting Constraint Programming and Integer Linear Programming solving tools and Algorithm Portfolios and Logic Based Benders Decomposition as integration and hybridization frameworks.

Formulations and Algorithms for Routing Problems

Combinatorial Optimization is a branch of optimization that deals with the problems where the set of feasible solutions is discrete. Routing problem is a well studied branch of Combinatorial Optimization that concerns the process of deciding the best way of visiting the nodes (customers) in a network. Routing problems appear in many real world applications including: Transportation, Telephone or Electronic data Networks. During the years, many solution procedures have been introduced for the solution of different Routing problems. Some of them are based on exact approaches to solve the problems to optimality and some others are based on heuristic or metaheuristic search to find optimal or near optimal solutions. There is also a less studied method, which combines both heuristic and exact approaches to face different problems including those in the Combinatorial Optimization area. The aim of this dissertation is to develop some solution procedures based on the combination of heuristic and Integer Linear Programming (ILP) techniques for some important problems in Routing Optimization. In this approach, given an initial feasible solution to be possibly improved, the method follows a destruct-and-repair paradigm, where the given solution is randomly destroyed (i.e., customers are removed in a random way) and repaired by solving an ILP model, in an attempt to find a new improved solution.

Algorithms for UAS insertion in civil air space

One of the most interesting challenge of the next years will be the Air Space Systems automation. This process will involve different aspects as the Air Traffic Management, the Aircrafts and Airport Operations and the Guidance and Navigation Systems. The use of UAS (Uninhabited Aerial System) for civil mission will be one of the most important steps in this automation process. In civil air space, Air Traffic Controllers (ATC) manage the air traffic ensuring that a minimum separation between the controlled aircrafts is always provided. For this purpose ATCs use several operative avoidance techniques like holding patterns or rerouting. The use of UAS in these context will require the definition of strategies for a common management of piloted and piloted air traffic that allow the UAS to self separate. As a first employment in civil air space we consider a UAS surveillance mission that consists in departing from a ground base, taking pictures over a set of mission targets and coming back to the same ground base. During all mission a set of piloted aircrafts fly in the same airspace and thus the UAS has to self separate using the ATC avoidance as anticipated. We consider two objective, the first consists in the minimization of the air traffic impact over the mission, the second consists in the minimization of the impact of the mission over the air traffic. A particular version of the well known Travelling Salesman Problem (TSP) called Time-Dependant-TSP has been studied to deal with traffic problems in big urban areas. Its basic idea consists in a cost of the route between two clients depending on the period of the day in which it is crossed. Our thesis supports that such idea can be applied to the air traffic too using a convenient time horizon compatible with aircrafts operations. The cost of a UAS sub-route will depend on the air traffic that it will meet starting such route in a specific moment and consequently on the avoidance maneuver that it will use to avoid that conflict. The conflict avoidance is a topic that has been hardly developed in past years using different approaches. In this thesis we purpose a new approach based on the use of ATC operative techniques that makes it possible both to model the UAS problem using a TDTSP framework both to use an Air Traffic Management perspective. Starting from this kind of mission, the problem of the UAS insertion in civil air space is formalized as the UAS Routing Problem (URP). For this reason we introduce a new structure called Conflict Graph that makes it possible to model the avoidance maneuvers and to define the arc cost function of the departing time. Two Integer Linear Programming formulations of the problem are proposed. The first is based on a TDTSP formulation that, unfortunately, is weaker then the TSP formulation. Thus a new formulation based on a TSP variation that uses specific penalty to model the holdings is proposed. Different algorithms are presented: exact algorithms, simple heuristics used as Upper Bounds on the number of time steps used, and metaheuristic algorithms as Genetic Algorithm and Simulated Annealing. Finally an air traffic scenario has been simulated using real air traffic data in order to test our algorithms. Graphic Tools have been used to represent the Milano Linate air space and its air traffic during different days. Such data have been provided by ENAV S.p.A (Italian Agency for Air Navigation Services).

Referee Assignment Problem Case: Italian Volleyball Championships

This thesis addresses the formulation of a referee assignment problem for the Italian Volleyball Serie A Championships. The problem has particular constraints such as a referee must be assigned to different teams in a given period of times, and the minimal/maximal level of workload for each referee is obtained by considering cost and profit in the objective function. The problem has been solved through an exact method by using an integer linear programming formulation and a clique based decomposition for improving the computing time. Extensive computational experiments on real-world instances have been performed to determine the effectiveness of the proposed approach.

Entwicklung eines Dispositionsleitstandes zur Bestimmung optimaler Torbelegungen in Stückgutspeditionsanlagen

Im operativen Betrieb einer Stückgutspeditionsanlage entscheidet der Betriebslenker bzw. der Disponent in einem ersten Schritt darüber, an welche Tore die Fahrzeuge zur Be- und Entladung andocken sollen. Darüber hinaus muss er für jede Tour ein Zeitfenster ausweisen innerhalb dessen sie das jeweilige Tor belegt. Durch die örtliche und zeitliche Fahrzeug-Tor-Zuordnung wird der für den innerbetrieblichen Umschlagprozess erforderliche Ressourcenaufwand in Form von zu fahrenden Wegstrecken oder aber Gabelstaplerstunden bestimmt. Ein Ziel der Planungsaufgabe ist somit, die Zuordnung der Fahrzeuge an die Tore so vorzunehmen, dass dabei minimale innerbetriebliche Wegstrecken entstehen. Dies führt zu einer minimalen Anzahl an benötigten Umschlagmittelressourcen. Darüber hinaus kann es aber auch zweckmäßig sein, die Fahrzeuge möglichst früh an die Tore anzudocken. Jede Tour verfügt über einen individuellen Fahrplan, der Auskunft über den Ankunftszeitpunkt sowie den Abfahrtszeitpunkt der jeweiligen Tour von der Anlage gibt. Nur innerhalb dieses Zeitfensters darf der Disponent die Tour einem der Tore zuweisen. Geschieht die Zuweisung nicht sofort nach Ankunft in der Anlage, so muss das Fahrzeug auf einer Parkfläche warten. Eine Minimierung der Wartezeiten ist wünschenswert, damit das Gelände der Anlage möglichst nicht durch zuviele Fahrzeuge gleichzeitig belastet wird. Es kann vor allem aber auch im Hinblick auf das Reservieren der Tore für zeitkritische Touren sinnvoll sein, Fahrzeuge möglichst früh abzufertigen. Am Lehrstuhl Verkehrssysteme und -logistik (VSL) der Universität Dortmund wurde die Entscheidungssituation im Rahmen eines Forschungsprojekts bei der Stiftung Industrieforschung in Anlehnung an ein zeitdiskretes Mehrgüterflussproblem mit unsplittable flow Bedingungen modelliert. Die beiden Zielsetzungen wurden dabei in einer eindimensionalen Zielfunktion integriert. Das resultierende Mixed Integer Linear Programm (MILP) wurde programmiert und für mittlere Szenarien durch Eingabe in den Optimization Solver CPlex mit dem dort implementierten exakten Branch-and-Cut Verfahren gelöst. Parallel wurde im Rahmen einer Kooperation zwischen dem Lehrstuhl VSL und dem Unternehmen hafa Docking Systems, einem der weltweit führenden Tor und Rampenhersteller, für die gleiche Planungsaufgabe ein heuristisches Scheduling Verfahren sowie ein Dispositionsleitstand namens LoadDock Navigation entwickelt. Der Dispositionsleitstand dient der optimalen Steuerung der Torbelegungen in logistischen Anlagen. In dem Leitstand wird planerische Intelligenz in Form des heuristischen Schedulingverfahrens, technische Neuerungen in der Rampentechnik in Form von Sensoren und das Expertenwissen des Disponenten in einem Tool verbunden. Das mathematische Modell sowie der Prototyp mit der integrierten Heuristik werden im Rahmen dieses Artikels vorgestellt.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

Scheduling in service systems: an application in the event-tourism industry

This paper deals with an event-bus tour booked by Bollywood film fans. During the tour, the participants visit selected locations of famous Bollywood films at various sites in Switzerland. Moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour; for organizational reasons, two or more buses cannot stay at the same location simultaneously. The planning problem is how to compute a feasible schedule for each bus such that the total waiting time (primary objective) and the total travel time (secondary objective) are minimized. We formulate this problem as a mixed-integer linear program, and we report on computational results obtained with the Gurobi solver.

Planejamento de sistemas de distribuição de energia elétrica considerando questões de confiabilidade e risco

O problema de Planejamento da Expansão de Sistemas de Distribuição (PESD) visa determinar diretrizes para a expansão da rede considerando a crescente demanda dos consumidores. Nesse contexto, as empresas distribuidoras de energia elétrica têm o papel de propor ações no sistema de distribuição com o intuito de adequar o fornecimento da energia aos padrões exigidos pelos órgãos reguladores. Tradicionalmente considera-se apenas a minimização do custo global de investimento de planos de expansão, negligenciando-se questões de confiabilidade e robustez do sistema. Como consequência, os planos de expansão obtidos levam o sistema de distribuição a configurações que são vulneráveis a elevados cortes de carga na ocorrência de contingências na rede. Este trabalho busca a elaboração de uma metodologia para inserir questões de confiabilidade e risco ao problema PESD tradicional, com o intuito de escolher planos de expansão que maximizem a robustez da rede e, consequentemente, atenuar os danos causados pelas contingências no sistema. Formulou-se um modelo multiobjetivo do problema PESD em que se minimizam dois objetivos: o custo global (que incorpora custo de investimento, custo de manutenção, custo de operação e custo de produção de energia) e o risco de implantação de planos de expansão. Para ambos os objetivos, são formulados modelos lineares inteiros mistos que são resolvidos utilizando o solver CPLEX através do software GAMS. Para administrar a busca por soluções ótimas, optou-se por programar em linguagem C++ dois Algoritmos Evolutivos: Non-dominated Sorting Genetic Algorithm-2 (NSGA2) e Strength Pareto Evolutionary Algorithm-2 (SPEA2). Esses algoritmos mostraram-se eficazes nessa busca, o que foi constatado através de simulações do planejamento da expansão de dois sistemas testes adaptados da literatura. O conjunto de soluções encontradas nas simulações contém planos de expansão com diferentes níveis de custo global e de risco de implantação, destacando a diversidade das soluções propostas. Algumas dessas topologias são ilustradas para se evidenciar suas diferenças.

Determining departure times in dynamic and stochastic maritime routing and scheduling problem

In maritime transportation, decisions are made in a dynamic setting where many aspects of the future are uncertain. However, most academic literature on maritime transportation considers static and deterministic routing and scheduling problems. This work addresses a gap in the literature on dynamic and stochastic maritime routing and scheduling problems, by focusing on the scheduling of departure times. Five simple strategies for setting departure times are considered, as well as a more advanced strategy which involves solving a mixed integer mathematical programming problem. The latter strategy is significantly better than the other methods, while adding only a small computational effort.

Simultaneous synthesis of heat exchanger networks with pressure recovery: optimal integration between heat and work

The optimal integration between heat and work may significantly reduce the energy demand and consequently the process cost. This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs) in which the pressure levels of the process streams can be adjusted to enhance the heat integration. A superstructure is proposed for the HEN design with pressure recovery, developed via generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation. The process conditions (stream temperature and pressure) must be optimized. Furthermore, the approach allows for coupling of the turbines and compressors and selection of the turbines and valves to minimize the total annualized cost, which consists of the operational and capital expenses. The model is tested for its applicability in three case studies, including a cryogenic application. The results indicate that the energy integration reduces the quantity of utilities required, thus decreasing the overall cost.

Simultaneous synthesis of work exchange networks with heat integration

The optimal integration of work and its interaction with heat can represent large energy savings in industrial plants. This paper introduces a new optimization model for the simultaneous synthesis of work exchange networks (WENs), with heat integration for the optimal pressure recovery of process gaseous streams. The proposed approach for the WEN synthesis is analogous to the well-known problem of synthesis of heat exchanger networks (HENs). Thus, there is work exchange between high-pressure (HP) and low-pressure (LP) streams, achieved by pressure manipulation equipment running on common axes. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as stand-alone compressors, turbines and valves. Helper motors and generators are used to respond to any demand and excess of energy. Moreover, between the WEN stages the streams are sent to the HEN to promote thermal recovery, aiming to enhance the work integration. A multi-stage superstructure is proposed to represent the process. The WEN superstructure is optimized in a mixed-integer nonlinear programming (MINLP) formulation and solved with the GAMS software, with the goal of minimizing the total annualized cost. Three examples are conducted to verify the accuracy of the proposed method. In all case studies, the heat integration between WEN stages is essential to improve the pressure recovery, and to reduce the total costs involved in the process.

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.

MINLP Optimization Algorithm for the Synthesis of Heat and Work Exchange Networks

This paper introduces a new optimization model for the simultaneous synthesis of heat and work exchange networks. The work integration is performed in the work exchange network (WEN), while the heat integration is carried out in the heat exchanger network (HEN). In the WEN synthesis, streams at high-pressure (HP) and low-pressure (LP) are subjected to pressure manipulation stages, via turbines and compressors running on common shafts and stand-alone equipment. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as helper motors and generators to respond to any shortage and/or excess of energy, respectively, in the SSTC axes. The heat integration of the streams occurs in the HEN between each WEN stage. Thus, as the inlet and outlet streams temperatures in the HEN are dependent of the WEN design, they must be considered as optimization variables. The proposed multi-stage superstructure is formulated in mixed-integer nonlinear programming (MINLP), in order to minimize the total annualized cost composed by capital and operational expenses. A case study is conducted to verify the accuracy of the proposed approach. The results indicate that the heat integration between the WEN stages is essential to enhance the work integration, and to reduce the total cost of process due the need of a smaller amount of hot and cold utilities.

MINLP Model for the Synthesis of Heat Exchanger Networks with Handling Pressure of Process Streams

This paper introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), wherein the handling pressure of process streams is used to enhance the heat integration. The proposed approach combines generalized disjunctive programming (GDP) and mixed-integer nonlinear programming (MINLP) formulation, in order to minimize the total annualized cost composed by operational and capital expenses. A multi-stage superstructure is developed for the HEN synthesis, assuming constant heat capacity flow rates and isothermal mixing, and allowing for streams splits. In this model, the pressure and temperature of streams must be treated as optimization variables, increasing further the complexity and difficulty to solve the problem. In addition, the model allows for coupling of compressors and turbines to save energy. A case study is performed to verify the accuracy of the proposed model. In this example, the optimal integration between the heat and work decreases the need for thermal utilities in the HEN design. As a result, the total annualized cost is also reduced due to the decrease in the operational expenses related to the heating and cooling of the streams.