"Algorithms for some Graph-Theoretical Optimization Problems".

Samenvatting Deze thesis situeert zich in het onderzoeksgebied van operationeel onder zoek. We richten ons op methoden om een aantal graaf-theoretische optima lisatie problemen op te lossen. Allereerst geven we een korte introducti e in lineair en integer programmeren en bespreken we enkele oplossingsme thoden die in deze thesis worden gebruikt. Het vervolg van deze thesis k an grofweg in twee delen worden opgesplitst. In het eerste deel komt het opdelen van een partial order aan bod. In het tweede deel be studeren we de structuur en de connectiviteit van het Internet. Het opsplitsen van een partial order in een zo klein mogelijk aantal cha ins is een welbekend en fundamenteel probleem in het vakgebied van opera tioneel onderzoek. Dilworth (1950) toonde aan dat het probleem polynomia al oplosbaar is en dat het minimum benodigde aantal chains gelijk is aan het aantal elementen in een maximale antichain. We generaliseren dit pr obleem door te stellen dat een chain niet meer dan een gegeven aantal el ementen mag bevatten. We stellen een aantal exacte algoritmen voor om di t probleem op te lossen en passen deze toe op een specifiek probleem bij een productiebedrijf in Nederland. Een interessant resultaat van dit on derzoek is dat we bij de probleem instanties van dit productiebedrijf ee n speciale structuur konden vaststellen, gerelateerd aan het concept van de clique-width van een graaf. Door deze structuur kunnen we aantonen d at het probleem, voor deze speciale instanties, polynomiaal oplosbaar is . Vervolgens behandelen we een tweede generalisatie van het probleem, waar bij we aan elk element van de partial order een gewicht toekennen. Het p robleem wordt dan om alle elementen op te delen in chains zod anig dat de som van de gewichten van de chains minimaal is. Hierbij word t het gewicht van een chain gedefinieerd als het gewicht van het zwaarst e element in de chain. Ook hier geldt de capaciteitsbeperking dat elke c hain ten hoogste een gegeven aantal elementen mag bevatten. We geven een aantal ondergrenzen voor de waarde van de optimale oplossing en we stel len een 2-approximatie algoritme voor. In het tweede deel van deze thesis bestuderen we de structuur en de conn ectiviteit van het Internet. Het Internet is de laatste decennia zeer po pulair geworden en de hoeveelheid data die via het Internet wordt verstu urd is enorm gegroeid. Het is zeer belangrijk dat communicatie die via I nternet verloopt efficiënt, veilig en betrouwbaar is, zeker in een tijd waarin virussen binnen enkele uren enorme computer netwerken kunnen stil leggen. Om de structuur en de connectiviteit van het Internet te bestude ren, modelleren we het Internet als een graaf. Een veel gebruikte manier om de connectiviteit van een graaf te analyseren is door het maximale a antal paden en de minimale sneden de bepalen. Het is welbekend dat deze twee problemen polynomiaal oplosbaar zijn voor gewone grafen, maar voor een Internet-graaf is dat niet het geval. Aangezien de definitie van een pad in de graaf in deze context anders is dan bij normale grafen, zijn beide problemen voor Internet-grafen NP-compleet. We stellen een aantal exacte algoritmen voor om deze problemen op te lossen en vergelijken de resultaten met de resultaten van twee 2-approximatie algoritmes voorgest eld door Erlebach et al. (2005).

Multi-Depot and Multi-School Bus Scheduling Problem with School Bell Time Optimization

69A43551747123The school bus transportation system is responsible for transporting students to and from schools safely and promptly. This research aims to optimize the school bus schedules and the school bell times simultaneously for improving the efficiency of the school bus system operation. The authors consider the school bus scheduling problem in a multi-depot multi-school bus system and incorporate the bell time optimization to make bus operations more efficient. The authors propose four different methods, including one exact method and three heuristic methods, to solve the Multi-depot and Multi-school Bus Scheduling Problem with School Bell Time Optimization (MDSBSPTW)

Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling

In the last decade, the Industrial Revolution 4.0 brought flexible supply chains and flexible design projects to the forefront. Nevertheless, the recent pandemic, the accompanying economic problems, and the resulting supply problems have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changed circumstances have become more valuable both in logistics and projects. There are already several competing criteria of project and logistic process planning and scheduling that need to be reconciled. At the same time, the COVID-19 pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistic processes, activities, and projects

Home care routing and scheduling problem with teams’ synchronization

Funding Information: This work is funded by Portuguese funds through the FCT - Fundação para a Ciência e a Tecnologia , I.P., under the scope of the projects UIDB/00297/2020 (Center for Mathematics and Applications), UIDB/00097/2020 (CEGIST), and the PhD scholarship grant SFRH/BD/148773/2019 . Publisher Copyright: © 2023 The AuthorsThe demand for home care (HC) services has steadily been growing for two main types of services: healthcare and social care. If, for the former, caregivers' skills are of utter importance, in the latter caregivers are not distinguishable in terms of skills. This work focuses social care and models caregivers' synchronization as a means of improving human resources management. Moreover, in social care services, several visits need to be performed in the same day since patients are frequently alone and need assistance throughout the day. Depending on the patient's autonomy, some tasks have to be performed by two caregivers (e.g. assist bedridden patients). Therefore, adequate decision support tools are crucial for assisting managers (often social workers) when designing operational plans and to efficiently assign caregivers to tasks. This paper advances the literature by 1) considering teams of one caregiver that can synchronize to perform tasks requiring two caregivers (instead of having teams of two caregivers), 2) simultaneously modelling daily continuity of care and teams' synchronization, and 3) associating dynamic time windows to teams' synchronizations introducing scheduling flexibility while minimize service and travel times. These concepts are embedded into a daily routing and scheduling MIP model, deciding on the number of caregivers and on the number and type of teams to serve all patient tasks. The main HC features of the problem, synchronization and continuity of care, are evaluated by comparing the proposed planning with the current situation of a home social care service provider in Portugal. The results show that synchronization is the feature that most increases efficiency with respect to the current situation. It evidences a surplus in working time capacity by proposing plans where all requests can be served with a smaller number of caregivers. Consequently, new patients from long waiting lists can now be served by the “available” caregivers.publishersversionpublishe

Learning Augmented Optimization for Network Softwarization in 5G

The rapid uptake of mobile devices and applications are posing unprecedented traffic burdens on the existing networking infrastructures. In order to maximize both user experience and investment return, the networking and communications systems are evolving to the next gen- eration – 5G, which is expected to support more flexibility, agility, and intelligence towards provisioned services and infrastructure management. Fulfilling these tasks is challenging, as nowadays networks are increasingly heterogeneous, dynamic and expanded with large sizes. Network softwarization is one of the critical enabling technologies to implement these requirements in 5G. In addition to these problems investigated in preliminary researches about this technology, many new emerging application requirements and advanced opti- mization & learning technologies are introducing more challenges & opportunities for its fully application in practical production environment. This motivates this thesis to develop a new learning augmented optimization technology, which merges both the advanced opti- mization and learning techniques to meet the distinct characteristics of the new application environment. To be more specific, the abstracts of the key contents in this thesis are listed as follows: • We first develop a stochastic solution to augment the optimization of the Network Function Virtualization (NFV) services in dynamical networks. In contrast to the dominant NFV solutions applied for the deterministic networking environments, the inherent network dynamics and uncertainties from 5G infrastructure are impeding the rollout of NFV in many emerging networking applications. Therefore, Chapter 3 investigates the issues of network utility degradation when implementing NFV in dynamical networks, and proposes a robust NFV solution with full respect to the underlying stochastic features. By exploiting the hierarchical decision structures in this problem, a distributed computing framework with two-level decomposition is designed to facilitate a distributed implementation of the proposed model in large-scale networks. • Next, Chapter 4 aims to intertwin the traditional optimization and learning technologies. In order to reap the merits of both optimization and learning technologies but avoid their limitations, promissing integrative approaches are investigated to combine the traditional optimization theories with advanced learning methods. Subsequently, an online optimization process is designed to learn the system dynamics for the network slicing problem, another critical challenge for network softwarization. Specifically, we first present a two-stage slicing optimization model with time-averaged constraints and objective to safeguard the network slicing operations in time-varying networks. Directly solving an off-line solution to this problem is intractable since the future system realizations are unknown before decisions. To address this, we combine the historical learning and Lyapunov stability theories, and develop a learning augmented online optimization approach. This facilitates the system to learn a safe slicing solution from both historical records and real-time observations. We prove that the proposed solution is always feasible and nearly optimal, up to a constant additive factor. Finally, simulation experiments are also provided to demonstrate the considerable improvement of the proposals. • The success of traditional solutions to optimizing the stochastic systems often requires solving a base optimization program repeatedly until convergence. For each iteration, the base program exhibits the same model structure, but only differing in their input data. Such properties of the stochastic optimization systems encourage the work of Chapter 5, in which we apply the latest deep learning technologies to abstract the core structures of an optimization model and then use the learned deep learning model to directly generate the solutions to the equivalent optimization model. In this respect, an encoder-decoder based learning model is developed in Chapter 5 to improve the optimization of network slices. In order to facilitate the solving of the constrained combinatorial optimization program in a deep learning manner, we design a problem-specific decoding process by integrating program constraints and problem context information into the training process. The deep learning model, once trained, can be used to directly generate the solution to any specific problem instance. This avoids the extensive computation in traditional approaches, which re-solve the whole combinatorial optimization problem for every instance from the scratch. With the help of the REINFORCE gradient estimator, the obtained deep learning model in the experiments achieves significantly reduced computation time and optimality loss

A flexible metaheuristic framework for solving rich vehicle routing problems

Route planning is one of the most studied research topics in the operations research area. While the standard vehicle routing problem (VRP) is the classical problem formulation, additional requirements arising from practical scenarios such as time windows or vehicle compartments are covered in a wide range of so-called rich VRPs. Many solution algorithms for various VRP variants have been developed over time as well, especially within the class of so-called metaheuristics. In practice, routing software must be tailored to the business rules and planning problems of a specific company to provide valuable decision support. This also concerns the embedded solution methods of such decision support systems. Yet, publications dealing with flexibility and customization of VRP heuristics are rare. To fill this gap this thesis describes the design of a flexible framework to facilitate and accelerate the development of custom metaheuristics for the solution of a broad range of rich VRPs. The first part of the thesis provides background information to the reader on the field of vehicle routing problems and on metaheuristic solution methods - the most common and widely-used solution methods to solve VRPs. Specifically, emphasis is put on methods based on local search (for intensification of the search) and large neighborhood search (for diversification of the search), which are combined to hybrid methods and which are the foundation of the proposed framework. Then, the main part elaborates on the concepts and the design of the metaheuristic VRP framework. The framework fulfills requirements of flexibility, simplicity, accuracy, and speed, enforcing the structuring and standardization of the development process and enabling the reuse of code. Essentially, it provides a library of well-known and accepted heuristics for the standard VRP together with a set of mechanisms to adapt these heuristics to specific VRPs. Heuristics and adaptation mechanisms such as templates for user-definable checking functions are explained on a pseudocode level first, and the most relevant classes of a reference implementation using the Microsoft .NET framework are presented afterwards. Finally, the third part of the thesis demonstrates the use of the framework for developing problem-specific solution methods by exemplifying specific customizations for five rich VRPs with diverse characteristics, namely the VRP with time windows, the VRP with compartments, the split delivery VRP, the periodic VRP, and the truck and trailer routing problem. These adaptations refer to data structures and neighborhood search methods and can serve as a source of inspiration to the reader when designing algorithms for new, so far unstudied VRPs. Computational results are presented to show the effectiveness and efficiency of the proposed framework and methods, which are competitive with current state-of-the-art solvers of the literature. Special attention is given to the overall robustness of heuristics, which is an important aspect for practical application

Investigation of Matching Problems using Constraint Programming and Optimisation Methods

This thesis focuses on matching under ordinal preferences, i.e. problems where agents may be required to list other agents that they find acceptable in order of preference. In particular, we focus on two main cases: the popular matching and the kidney exchange problem. These problems are important in practice and in this thesis we develop novel algorithms and techniques to solve them as combinatorial optimisation problems. The first part of the thesis focuses on one-sided matching on a bipartite graph, specifically the popular matching. When the participants express their preferences in an ordinal order, one might want to guarantee that no two applicants are inclined to form a coalition in order to maximise their welfare, thus finding a stable matching is needed. Popularity is a concept that offers an attractive trade- off between these two notions. In particular, we examine the popular matching in the context of constraint programming using global constraints. We discuss the possibility to find a popular matching even for the instances that does not admit one. The second part of the thesis focuses on non-bipartite graphs, i.e. the kidney exchange problem. Kidney transplant is the most effective treatment to cure end-stage renal disease, affecting one in every thousand European citizen. Motivated by the observation that the kidney exchange is inherently a stochastic online problem, first, we give a stochastic online method, which provides an expected value estimation that is correct within the limit of sampling errors. Second, we show that by taking into consideration a probabilistic model of future arrivals and drop-offs, we can get reduce sampling scenarios, and we can even construct a sampling-free probabilistic model, called the Abstract Exchange Graph (AEG). A final contribution of this thesis is related to finding robust solutions when uncertainty occurs. Uncertainty is inherent to most real world problems