E-mobility, in particular electric vehicles (EVs), play a crucial role in the energy transition. While businesses are increasingly adopting EVs, there is still a lot of opportunity to grow. One aspect of this growth is the way these vehicles are used by companies, especially when it comes to the logistics of EV charging. To encourage companies to further reduce their carbon footprint by more efficiently utilizing EVs, this project proposes a combined vehicle routing and charging model. These models can be used separately, as well as together, allowing the charging model to be combined with any pre-existing routing engine. The goal of this project is to show the benefits of allowing EVs to be charged between shifts during the day, rather than exclusively overnight, as well as to show how such schedules can be made. Our results show that giving vehicles the opportunity to charge between shifts can significantly reduce the costs associated with fleet operations. If the fleet contains non-electric vehicles as well as electric ones, we also see a significant reduction in the number of kilometers driven using fossil fuels. When sufficient chargers were available, even when the vehicles had little time to charge, a feasible schedule could always be found. Moreover, when more realistic charging intervals were used, most vehicles were even able to fully recharge before the start of their next shift. Finally, we concluded that the set of chargers needed to find such a feasible schedule can be relatively small, meaning that even without extensive additions to the charging infrastructure, companies can still benefit from this policy change.

This research addresses the operational challenges faced by the Sophia Children’s Hospital through a comprehensive analysis of its current state, literature review, and mathematical modeling. A model is created that produces a master surgery schedule, allowing for the allocation of patients to specific specialties, operating rooms, and days. Our aim is to maximize the utilization of the OR while also striving for a leveled bed occupancy and a balanced relative OR assignment for the specialties.

To address the uncertainty of future patient characteristics, we consider the surgery durations and the downstream to the nursing wards in a probabilistic manner. For the latter, we follow the approach of Schneider et al. (2020). For the first aspect, we devised a column generation based approach in which, assuming that individual surgery durations follow a log-normal distribution, we employ the
Fenton-Wilkinson method to estimate the distribution of the total sum of individual surgery durations. When this distribution is known, it becomes feasible to identify pairs of specialties with corresponding surgery counts that can be scheduled within our overtime restriction. The resulting model that includes this incorporation is referred to as the Log-normal Column model.

For our research, we use historical data provided by the Sophia Children’s Hospital. The data included properties about the patients’ surgeries and bed assignments. Due to the presence of errors in the data, we conducted preprocessing before utilizing it as input in our modeling. Additionally, we conducted goodness of fit tests to assess whether adopting the log-normal distribution for surgery duration was genuinely superior to the normal distribution. Our analysis revealed that, for the majority of instances, the log-normal distribution outperformed the normal distribution. This was the case for individual surgeries, as well as the Fenton-Wilkinson approximation for the duration of multiple surgeries.

We compared the performance of our Log-normal Column model to two other models which assume normality for the surgery durations. One is, similar to the Log-normal Column model, created with the column generation based approach, while the other is the model described by Schneider et al. (2020). The two column generation based approach models performed significantly better than the model proposed by Schneider et al. (2020). Furthermore, we compared our Log-normal Column model to the real-life situation with the help of a simulation.

Access to healthcare is a requirement for human well-being that is partly dependent upon safe infrastructure. One of the UN Sustainable Development Goals regarding healthcare is to achieve universal healthcare coverage, which includes access to qual- ity essential health-care services. In many developing nations, roads are often vulner- able to floods. Floods can cause roads (especially roads with a dirt or gravel surface type) to become inaccessible for a long period of time. This inaccessibility can cause many inhabitants to lose access to a healthcare facility within a crucial traveling time span. Upgrading flood prone roads on which many households are dependent in or- der to access a healthcare facility, could reduce this threat to healthcare accessibility for many inhabitants. This research aims to use optimization techniques to reduce the impact floods can have on healthcare accessibility, and apply a case study to the country Timor-Leste. We formulate an optimization model that maximises the num- ber of households that can access a healthcare facility within a 5 kilometer traveling distance via a flood resilient route, given a specific budget. Alongside this formula- tion, we provide a (simple) flood and costs model for the road as well as di↵erent heuristics to find (near-)optimal solutions. Our research includes multiple tests to de- termine which heuristic works best and which parameters and other settings increase the computational performance of these heuristics for Timor-Leste. The heuristic that performs the best is a dynamic greedy heuristic. This algorithm is able to generate an optimal solution for all possible budgets within 4 hours.

Large fault­tolerant universal gate quantum computers will provide a major speed­up to a variety of common computational problems. While such computers are years away, we currently have noisy intermediate­scale quantum (NISQ) computers at our disposal. In this project we present two quantum machine learning approaches that can be used to find quantum circuits suitable for specific NISQ devices. We present one gradient­based and one non­gradient based machine learning approach to optimize the created quantum circuits, to best mimic the behaviour of a given function up to measurement. We make sure that the created quantum circuits obey the restrictions of the chosen hardware, therefore the approaches can be used to find circuits perfectly suited for specific NISQ devices. This enables the user to make the best use of quantum technology in the near future. In doing this we created our own quantum simulator which can be used to simulate small quantum circuits that obey hardware restrictions. We also present the method used to implement this simulator. Finally we present the results of applying both machine learning approaches to different problem types and compare their performance.

The construction of cyclic railway timetables is an important task for Netherlands Railways (NS).This construction can be formulated as a Periodic Event Scheduling Problem (PESP). The most powerful technique for solving cyclic railway timetabling problems is constraint programming, especially via SAT solvers when PESP instances are encoded as SAT instances. SAT solvers can determine the feasibility of problem instances of NS quickly and reliably. However, in previous implementations the problem specification must explicitly indicate the track use within stations and on four-track sections. As a result, the solver also reports infeasibility if a small adjustment of the track allocation could lead to a feasible timetable. In this thesis, the Open Periodic Event Scheduling Problem (OPESP) is introduced, which is used in a new method to incorporate flexible track use in the SAT formulation. This method yields promising results that could help improve the timetabling process at NS.

In this thesis we look at three different algorithms within the field of phylogenetics and create a proof of concept for using machine learning to improve the algorithms. The problems are the maximum agreement forest problem, the hybridization number problem and finally the tail move problem. A study of the problems show that they can all benefit from machine learning. For each of the problems we find a machine leanring implementation using basic decision trees. The results show that the MAF problem and the tail move problem can both benefit from machine learning and for the hybridization number problem we give an implementation that is faster than the studied algorithm.

This research is focused on the proactive-reactive rescheduling process of the Train Unit Shunting Problem (TUSP) on train maintenance shunting yards. An important difference between a scheduling process and the rescheduling process is that a reschedule must be both feasible and desirable (similar to pre-schedule), while a schedule does not require desirability. Firstly, an abstract proactive-reactive rescheduling framework is proposed. This framework is proposed as a base for the general problem of proactive-reactive rescheduling. A total of four reactive rescheduling methods for the TUSP are proposed and implemented as extensions to the Simulated Annealing local search algorithm. The extensions are created in order to achieve reschedule desirability by either guiding the local search process during its iterations or influencing its starting point. Using experiments based on realistic data, it is concluded that the Simulated Annealing can be used to create reschedules that are both feasible as well as desirable. It is shown that both proposed extensions are required for the best reschedule quality. Finally, further analysis of the results shows that the schedule resilience to late arrival of trains can be improved upon by increasing the amount of time between a train arrival and the time at which its services are scheduled.

In line with the growing trend of using machine learning to improve solving of combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming branch-and-bound tree by using a learned policy. In contrast to previous work using imitation learning, our policy is focused on learning which of a node's children to select. We present an offline method to learn such a policy in two settings: one that is approximate by committing to pruning of nodes; one that is exact and backtracks from a leaf to use a different strategy. We apply the policy within the popular open-source solver SCIP. Empirical results on four MIP datasets indicate that our node selection policy leads to solutions more quickly than the state-of-the-art in the literature, but not as quickly as the state-of-practice SCIP node selector. While we do not beat the highly-optimised SCIP baseline in terms of solving time on exact solutions, our approximation-based policies have a consistently better optimality gap than all baselines if the accuracy of the predictive model adds value to prediction. Further, the results also indicate that, when a time limit is applied, our approximation method finds better solutions than all baselines in the majority of problems tested.

Storage systems, such as Flash memories, suffer, apart from the always present
noise, also from offset. The presence of this noise can decrease the performance
of a decoder using the Euclidean distance significantly. To negate the effects of
offset, a new distance, the modied Euclidean distance, was introduced, which
offers immunity to offset. However, the modified Euclidean distance is less
resistant to noise, which calls for methods to improve its resistance. The coset
of Hamming codes, constant weight codes and Berger codes are discussed and are simulated to investigate their performance with both distances. These codes are compared to each other for the Euclidean distance and the modified Euclidean
distance.

Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NN). However little research has gone into training NNs with MIP solvers. State of the art methods to train NNs are typically gradient-based and require significant amounts of data, computation on GPUs and extensive hyper-parameter tuning. In contrast, training with MIP solvers should not require GPUs or hyper-parameter tuning but can likely not handle large amounts of data. This work builds on recent advances that train binarized NNs using MIP solvers. We go beyond current work by formulating new MIP models to increase the amount of data that can be feasibly used. We also extend current work to be able to train non-binary integer-valued networks. We show the potential benefits of optimizing NNs with regards to fairness and model compression. We also propose a novel batch training method to considerably increase the amount of training data that can be used. We conduct experiments to test our proposed methodology. The experimental results firstly show that we have improved upon recent work and that comparable results to gradient-based methods can be achieved with minimal data. Secondly, we find that there is potential in optimizing with regards to fairness and model compression. Finally, our results show that batch training can be used to utilize more data, increase generalization and reach comparable results to gradient-based training for integer-valued networks.

Phylogenetic networks are a generalization of evolutionary trees that can be used to represent reticulate events. Level-k phylogenetic networks are such networks, but with a at most k reticulations per biconnected component of the network. For level-1 networks there exists an algorithm, called TriLoNet (Trinet Level-one Network algorithm), that constructs these networks directly from sequence alignments which works by piecing together smaller level-1 networks on three taxa. Here, we introduce TriL2Net (Trinet Level-2 Network algorithm), an algorithm similar to TriLoNet that works for the larger class of level-2 networks. More specifically, TriL2Net constructs a level-2 phylogenetic network from a set of level-2 trinets. We show that TriL2Net performs better on sampled level-2 networks than TriLoNet performs om sampled level-1 networks. We hypothesize that this result is either due to the different ways the data is sampled, or the difference in heuristics used. Moreover, we applied TriL2Net to level-1 trinet sets derived from real sequence data involving recombination. When comparing the networks generated by TriL2Net from these data sets to the networks generated by TriLoNet from these same data sets, we found that TriL2Net’s networks are at least as consistent with the input as TriLoNet’s networks. TriL2Net has been implemented in Python and is freely available at https://github.com/KSjors/TriL2Net.

Automated vehicles have the potential to create a future in which most cars are shared instead of being individually owned and used. The advantages of vehicle sharing are expected to be multiple: reduced traffic, freed-up parking space, safer trips and a lower environmental impact of traveling. The dial-a-ride problem with transfers (DARP-T) consists in finding a set of minimum cost routes that satisfies a set of transportation requests. Requests may share a vehicle and may be transferred from one vehicle to another at any node during their journey. In this thesis, we describe a heuristic solving moderate to large instances of the static heterogeneous DARP-T in which the requests have demanding time constraints. The heuristic builds a solution in a constructive greedy randomized procedure and subsequently improves it with a destroy and repair procedure. The heuristic is tested on instances we randomly generated containing up to 1000 requests traveling between any two of the 100 most populated cities in the Netherlands inside a four-hour timescale. These instances are also solved without transfers to determine the benefits transfers can bring and the user inconvenience they may cause. We also investigate the influence of the demand on the objective function value, look into the influence of the fleet size on the fleet usage, and present some visualizations of the solutions found.

Mixed Integer Linear Programming (MILP) is a generalization of classical linear programming where we restrict some (or all) variables to take integer values. Numerous real-world problems can be modeled as MILPs, such as production planning, scheduling, network design optimization and many more. MILPs are, in fact, NP-hard. State-of-the-art solvers use the branch-and-bound algorithm, an exact method that, in combination with a diverse mixture of heuristics, can tackle a fair range of practical problems. This algorithm sequentially partitions the search space using linear relaxations, thus creating a search tree. The exploration ends only when a solution, together with its proof of optimality, is found. The tree’s size can vary dramatically depending on the approach that is used to create it and explore it. One of the most influential decision-making strategies within the branch-and-bound algorithm is the branching rule, i.e., the criterion that is used to subdivide the search space. Currently, there is no mathematical understanding of this complex process. For this reason, all widely accepted branching rules are based on hand-crafted strategies which have been shown to perform well in practice. The work presented in this report is part of a blossoming line of research in the intersection of Combinatorial Optimization and Machine Learning. Specifically, we take further steps in the direction of branching rule discovery through machine learning techniques. In contrast to previously proposed methods which relied on supervised learning, we take the novel approach of leveraging a Reinforcement Learning (RL) algorithm. Our goal is to achieve a data-driven acceleration of the tree search. In this thesis, we lay the fundamental groundwork for the integration of RL into the branch-and-bound process. Through the proposed model, we gain insights on the benefits and limitations of RL, while improving on the state-of-the-art branching rules for a particular class of instances.

Packing problems are concerned with filling the space with copies of a certain object, so that the least amount of space stays unoccupied. The famous Kepler conjecture asserts that the cannonball packing of spheres is the most efficient packing achievable, and was recently formally proven by Hales.

Dostert, Guzman, Oliveira Filho and Vallentin investigated the packing problem for other shapes. They focused on translative packings, in which all objects are oriented in the same direction. They proved several new upper bounds on translative packing densities of various Platonic and Archimedean solids. However, their results rely heavily on complex computer calculations to ensure they satisfy the conditions of a theorem.

In this thesis, proof assistant Coq is used to formally verify these conditions. An introduction to Coq is provided, aimed at the working mathematician. Then, the theorems required for the proof are developed. Several results from multivariate calculus and convexity were required for the proof, but not available in Coq. The proof also requires a large amount of floating point calculations. A method is developed to efficiently perform floating point calculations on a large scale in Coq.

Using the developed techniques, the improved upper bound of Dostert et al. on the translative packing density of the truncated tetrahedron is formally verified. These techniques can be reused to formally verify the other improved upper bounds of Dostert et al.

The current sourcing strategy of a company which relies on the backhauls of third party logistic providers for transportation currently does not take the availability of backhauls into account. Therefore, there is uncertainty in the number of trucks that are available for transporting freight from a supplier to a customer. This uncertainty can lead to under deliveries of customer demand, and purchased product which cannot be picked up, which is undesirable. The problem is modelled as an extension of the Transportation Problem, adding product, time and size dimensions. The risks of unavailable backhauls in the sourcing strategy are modelled as expected penalties which are subtracted from the expected profit. A mixed integer linear program is developed to optimise the sourcing strategy. This program produces a truck schedule with corresponding contracts to buy at the suppliers. The real life instances that need to be solved on a daily basis, yield (tens of) millions of variables to optimize. As the solution is needed within an hour, using a global approach to obtain an exact solution is undesirable, due to the computing time needed. Therefore, a simulated annealing method is developed. The results of both these methods are analysed in terms of objective function value and computing time. It is recommended that the company implements exact solution method with a limited run time.

Model-based evolutionary algorithms (MBEAs) are praised for their broad applicability to black-box optimization problems. In practical applications however, they are mostly used to repeatedly optimize different instances of a single problem class, a setting in which specialized algorithms generally perform better. In this paper, we introduce the concept of a new type of MBEA that can automatically specialize its behavior to a given problem class using tabula rasa self-learning. For this, reinforcement learning (RL) is a naturally fitting paradigm. A proof-of-principle framework, called SL-ENDA, based on estimation of normal distribution algorithms in combination with reinforcement learning is defined. SL-ENDA uses an RL-agent to decide upon the next population mean while approaching the rest of the algorithm as the environment. A comparison of SL-ENDA to AMaLGaM and CMA-ES on unimodal noiseless functions shows mostly comparable performance and scalability to the broadly used and carefully manually crafted algorithms. This result, in combination with the inherent potential of self-learning model-based evolutionary algorithms with regard to specialization, opens the door to a new research direction with great potential impact on the field of model-based evolutionary algorithms.

We have tried to create a bin-packing algorithm that assigns items from a customer-order to totes such that the amount of totes is minimized. Analyzing the bin-packing algorithm that was used before this thesis had been written, taught us that xxx.xx% of the customer-orders was packed non optimal. In this thesis four algorithms are applied to Picnic data. The order in which the algorithms assign items to a tote has major consequences for the solutions. Eight different ways to order the items are combined with each algorithm, resulting in 32 different tote-calculations. Out of those 32 tote-calculations, the Best Fit Algorithm with items ordered in decreasing normalized values generates the best results. Remarkably, ordering items randomly also gives good solutions. This brought us to introducing a new method, where each customer-order is calculated at most eight times, each time shuffling the items before rerunning the algorithm and remembering the better solution. This heuristic is optimal for xxx.xx% of the customer-orders.

Let G=(V,E) be a connected undirected graph, where every edge has two weights assigned to it. This thesis considers the partitioning of the edge set E of G into subsets with three objectives in mind: i) balance the total amount of the first weight among the subsets, ii) balance the total amount of the second weight among the subsets and iii) create a non-chaotic partition. Here non-chaotic means that every subset forms a distinguishable and compact subgraph. We call this Unrelated Unconnected Multi Constrained Graph Partitioning, or UUMCGP. It has applications in the collection of debris after natural disasters and in the assignment of tasks to computers in a distributed network. We are the first to define UUMCGP and we show that for specific cases close-to-optimal solutions can be obtained in polynomial time. Moreover, an algorithm is developed that gives good approximate solutions to the general case of UUMCGP. The algorithm is tested on real-life cases of debris management and gives better results than commercial solvers when they are set to find the optimal solution.

A switching max-plus linear model is a framework to describe the discrete dynamics of the timing of events. To influence these systems one can choose the routes of jobs and the orderings of operations as input for the system. In this thesis the techniques of model predictive control are used to find good input values. The problem of finding the optimal input is however NP-hard, which means there is no guarantee to find the optimal in a reasonable amount of time. This is an issue for model predictive control on real applications of the switching max-plus model. In applications, on-line performance is used where there is limited time to compute the input values for control.\\ This thesis takes a look into methods to reduce the computational complexity of the MPC-SMPL problem. Alternative formulations such as reparameterization, model based-partitioning and the cutting plane method are developed and tested for the MPC-SMPL problem. To solve the MPC-SMPL problem 3 heuristics are designed and implemented for simulation. The heuristics are partition-based optimization, tabu search and simulated annealing. The goal is to find a strategy that obtains the best solution to the problem in a limited amount of time.

Logistics service providers (LSPs) offering container transport to the hinterland of the Netherlands face the challenge of efficiently using the capacity of the barge in order to minimize cost, while part of the relevant information is still lacking at the moment decisions have to be made. The existing infrastructure and the transportation activities are studied and modeled as an online optimization problem with simultaneously vehicle routing and container-to-mode assignment. A characteristic of great importance in the problem is the uncertainty element that reflects in the requested appointment times that have to be confirmed by another agent in the network. An online optimization approach is proposed, where the input data come in sequentially and decisions have to be made in between, because new information becomes available only after the decision has been made. At each decision moment, the uncertainty element is converted to an offline optimization problem by disregarding the uncertainty or by simulating various potential future scenarios. Subsequently, the problem is modeled as a multi-commodity network design problem on a time-space graph. Four different solution methods are developed in order to solve the online optimization problem. Three confirmation based methods concern a model in which the uncertainty element is partially disregarded, by assuming that each requested appointment time will be scheduled at a specific time relative to the requested one. Alternatively, a much more complex method is developed in which various future scenarios are simulated for the requested appointment times given their probability vector. The simulation based model seeks robust solutions that are resistant to change, i.e., feasible and (sub)optimal for every potential future scenario that has been simulated. Using randomly generated (but realistic) instances, the computational results show that the proposed simulation model surpasses the simpler models both in terms of outcomes, robustness and reliability. However, the practical relevance is somewhat restricted in the sense that the model is built on several assumptions.