The primary goal of this work was to develop a model that solved the market clearing problem while abiding by all the special requirements set by the European power ex- changes. The methodology that we applied is derived from Madani and Van Vyve, who referred to it as the Primal-Dual approach. It is assumed that the optimal set of blocks for the market clearing problem is known a priori. The integrality constraints of the market clearing problem are then replaced with inequalities that force the decision variables of the blocks to their optimal values, resulting in an LP. Next, the dual of this problem is defined, so that now the dual variables related to the constraints forcing the blocks to be accepted or rejected. can be interpreted as upper boundaries to the incurred losses or missed opportunity costs, respectively. Finally, a new problem is defined that includes all constraints from the original MILP (including integrality constraints) as well as the dual problem, and in which all dual variables related to the upper bound of incurred losses are set to zero. The resulting MILP now satisfies all requirements. Modifications to Madani and Van Vyve's model were made to include different kind of block orders and a flow based intuitive network model, while maintaining uniform prices.

In this thesis, we consider the Multi Depot Vehicle Scheduling Problem with Time Windows with driver day duration restrictions that addresses the task of assigning a given set of time window shipments to trucks with consideration of practical requirements. The goal of this thesis is to design an algorithm that finds a good solution for the problem within 15 minutes. In the literature, the problem is usually applied to public transport cases. We consider the freight transport application of an online grocer. We introduce a Multi-Commodity Minimum Network Flow ILP implementation for MDVSPTW with short computation time. Also, based on the Concurrent Scheduler algorithm for MDVSP from the literature, we introduce the Greedy Scheduler algorithm that is able to find a feasible solution within short computation time for our problem. These two implementations form building blocks for the three main algorithms we introduce, that find good feasible solutions for our problem within 15 minutes: the ILP + Greedy algorithm, the Random Search algorithm and the Random Search and Fix algorithm. We incorporate the driver day duration restriction in the three algorithms by either allowing a driver change, that is two drivers executing one truck day, or not, and compare the results. We show that the ILP + Greedy algorithm performs the best. In the case an algorithm that does not involve an ILP is preferred, e.g., for robustness reasons, the Random Search and Fix algorithm performs better than the Random Search algorithm.

The maritime inventory routing problem (MIRP) is a tactical and operational planning problem, that takes an integrated view on ship scheduling and inventory management for bulk products. Given production and consumption levels during a predetermined planning horizon, the problem aims at finding delivery schedules with minimal travel costs, such that the inventory bounds at both production and consumption ports are satisfied during the entire planning horizon.

In this thesis, we consider instances of the MIRP with a heterogenous fleet and multiple products. We formulate both a mixed integer programming (MIP) and constraint programming (CP) model for these instances. These models are solved using commercially available dedicated solvers for both formalism. For small instance sizes and short planning periods, the MIP approach is prevalent in finding solutions quickly and of good quality. Due to the inventory constraints in the problem however, the MIP approach suffers from scalability issues more heavily than the CP approach. A rolling-horizon heuristic is proposed in order to find solutions of better quality in comparable running time.

We consider a simplified version of the Monte Carlo tree search (MCTS) problem, a problem where, given a game tree with stochastic reward, one is tasked with finding the best move from the root. This problem is well studied, and recently impressive results have been obtained. For example, in 2016, when the AlphaGo program beat the professional Go player Lee Sedol. Even though these results were spectacular, not much is known about the guaranteed accuracy of these algorithms. In this work, we review the FindTopWinner algorithm for the MCTS problem. The FindTopWinner algorithm is guaranteed to give an accurate result with high probability, as is formalized in the (ε,δ)-PAC learning framework. However, its sample complexity is not optimal. We improve FindTopWinner by introducing the Spherical Confidence Region- MCTS (SCR-MCTS) algorithm, which operates by creating a spherical confidence region on the joint values of the leaves in multiple iterations called epochs. We show that SCR-MCTS has the (ε,δ)-PAC guarantee, and we show that empirically SCR-MCTS draws fewer samples than FindTopWinner does on various benchmark trees.

Machine learning has been a computer sciences buzzword for years. The technology has a lot of potential and a huge number of applications that spoke to people with and without knowledge of computer sciences. Image, text and speech recognition, social profiling, computergames, everything seemed possible. Machine learning is not as much in the spotlight now since the rise of blockchain technology, but the field is still relevant and used widely. The field concerns itself with ‘teaching’ computers to make choices or recognize data by repeating experiments or looking at data, and then making changes to itself to achieve better results. Now consider the field of optimization. It is not as well known outside of the mathematics community but incredibly important nonetheless. It has a miriad of uses: flight scheduling, ambulance placement and route planning are a minimal selection of all the problems that Optimization gets used in. Optimization is about solving problems as quickly and optimally as possible, looking at ways to speed up the process or finding the solution with the lowest cost. Both fields have an extensive range of methods and applications but have not been combined a lot before. This report takes a versatile topic within machine learning, namely deep learning and combines it with a classic problem from Optimization. This model was first proposed in 2017, meaning that is a very young line of research. This report will further explore this crossover and look into the performance and possible applications. There will first be an introduction to both fields to make the report understandable for students from either mathematics or computer sciences faculties. The model will then be established and explained in detail. There will then be time devoted to looking into applications of the model and seeing how they perform in experiments. Lastly the results of the experiments will be discussed and their implications.

Quantum coin flipping is a cryptographic primitive in which two or more parties that do not trust each other want establish a fair coin flip. These parties are not physically near each other and use quantum communication channels to interact. A quality of protocols is measured by the best possible cheating strategy, which is the solution of a complex semidefinite optimization problem. In this master thesis we show new explicit bounds in multiparty quantum coin flipping, we investigate how to explicitly formulate these problem in a standard form, we show that a fair coin flip results in the lowest possible bias and we determine more measures of the quality of a protocol. Furthermore, this master thesis presents a rigorous and detailed mathematical description of semidefinite optimization, quantum information theory and quantum coin flipping. This thesis also includes an article written together with J. Mulderij, T. Attema, I. Chiscop and F. Phillipson on distributed quantum computing. In this article, we pose new questions and formulate integer linear programs that solve to find optimal assignment of qubits to computers for a given network of quantum computers and quantum algorithm.

Over the course of the last decade, an interest has emerged in nearest neighbor constraints for quantum circuit design. The challenge herein is to bothminimize the running time of a circuit and tomodify it such that quantum gates only act on adjacent qubits while leaving the desired computational operation intact. These modifications involve the insertion of SWAP gates, which introduces computational overhead. Several exact and heuristic methods have been developed to determine the minimal number of required SWAP gates. Until now, the model sizes of exact methods scale superexponentionally in the number of qubits of the quantum circuit. The main research goal of this project was to develop an integer linear program that instead scales polynomially both in the number of qubits and the number of quantum gates in the quantumcircuit. 7 First, qubits located on a linear array were considered. The resulting integer linear program proposed requires O(n^2 m) variables and constraints, where n denotes the number of qubits and m denotes the number of quantum gates of the quantum circuit under consideration. Second, qubits located on a two- or threedimensional grid were considered. The programs both require O(n4m) variables and O(n^3 m) constraints. Subsequently we prove that, for a fixed quantum circuit, the optimal objective value of the one-dimensional problem is an upper bound for the optimal objective value of the corresponding two- and three-dimensional problems. Using CPLEX’s Branch & Bound method, 131 benchmark instances of various circuit sizes were evaluated. The largest of which contained either eighteen qubits and sixteen quantum gates, or five qubits and 112 quantumgates. Furthermore, we identify problems on the interface of nearest neighbor compliant quantum circuit design and distributed quantum computing. Integer linear program formulations are provided for these additional problems.

The goal of this thesis is to provide a method to obtain a User Equilibrium (UE) in a synchromodal transportation network in which we transport containers for multiple customers.
We use the Space Time Network (STN), in which the travel time of modalities is fixed and independent of the occupancy of the network.
We define the User Equilibrium solution as the solution wherein each customer can travel via their cheapest paths possible, and no customer is harmed by the route choice of other customers. We define the System Optimal (SO) solution as the solution in which the total costs of the network are minimized.
We expand the goal of finding a UE on the STN to finding a solution where the solution is both SO as well as UE.
The solving method we developed in this thesis, consists of finding SO solutions by solving the Minimum Cost Multi-Commodity Flow (MCMCF) problem on the STN to find an SO solution, and create tolls schemes to create a UE solution, while maintaining the SO solution.
We investigate several types of tolls in order to obtain sufficient both SO and UE solutions.

Parcel delivery companies offer time-guaranteed transportation of parcels, letters and packages, picked up at one customer and delivered at another. The time in which this has to be done depends on the service level that the customer pays for. To transport the parcels, a network is used consisting of facilities and links, where the facilities have either a regional collection and distribution function, or an inter-regional processing function. The market share that a company has depends on the price and service time the company offers the customers in comparison with the offer of competitors in the market. Optimizing the total profit, the total revenue minus the total cost, is an important objective for these companies. The classical approach to this, is to first determine the prices for the different services, which in turn determine the demand, and then to minimize the costs in the network. This project is aimed at finding a solution approach that integrates this process, and in this way finds better quality solutions in a shorter amount of time. The chosen approach uses efficient formulations and a general purpose MILP-solver for relatively easy problems, and a local search algorithm based on local branching for more difficult problems.

In recent years, the offshore wind industry has grown significantly. The wind turbines are constructed in wind farms, and are serviced with relatively small crew transfer vessels. These vessels transport repair crews from the mainland to the farms and back within a day. One of the big challenges is that these transits can cause motion sickness. If one crew member gets sick, the vessel is legally required to return to the harbour, without performing the repair. It is of interest to predict motion sickness, since both a failed repair and a broken wind turbines that could have been repaired are costly. This can be done by predicting the motion sickness incidence (MSI), which is an objective measure for motion sickness.
The goal of this thesis is to predict MSI using the wave conditions measured in or near the wind farms, by means of an analytical and numerical approach using machine learning. Testing is done on two sites: the Greater Gabbard wind farm and the Westermost Rough wind farm. The analytical approach relates the recorded wave spectrum to the motion spectrum of the vessel, but proves infeasible as a stand-alone method. Gaussian regression, tree ensemble regression and neural networks with Bayesian regularization and backpropagation are the best performing machine learning techniques for MSI prediction. We conclude that the methods from this thesis have sufficient accuracy, by comparing our results with those from Orsted, whose model is already successfully deployed.

The offshore wind industry is rapidly growing, and so is the competition in this market. Normally, offshore installation companies receive a subsidy for building offshore wind farms, but due to multiple companies bidding to install for lower and lower subsidies, the point where wind farms are installed without subsidy has been reached. Therefore, companies have to install wind farms as efficient as possible. Since logistics are a major contributor to costs during the installation of an offshore wind farm, Van Oord and Deltares are doing research methods to solve logistic and scheduling problems. In this thesis, research is done in algorithms to solve two typical planning problems which arise during the installation of offshore wind farms: The Component Relocation Problem (CRP) and the Ship Installation Routing Problem (SIRP).


In the CRP, the storage and movement of turbine components in the harbour is considered. The crane operator manages the storage yard to fulfil a schedule of arriving and departing components. Since access of a storage location by crane can be hindered due to surrounding components, placement and relocation of components such that the requested component is accessible at the requested time, is a challenge. This challenge is solved in the component relocation problem, while minimizing the amount of relocations carried out by the crane.

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A Mixed Integer Linear Programming (MILP) model is developed for this problem, along with an improved formulation to increase the solver performance and solve small instances to optimality. For practical use during offshore installation projects, a rolling horizon heuristic algorithm is developed.

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In the SIRP, an installation schedule with corresponding ship routes is created. To install a turbine, multiple components have to be transported to the required locations, where they will be installed by multiple ships. While creating an installation schedule, it is desired to both minim the travelling time for ships, as the time ships are waiting on other ships and objects. An MILP for this scheduling problem is given, which models this problem as a Vehicle Routing Problem, with extensions to account for installation by multiple vehicles and time synchronization. Furthermore, to solve larger problems, an Adaptive Iterative Simulated Annealing (AISA) algorithm is developed.


The heuristic methods were validated against the exact methods and for small instances the heuristic methods were able to replicate the optimal solutions. The heuristic algorithms provided decisions in less than 12 hours, a relatively short time in comparison to installation times for offshore wind turbines. The AISA was able to create a schedule which drastically decreased the synchronization conflicts in a real world installation project. Although the sailing distance increased in comparison with the original planning, it was improved compared to the executed route. Furthermore, for the same project, the crane routing optimisation led to a reduction of 55% based on non-essential crane actions.

Almost one third of the Dutch population has a fibre optic connection, also called Fibre to the Home (FttH). Fibre is currently the fastest and most reliable Internet technology. It consists of strong and flexible wires that are able to transport light signals over long distances. With such fibre optic connections, information is transmitted from one place to another when pulses of light are sent through an optical fibre and can reach Internet speeds of 500 Mb per second. In an ideal situation, all copper in the networks would be replaced by fiber. However, such an operation would be too expensive to complete all at once, so therefore, it would not be a feasible solution. However, it is also possible to replace parts of the copper network by fibre. For example, the extension of Fibre to the Curb could significantly increase the bandwidth, compared to services offered over a copper cable starting at the Central Office. Furthermore, for this extension, less costs are also involved compared to an extension of Fibre to the Home. On the other hand, the extension to a total fibre network will reach a higher bandwidth compared to an extension of Fibre to the Curb.

In this thesis we develop techniques for solving problems in extremal geometry. We give an infinite dimensional generalization of moment techniques from polynomial optimization. We use this to construct semidefinite programming hierarchies for approximating optimal packing densities and ground state energies of particle systems. For this we define topological packing graphs as an abstraction for the graphs arising from geometric packing problems, and we prove results concerning convergence and strong duality. We use harmonic analysis to perform symmetry reduction and reduce to a finite dimensional variable space in the optimization problems. For this we explicitly work out the harmonic analysis for kernels on spaces consisting of subsets of another space. We show how sums of squares characterizations from real algebraic geometry can be used to reduce the infinitely many constraints to finitely many semidefinite constraints, where we focus in particular on numerical conditioning and symmetry reduction. We perform explicit computations for concrete problems: We give new bounds for binary spherical cap packings, binary sphere packings, and classical sphere packing problems. This can be used, for instance, to give a simple optimality proof of a binary spherical cap packing. We compute the second step of our hierarchy where the numerical results suggest the bound is sharp for the 5-particle case of the Thomson and related problems. This is the first time a 4-point bound has been computed for a continuous problem.@en