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In this paper, we present implementations of an annealing-based and a gate-based quantum computing approach for finding the optimal policy to traverse a grid and compare them to a classical deep reinforcement learning approach. We extended these three approaches by allowing for stochastic actions instead of deterministic actions and by introducing a new learning technique called curriculum learning. With curriculum learning, we gradually increase the complexity of the environment and we find that it has a positive effect on the expected reward of a traversal. We see that the number of training steps needed for the two quantum approaches is lower than that needed for the classical approach.

Operations Research (OR) can be dened as a scientic approachto the solution of problems in the management of complex systems.It uses quantitative methods to help decision makers design, analyse,and improve the performance or operation of these systems. An im-portant part of this, is dening and solving optimisation problems.One can only be interested in nding the best solution, but often (inpractice) a combination of, or interaction between, the quality of thesolution and the computation time is important. Model-based algo-rithms and heuristics have traditionally played a role in this, however,data-based methods such as machine learning are increasingly used.Hardware improvements are also not to be underestimated. A majorimprovement in the computing power of conventional computers hasmade problem solving methods more ecient over the past 40 yearsand is still ongoing. This is currently being reinforced by the useof GPU processors, the emergence of quantum computers and othertechnological solutions such as photonic accelerators. This playingeld of OR problems and the use of machine learning and existingand emerging hardware accelerations to dene and solve them is thetopic of the eld of `Computational Operations Research', which isdiscussed further in this article.

Quantum computers have the potential to outshine classical alternatives in solving specific problems, under the assumption of mature enough hardware. A specific subset of these problems relate to military applications. In this paper we consider the state-of-the-art of quantum technologies and different applications of this technology. Additionally, four use-cases of quantum computing specific for military applications are presented. These use-cases are directly in line with the 2021 AI strategic agenda of the Netherlands Ministry of Defense.

Quantum machine learning has the potential to overcome problems that current classical machine learning algorithms face, such as large data requirements or long learning times. Sampling is one of the aspects of classical machine learning that might benefit from quantum machine learning, as quantum computers intrinsically excel at sampling. Current hybrid quantum-classical implementations provide ways to already use near-term quantum computers for practical applications. By expanding the horizon on hybrid quantum-classical approaches, this work proposes the first implementation of a gated quantum-classical hybrid Helmholtz machine, a gate-based quantum circuit approximation of a neural network for unsupervised tasks. Our approach focuses on parameterized shallow quantum circuits and effectively implements an approximate Bayesian network, overcoming the exponential complexity of exact networks. In addition, a new balanced cost function is introduced, preventing the need of millions of training samples. Using a bars and stripes data set, the model, implemented on the Quantum Inspire platform, is shown to outperform classical Helmholtz machines in terms of the Kullback–Leibler divergence.

In quantum circuit design, the question arises how to distribute qubits, used in algorithms, over the various quantum computers, and how to order them within a quantum computer. In order to evaluate these problems, we define the global and local reordering problems for distributed quantum computing. We formalise the mathematical problems and model them as integer linear programming problems, to minimise the number of SWAP gates or the number of interactions between different quantum computers. For global reordering, we analyse the problem for various geometries of networks: completely connected networks, general networks, linear arrays and grid-structured networks. For local reordering, in networks of quantum computers, we also define the mathematical optimisation problem.

With quantum computers entering a new phase of maturity and quantum algorithms covering a growing range of applications, it is important that the two meet at some point in the middle. Currently, the two meet only by toy-problem implementations for some algorithms. In this work, we extend a recently proposed distance-based classifier and give explicit quantum circuit implementations, and we give a method to overcome restrictions on the data, present in the original work.

In vehicular ad-hoc networks a path has to be found to send a message from one vehicle to another vehicle. This path has to have a connectivity rate that is high enough to obtain a high probability of arrival of the message. In other approaches, the average distance between vehicles on a link of the network is used as metric for connectivity. In this paper, an other metric is proposed, based on the average and standard deviation of the distances between the vehicles to reach a metric that performs better. © Springer Nature Switzerland AG 2019.

In logistic delivery chains time windows are common. An arrival has to be in a certain time interval, at the expense of waiting time or penalties if the time limits are exceeded. This paper looks at the optimal placement of those time intervals in a specific case of a barge visiting two ports in sequence. For the second port a possible delay or penalty should be incorporated. Next, recognising these penalty structures in data is analysed to if see certain patterns in public travel data indicate that a certain dependency exists.

Problem statements and solution methods in mathematical synchromodal transportation problems depend greatly on a set of model choices for which no rule of thumb exists. In this paper, a framework is introduced with which the model choices in synchromodal transportation problems can be classified, based on literature. This framework should help researchers and developers to find solution methodologies that are commonly used in their problem instance and to grasp characteristics of the models and cases in a compact way, enabling easy classification, comparison and insight in complexity. It is shown that this classification can help steer a modeller towards appropriate solution methods.

Research regarding the optimal planning of distributed generation is often based on coarse energy use and generation data, which does not accurately reflect real variations in energy profiles. This paper investigates the impact of this lack of temporal variation on the optimal planning of distributed generation. The problem of loss minimization in the residential setting is used as a guideline. The outcomes of a stochastic optimization model for energy profiles defined on different time aggregation levels are compared. At first glance, modeling on a finer time scale seems to affect optimal planning solutions, with a shift from variable stochastic sources to sources that provide constant generation. However, it turns out that the gains of using these new optimal solutions in terms of reducing energy losses are limited. The results suggest that for optimization purposes it is not necessary to use data at a resolution smaller than hourly time steps. If energy profiles are defined on time steps smaller than one hour it is important that the full range of the stochastic fluctuations is taken into account, rather than evaluating a couple of scenarios.

Mobile operators' investments depend largely on the costs of the radio network. The efficiency of building and maintaining the radio network is determined largely by the quality of the radio planning process. The planning tool, the propagation predictions and the spatial traffic input together are the key ingredients of the planning process. In this paper we describe a method to create high quality spatial traffic grid by combining network measurements and propagation predictions with demographic, vector and clutter type data in a statistical model. This gives results of a precision that commonly applied traffic spreading methods in planning tools cannot achieve and gets more and more important when planning micro cells. Operators can achieve large savings on network investments and manual optimisation, while delivering the desired quality by applying these traffic grids.

The need for higher bandwidth by customers urges the network providers to upgrade their networks. Fibre to the home or Fibre to the curb are two of the scenarios that are considered. To make a proper assessment on the economic viability, a good estimation of the roll-out costs of the networks are important. Geometric models are easy to use for this estimation, but can be inaccurate. In this paper a new method to enhance the parameters of the geometric model is presented. The performance of this method is shown in comparison with geographic models on real cases both for Fibre to the Home as for Fibre to the Curb.

With 23 percent of all births taking place at home, The Netherlands have the highest rate of home births in the world. Also if the birth did not take place at home, it is not unusual for the mother and child to be out of hospital in a few hours after the baby was born. The explanation for both is the very well organised maternity care system. However, getting the right maternity care nurse available on time introduces a complex planning issue that can be recognized as a Stochastic Assignment Problem. In this paper an expert rule based approach is combined with scenario analysis to support the planner of the maternity care agency in his work.

Rolling out a Fibre to the Home (FttH) architecture is very expensive, mainly due to all the trenching that is labour extensive. In this paper we present a method for planning the last mile in FttH in a cost effective way and extend this method for incorporating and minimizing the inconvenience and social costs this work brings. To do this, we model the problem of connecting the houses with FttH in a novel way: we know already where the fibre segments have to be, but how to connect them to create a coherent network? This can be modelled as a Minimal Steiner Tree problem. Next we present a heuristic approach to solve this node and edge weighted Minimum Steiner Tree problem and introduce a method to incorporate smart co-laying opportunities in this approach, which are called the the timing benefits.

At this moment consumers want an internet connection with 20-50 Mb/s speed and around 100 Mb/s in the near future. Rolling out Fibre to the Curb networks quickly will be the only way for telecom operators in some countries to compete with cable tv operators. This requires a fibre connection to the cabinets. When the telecom operator wants toconnect the cabinets in a ring structure, he has to decide how to divide cabinets over a number of circuits, taking into account a maximum number of customers per circuit. This we call the cabinet clustering problem. In this paper we formulate this problem, present the heuristic approch we developed and show the results of our extensive testing that shows the method is accurate and fast. Finally we demonstrate the method on a real life case.

If an operator has as starting position a Full Copper topology in which ADSL or VDSL is offered from the Central Office, the next choice he has to make is to provide Full FttH or use an other topology option, e.g. FttCab, first as intermediate step to provide a next generation service package. In this paper we present a gradual topology migration path from Full Copper via FttCab and Hybrid FttH towards Full FttH. We look at the planning issues of this topology migration and the financial impact in comparison to the direct FttH roll-out. For this we present a case study in which we compare the costs of the presented gradual topology migration path to the alternative Full FttH direct option

A first step in congestion management is making sure that the average production and consumption per time unit over time match as well as possible, we call this tactical congestion management. The main question in this paper is: what is an optimal mix of DGs such that electricity loss is minimized.