In this paper we study encounter-based density estimation using different random walks and analyse the effects of the step-size on the convergence of the density approximation. Furthermore, we analyse different types of random walks, namely, a uniform random walk, with every position equally likely to be visited next, a classical random walk and a quantum-inspired random walk, where the probability distribution for the next state is sampled from a quantum random walk. We find that walks with additional steps lead to faster convergence, but that the type of step, quantum-inspired or classical, has only a marginal effect.

With the rise of quantum computing, many quantum devices have been developed and many more devices are being developed as we speak. This begs the question of which device excels at which tasks and how to compare these different quantum devices with one another. The answer is given by quantum metrics, of which many exist today already. Different metrics focus on different aspects of (quantum) devices and choosing the right metric to benchmark one device against another is a difficult choice. In this paper, we aim to give an overview of this zoo of metrics by grouping established metrics in three levels: component level, system level and application level. With this characterization, we also mention what the merits and uses are for each of the different levels. In addition, we evaluate these metrics on the Starmon-5 device of Quantum Inspire through the cloud access, giving the most complete benchmark of a quantum device from an user experience to date.

Quantum computing could be a potential game-changer in industry sectors relying on the efficient solutions of large-scale global optimization problems. Exploration geoscience, is full of optimization problems and hence is a good candidate for application of quantum computing. It was recently suggested that quantum annealing, a form of adiabatic quantum computer, is a much better suited quantum computing platform for optimization problems than gate-based quantum computing. In this work, we show how the residual statics estimation problem can be solved on the quantum annealer and present our first results obtained on a quantum computer.

In logistic problems, an Integral Multi-Commodity Network Design Problem on a time-space network is often used to model the problem of routing transportation means and assigning freight units to those means. In Physical Internet and Synchromodal networks an interactive planning approach is preferable, meaning that calculation times of a single planning step should be short. In this paper we provide ways to reduce the size of the problem formulation based on cutting planes, that are effective in reducing the computation time for Integer Linear Programming problem-based solution methods.

In this paper an online optimisation approach is proposed which can be used to find an appropriate combined schedule and container assignment in a Network Design Problem under uncertainty. For this, a simulation based approach on a multi-period time window is proposed, moving forward on the time window after each decision made, assuming that the status of the system is updated as soon as the stochastic and unknown elements become deterministic and known. This approach provides new insight and knowledge into synchromodal and multimodal planning problems. The results of the approach are compared to the results of three simpler online optimisation methods and to the solution of the offline approach where all information is known.

Central in this paper is a transportation network, in which containers are transported for multiple agents. This network is modelled by a Space Time Network, in which the travel time of modalities is fixed and independent of the occupancy of the network. To find the best allocation of containers to paths in this network, a flow problem can be solved. The System Optimal solution found then is the solution in which the total costs of the network are minimised. This paper introduces the idea of a fair User Equilibrium solution in such problem. The proposed approach changes the network, using a toll scheme, such that the fair User Equilibrium Solution in this changed network equals the System Optimal solution in the original network. This can be used to fairly redistribute the cost of the network among the users.