Recent developments in quantum annealing have shown promising results in logistics, life sciences, machine learning and more. However, in the field of geophysical sciences the applications have been limited. A quantum annealing application was developed for residual statics estimation. Residual statics estimation is a highly non-linear problem in geophysical subsurface imaging. The problem is run on a quantum annealer as well as on a hybrid solver. Quantum annealers solve binary quadratic models, which are a specific type of NP-Hard problem. The hybrid solver uses quantum annealers together with classical computers to solve optimisation problems. Two binary quadratic models were developed for the purpose of residual statics estimation, one based on the one-hot encoding and the other on standard binary encoding. These two models were theoretically analysed and subsequently implemented and tested. Tests with synthetic data were done using the quantum annealer. The solutions found with quantum annealing were often only a few bit-flips away from the global optimum. Therefore, the results were further improved by post-processing of the data with the steepest descent method. It was found that the one-hot encoding with steepest descent performed superior to the other methods. As a final test the hybrid solver was used to solve a business-sized and realistically difficult problem. The hybrid solver outperformed a current industry standard cross-correlation solver.

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.

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.

Synchromodal freight transport is introduced as intermodal transport, so container transport that uses several transportation vehicles, with an increased focus on a-modal booking, cooperation and real-time flexibility.

It is confirmed that general synchromodal network planning methods are rare or non-existent at the operational level. An extensive framework is developed that describes characteristics of different mathematical synchromodal optimisation problems on the tactical-operational levels.

Three different problems are defined using this framework. Solution methods for these three problems are developed in this thesis, with a focus on low computation times so as to facilitate decision-support and real-time flexibility, and a focus on generality so as to make the methods applicable throughout different organisation structures.

In the first problem, it is assumed that the transportation vehicles have fixed time tables and one only has to decide on a container-to-mode assignment, so by what modality-paths all containers reach their destination against minimal total cost. The containers have release times and deadlines. A model that also allows soft due dates is developed. Moreover, the option of using trucks or other ‘infinite resources’ to help fulfil requests is added. With appropriate graph reductions, this problem can be solved to optimality in little time by solving
the minimum cost multi-commodity flow problem on an appropriate space-time network.

In the second problem, the goal is the same but almost any element can be stochastic: for instance, travel times and container release times could be given a discrete probability distribution rather than a fixed value. Rigorous definitions are formulated to capture the generalities in this stochasticity. Multistage stochastic optimisation and Markov Decision Processes are illustrated, but advised against for their computing time: instead, Expected Future Iteration
and 70%-Pessimistic Future Iteration are developed and shown to yield near-optimal results in a small amount of time in the simulated environment.

In the final problem, there are no stochastic elements, but the decision-maker is given control over the vehicle time tables in addition to the control over container-to-mode assignments. This problem is argued to be a departure from classical optimisation problems, but shown to still be strongly NP-hard. An integer linear program is developed to solve the problem, but
the results show that it scales too poorly to solve problems of ‘real life size’ in an appropriate amount of time for decision support. The Greedy Gain heuristic and Compatibility Clustering heuristic are developed: they solve much more limited sub-problems with the ILP, but unfortunately, even these sub-problems require too much computational effort at the wished instance size.

A number of topics for future research are formulated, giving concrete advice on how to solve the second problem more robustly and how to solve the third problem more quickly.