Decision diagrams have steadily become more prominent in the field of combinatorial optimization, being able to outperform the state-of-the-art in e.g. scheduling problems[13]. They have proven even more capable with the introduction of methods such as decision diagram-based Branch & Bound. Often, layer-based binary decision diagram (BDD) encodings are used to encode the problem domain, where a layered structure determines the decisions and decision variables. Recently, state-based multivalued decision diagram (MDD) encodings have also been considered. These do not rely on a layered structure, as instead, each state makes its decisions on the variables independently of other states. This allows for more flexible decision-making as states do not have to compromise with other states on the decisions they make.

This thesis compares these newer state-based MDDs with the commonly used layer-based BDDs, while also introducing and evaluating heuristics for the state-based MDDs. These heuristics include a new beam restriction heuristic that limits the branching factor of the MDDs, a dynamic variable ordering strategy adapted for the new state-based context, and a new local bound for the maximum independent set problem (MISP).

The experiments of this thesis show that the state-based MDDs generally outperform the layer-based BDDs in both runtime and search tree size. Only for some instances with low graph densities, the state-based MDDs were slower. This is resolved with the newly introduced beam restrictions, which can significantly lower the runtime. This speedup is also shown for the graph coloring problem, although the application of the beam restrictions is not as straightforward there as with the MISP. Both the dynamic variable ordering and the new local bound for the MISP show great promise in increasing the efficiency of the search, but are both held back by the additional overhead they introduce. Fortunately, these two techniques can share the added overhead while gaining the combined benefits, resulting in great performance for the MISP when both methods are used together.

This study investigates scheduling strategies for the stochastic duration flexible job-shop problem with no-wait and general time lags constraints (FJSP/NW-GTL). Progress in Constraint Programming (CP) and temporal-networks has renewed interest in assessing the strengths and limitations of different proactive and reactive scheduling approaches. This paper covers the application of a CP-based fully proactive method, a reactive method and STNU-based method on the FJSP/NW-GTL problem comparing results in terms of predetermined objectives and feasibility. In addition, the paper aims to answer how different distributions for task duration affect feasibility and performance. Our results show that strictly proactive methods are infeasible for no-wait constraints and very tight schedules, which lead to adding an online step in the proactive implementation to pursue the comparison between the approaches. With this change, plotting the average makespan across methods by distribution shows that there is not much fluctuation between distribution types in terms of makespan. Moreover, it appears that the proactive method performs the best, followed closely by the reactive method, while the STNU approach results in a notably higher makespan for the same instances. Notably, in terms of feasibility, the proactive and reactive approach have 100% rate of success compared to the STNU approach which is infeasible on 35% of the instances in the dataset.

This report investigates the effectiveness of Simple Temporal Networks with Uncer- tainty (STNUs) for solving the Stochastic Flexible Job-Shop Scheduling Problem with Sequence-Dependent Setup Times (SFJSP-SDST), comparing it against proactive and reactive Constraint Programming (CP) approaches. Using a benchmark dataset with varying noise levels, the study evaluates solution quality, feasibility, and computational cost. Results show that the reactive method achieves the lowest makespan due to its dy- namic rescheduling capability but incurs high online computation time. The proactive method offers fast execution, while the STNU-based approach provides a dynamically controllable schedule, albeit with conservative makespans.

This study investigates the performance of three dynamic scheduling approaches—proactive, reactive, and STNU-based—for solving the Multi-Mode Resource-Constrained Project Scheduling Problem with maximal time-lags and no-wait constraints (MMRCPSP/max) in uncertain environments. The performance of the approaches is validated on three key performance measures: solution quality (makespan), offline computation time, and online computation time. Drawing from the current work on stochastic RCPSP/max, this research introduces a more realistic formulation of the problem with multi-mode execution, generalised time lags, and no-wait constraints, under the PyJobShop library and stochastic duration modelling. Experimental results, based on altered PSPLIB instances, show that the three algorithms yield similar feasibility rates. However, they show distinct trade-offs in terms of solution quality, time offline, and time online. The proactive algorithm requires the shortest offline and online computational times, but provides slightly worse makespans. The STNU-based algorithm produces the best average solution quality, with significantly higher offline time. The reactive algorithm offers competitive offline times and solution quality, but has the largest online computational time. The findings provide insight into the trade-offs in solution quality and computational time in dynamic project scheduling and offer insight for using the strategies in the real world.

Modern manufacturing systems must meet hard delivery deadlines while coping with stochastic task durations caused by process noise, equipment variability, and human intervention. Traditional deterministic schedules break down when reality deviates from nominal plans, triggering costly last-minute repairs. This thesis combines offline constraint-programming (CP) optimisation with online temporal-network execution to create schedules that remain feasible under worst-case uncertainty.

First, we build a CP model of the flexible job-shop with per-job deadline tasks and insert an optimal buffer Δ* to obtain a fully pro-active baseline. We then translate the resulting plan into a Simple Temporal Network with Uncertainty (STNU) and verify dynamic controllability, which guarantees that a real-time dispatcher can retime activities for every bounded duration realisation without violating resource or deadline constraints. Extensive Monte-Carlo simulations on the open Kacem 1–4 benchmark suite show that our hybrid approach eliminates 100 % of deadline violations observed in state-of-the-art meta-heuristic schedules, while adding only 3 – 5 % makespan overhead. Scalability experiments confirm that CP solve-times and STNU checks remain sub-second on medium-size instances.

The work demonstrates how temporal-network reasoning can bridge the gap between proactive buffering and dynamic robustness, moving industry a step closer to truly digital, self-correcting factories.

The transition towards renewable energy requires long-term energy system planning, which depends on solving constrained optimization (CO) problems. These CO problems are becoming increasingly complex, particularly due to the variability introduced by renewable energy sources. Traditional optimization methods struggle to scale with this growing model complexity. In contrast, machine learning approaches allow faster solution computation, but offer only approximate solutions with no guarantees on solution quality, thereby limiting reliability and interpretability in planning applications.

This research addresses these limitations by exploring the use of neural networks to predict feasible solution pairs for the primal and dual formulations of the CO problem, enabling approximate solutions accompanied by bounds on suboptimality. Self-supervised primal-dual learning (PDL) is adapted and extended to produce paired feasible solutions for both the primal and dual formulations of an economic dispatch problem. Feasibility in the primal network is enforced through differentiable repair and completion layers, including novel domain-specific extensions that adjust supply-demand balancing priorities, which were found to be essential for predictive accuracy. This then exposes a structural limitation of PDL: while repair and completion layers are essential for primal learning, they prevent the learning of meaningful dual predictions. To address this, the dual network is trained using a modified loss function that directly optimizes the dual problem, enabling the use of a completion layer adopted from the literature to ensure dual feasibility. An additional novel classification-based layer that incorporates prior knowledge on the dual variables further improves the dual prediction quality when applied to the economic dispatch problem. Finally, the trained networks are integrated into Benders decomposition, a technique that breaks CO problems into easier, independent problems. This enables a hybrid approach: approximate solutions with bounds on suboptimality can be obtained swiftly, whereas exact solving remains available if necessary, retaining all theoretical convergence and optimality guarantees and potentially reducing computational time.

The proposed framework is evaluated on a generation expansion planning problem, where the economic dispatch subproblems are solved iteratively using the trained networks. The results demonstrate a theoretically grounded and empirically validated proof of concept for producing solutions with quality guarantees using learning-based methods, which is generally applicable to any problem compatible with Benders decomposition where the resulting subproblem admits a conic formulation. However, the results do not show conclusive speed-ups due to a mismatch between the training data and the data encountered during Benders iterations. By demonstrating how neural networks can be used to generate approximate, feasible solutions accompanied by theoretical guarantees on solution quality, this research contributes to the advancement of scalable and reliable constrained optimization methods for energy systems.

Production planning in the biomanufacturing sector presents significant challenges due to uncertainties in job durations caused by biological variability, environmental conditions, and raw material quality. Traditional scheduling methods typically fail to adapt to these uncertainties, leading to suboptimal outcomes. This research addresses this issue at DSM-Firmenich, focusing on optimizing production planning while maximizing profit, adhering to deadlines, and efficiently utilizing resources. We propose an integrated approach using Mixed-Integer Linear Programming (MILP) and Constraint Programming (CP) models, alongside Probabilistic Simple Temporal Networks (PSTNs) to handle uncertainty in real-time scheduling. The study introduces an offline optimization procedure for proactive scheduling decisions and a reactive real-time algorithm for adjustments of the planned schedule. This work showcases the potential of applying PSTNs in biomanufacturing and sets the stage for future research aimed at enhancing real-time execution strategies in factory environments.

This thesis investigates improving the group project matching algorithm of TU Delft's Project Forum platform. We formalize the matching problem as a many-to-one, one-sided matching with group formation, where students have preferences over project topics and may wish to pregroup with peers.

We implement and evaluate two mechanisms: Chiarandini – a mechanism reimplemented from the literature and adapted to our grouping setting – and our novel Fair mechanism which incorporates additional fairness considerations for pregrouping. Both use mixed integer linear programming. Leximin is selected as the objective function. These two mechanisms are compared to our previous mechanism, BEPSys, which matches greedily determined groups of students to projects using an optimal algorithm.

Our evaluation uses historical instances from TU Delft and SDU as well as synthetic instances that we generate. Results show that both new mechanisms significantly outperform the prior BEPSys algorithm, both in terms of quality of results and runtime. Our novel Fair mechanism successfully allows pregrouping without disadvantaging solo students, although sometimes at significant cost to pregrouping students. The leximin objective, implemented using an ordered weighted averaging function, is shown to not work optimally in some tested instances.

Decision-Focused Learning (DFL) focuses on a setting where a system gets as input some features and needs to predict coefficients to a downstream optimization problem. Classically, one would apply a two-stage solution, which trains the predictor as a regression task and only uses the optimizer during evaluation. However, the two-stage solution fails to optimize the downstream optimization problem. As such, one might use DFL techniques to train the predictor. Nonetheless, these fail to take the entire solution space into account and only optimize toward the optimal true solution, and as such, they might fail to optimize the total downstream value. Furthermore, these techniques are computationally expensive.

We tackle these two problems using Decision Diagrams (DDs) for DFL. DDs for DFL have three main benefits. First, the DD can be cached between runs, speeding up the training loop. Second, we present four novel loss functions that use DDs to reason efficiently over entire solution spaces. Furthermore, we introduce a novel method to relax the DDs to reduce solve-time during training.

We experimentally show that the DDs speed up the training loop substantially. We further show that the DFL losses perform on par with other state-of-the-art DFL losses. Finally, we experimentally show when and which losses work with relaxed DDs.

Path finding is an important component in solving a wide array of engineering problems, ranging from video games to real-life applications such as automated warehouse management and autonomous vehicles.
Path finding algorithms are designed to solve complex problems, and in order to do so, assumptions are necessary to simplify the problems.
While these assumptions are important, using them makes the obtained algorithms less applicable to a real-life scenario, and as such, verifying how lifting some of them would affect the obtained results is worth pursuing.

Two main assumptions were identified and subsequently lifted.
First, classic multi-agent path finding algorithms use a centralized approach, where solutions are computed before execution.
This results in a long computation period followed by execution. Lifting this assumption results in a decentralized approach where agents solve conflicts on the go, while approaching their target.
The second assumption made by state of the art algorithms is that agents participating in a multi-agent path finding problem share a common goal: minimizing a global cost function.
This is not always applicable, as in a real-life scenario participating agents can have selfish goals.
This assumptions has been lifted by allowing agents to negotiate their paths by trading with the other participants to create better solutions for themselves.

The Selfish Localized Pathfinding (SLP) algorithm has been designed to lift these assumptions. It describes a decentralized algorithm that allows participating agents to negotiate their paths, which makes a good candidate for an application closer to real-life.

The SLP algorithm has been tested in order to evaluate its performance, both in terms of its ability to solve a set of test cases, and in terms of the cost incurred by the participating agents.
SLP performed well in varied domains.
SLP solved significantly more cases than Conflict Based Search, a centralized state of the art path finding algorithm.
This comes at the expense of an increase in the path lengths obtained by the algorithm.
This downside is offset by the significant decrease in the time required to solve problems, which can be divided in small clusters due to the decentralized approach of the algorithm.
On the whole, SLP can provide a good alternative to Conflict Based Search.

When addressing combinatorial optimization problems, the focus is predominantly on their computational complexity, and it is often forgotten to look at the bigger picture. As a result, it is common to miss critical details which could play a major role in the overall process. One such detail is the presence of uncertainty in the real world. A naive approach might directly predict values for the uncertain parameters, without taking into account that the ultimate goal is to obtain sound decisions. Consequently, in many cases, the resulting solutions are suboptimal. This challenge is precisely the premise behind Decision-Focused Learning (DFL) framework, which is a core of this work. This study pioneers the application of the DFL framework to scheduling problems with uncertain processing times, utilizing contextual features to predict these uncertainties. By employing the promising Score Function Gradient Estimation method, the research tackles the issue of non-differentiable regret loss functions in DFL. Key contributions include the development of techniques to enhance the performance of the Score Function, an in-depth analysis of DFL's applicability to complex scheduling scenarios, and a detailed evaluation of its strengths and weaknesses. This work not only demonstrates the potential of DFL in this new context but also lays the groundwork for future research and improvements in handling uncertainty in combinatorial optimization.

Shunting yards are locations next to train stations that serve as parking places for trains when they are not in operation and often contain facilities for maintenance and cleaning for passenger trains. Planning of the tasks regarding shunting trains involves routing, assignment of tracks, and scheduling tasks. This is done manually and requires a lot of effort, making it inefficient. Identifying patterns specific in the arrival times of trains at shunting yards can help to predict future train arrivals and potential delays throughout the year more accurately. This enables the alignment of staff and equipment with train arrivals, minimizing idle time and optimizing cost efficiency.
This research focuses on extracting and analyzing the arrival times of trains at shunting yards using a dataset consisting of GPS data. It conducts two algorithms to cluster the given data for each train unit within and across days to identify the same train across different days. Distributions and heatmaps of the arrival times and delays are created based on the identified train series. They are analyzed to identify patterns in train arrival times and delays across different months.

Solutions for the Train Unit Shunting Problem are constantly being researched and improved to be- come more efficient and match the needs of train transport in the Netherlands. For this reason, we are exploring new ways to find patterns in the train data to identify where those solutions could be en- hanced. More specifically, we are trying to find patterns that make identifying different locations possible. We identify patterns in the capacity of the shunting yards and the types of trains used in various locations, which result in reasonable ac- curacy in classification. Some locations operate closer to their capacity, and some require longer paths to get inside the shunting yards. These find- ings could be helpful not only for the planning algo- rithms but also in identifying which locations might need expansion or restructuring and where more of the train fleet should be allocated.

This paper analyses manually realised solutions to the Train Unit Shunting Problem (TUSP) to find patterns in train type. The parking element is most important for the TUSP. Therefore, this research specifically investigates the presence of train type patterns in parking track and parking time. The difference in the patterns between main train type and train subtype is also analysed. The study uses statistical hypothesis testing to look for biases between individual train types and parking tracks. Kernel density estimation is used to analyse the differences in parking time between the types. The results show that there are strong patterns in type and parking track, but no clear difference in parking time. Considering subtype results in the differences being more specific. It is suspected that the strongly present track pattern is a strategy used by human planners.

We investigate the generalization performance of predictive models in model-based reinforcement learning when trained using maximum likelihood estimation (MLE) versus proper value equivalence (PVE) loss functions. While the more conventional MLE loss aims to fit models to predict state transitions and rewards as accurately as possible, value-equivalent methods (e.g. PVE) prioritize value-relevant features. We show that in a tabular setting, MLE-based models generalize better than their PVE counterparts when fit to a small number of training policies, whereas PVE-based models perform better as the number of policies increases. With increasing model rank, generalisation error tends to improve for MLE and PVE, and the two become closer in generalisation ability.

This research aims to find patterns in the live position data of trains within shunting yards. These patterns can be converted to heuristics and applied in algorithms developed by railway operators in the Netherlands to tackle the Train Unit Shunting Problem. The usage patterns were extracted from real-world location data of train units. Specifically, this research focuses on finding patterns in the paths taken in both temporal and spatial metrics. These investigations identified the busiest times in the shunting yards according to various metrics, such as the total number of trains and the number of serviced trains. These metrics are extracted from the type of train movement at a given moment, which was provided with the dataset. The accuracy of the provided train movement category has been analyzed and shown to be inaccurate for uses within shunting yards compared to a proposed approach. Finally, an algorithm for classifying train units that belong to the same train has been shown to have initial success.

When not in service, trains are parked and serviced at shunting yards. The Train Unit Shunting Problem (TUSP), an NP-hard problem, encompasses the challenge of planning movements and tasks in shunting yards. A feasible shunting plan serves as a solution to the TUSP. Current automated planning tools utilized to assist human planners in this computationally heavy planning task are not able to distinguish inherent patterns in input train data, as opposed to humans. This paper aims to address this technological gap by examining whether valuable patterns could be extracted from shunting plan data, consisting of solutions to the TUSP. More specifically, it is mainly concerned with the automatic detection of whether a solution to the TUSP is a week or a weekend day. Therefore, the data is examined for the presence of several groups of patterns. Moreover, binary classification is performed on the data. The experiments conducted in this study suggest the presence of valuable patterns in the data, which could be leveraged to design specialized heuristics for automated planning models tailored to generate shunting plans for weekdays and weekends.

Due to the increased demand for train travel, train operators are considering increasing their rolling stock. Before achieving this, they must enhance the capacity of their shunting yards. This is attempted by improving methodologies for solving the Train Unit Shunting and Servicing (TUSS) problem. To address the TUSS problem, a planner determines routes on shunting yards for trains, ensuring they visit designated service tracks before parking in a configuration that facilitates a smooth departure.
TUSS is a well-studied problem, and various approaches have been proposed. The first approach capable of solving real-world, complete TUSS instances is a local search method introduced by van den Broek et al. In this thesis, we explore an alternative approach using PDDL models. PDDL is the standard language for describing Automated Planning problems. Automated Planning is a well-established field within artificial intelligence, and new, improved algorithms are continually developed to solve PDDL models for problems similar to TUSS.
In this thesis, we design a detailed model in PDDL and propose several methods to simplify the model so that planning algorithms perform more efficiently compared to the detailed model. When solving simplified models, a post-processing routine is employed to generate detailed shunting plans. The performance of several model-independent PDDL planners was analysed, and the best-performing planner was identified as Temporal FastDownward.
By analysing plans obtained from experiments, we identified areas for improvement. Based on this knowledge, we developed a new TUSS-specific planner called Train Order Preserving Search (TOPS). TOPS employs a search algorithm with effective pruning of symmetrical states and a custom heuristic that guides the search towards states where the order of trains aligns with the departure order. TOPS significantly outperformed Temporal FastDownward in these experiments.

Computational efficiency is essential for large-scale mathematical optimisation problems, such as the generation expansion planning problem, to be practically applicable. In linear programming solvers, crossover is frequently a bottleneck when solving optimisation problems. This study aims at determining why crossover is a bottleneck in solving the generation expansion planning problem and deriving a method which obtains an optimal solution faster. Symmetry was found to be disrupting crossover, causing its runtime to significantly increase. However, the preceding barrier method benefit from the symmetry handling of the solver. An alternative approach using problem-specific knowledge to reduce symmetry before serving the model to a solver was proposed. The key to the efficiency of this method is using the information of how symmetries are reduced when retrieving the solution to the original problem. The approach was applied to two types of symmetry we identified in the generation expansion planning problem, leading to a significant speed-up of the crossover phase and total runtime for the algorithm resolving a formulation symmetry, but a longer runtime for the method resolving a more practically available non-formulation symmetry. However, the latter was faster in a couple of cases and has many directions for future improvements. The results of this research, thus, demonstrate that domain knowledge of linear programming problems can be applied to reduce symmetry that state-of-the-art solvers cannot detect and to more efficiently obtain an optimal solution than traditional crossover.

When trains are not actively traveling on the main rail network, they to be parked and prepared for their next journey. This is a complex problem, involving several interconnected subproblems. Additionally, there is uncertainty in this environment which can render initial plans infeasible during their execution. To ensure trains are able to depart in time, having finished all their required service tasks, a schedule is created in advance.

The focus of this thesis is to address the challenges associated with generating robust initial shunting plans in an uncertain environment. This thesis focuses on a sequential problem formulation, modeled as a Markov Decision Process (MDP) and uses a policy optimized for this environment. The goal is to design a method capable of deriving robust initial shunting plans from the policy that are likely to remain feasible for a large number of possible plan executions.

The limitation addressed in this thesis, is that conventional policy-rollout techniques generate action sequences that overlook most alternative outcomes, thereby making the overall plan not feasible for a large number of plan realizations. To address this issue, the thesis proposes two distinct solution methods, aimed to consider every possible state that might be encountered, either directly or indirectly.

Through experimentation on realistically generated problem instances, the research concludes that both proposed methods significantly outperform the baseline approach, demonstrating the possibility of extracting robust initial shunting plans from a given policy that was not explicitly designed for this purpose.