Kosten- en Tijdsefficiënte Experimentele Ontwerpen met Meerdere Moeilijk te Veranderen Factoren

Design of Experiments (DoE) stands as a cornerstone of scientific and industrial progress, providing a systematic and rigorous methodology for optimizing processes and understanding complex factor-response relationships. Its application is critical for accelerating innovation, reducing development costs, and ensures product quality across diverse fields, from manufacturing and pharmaceuticals to agriculture. However, despite its established power, the practical application of DoE is often hindered, particularly when experiments involve multiple factors that are difficult or expensive to change between consecutive tests. To address challenges within established experimental structures, this thesis first enhances existing methods for generating designs used to manage experiments with hard-to-change factors, such as split-plot designs. This common design structure efficiently organizes an experiment into 'whole plots', within which the levels of the hard-to-change factors are held constant. Within each whole plot, the levels of easier-to-change factors are then varied across 'subplots'. This hierarchical structure of whole plots and subplots reduces the number of costly or time-consuming resets of the hard-to-change factors. Current algorithms to generate these designs are often computationally slow for cases with more than three levels of nesting (beyond split-split-plot), or rely on assumptions of large variance ratios that may not hold in practice. We address this limitation by generalizing the widely used coordinate-exchange algorithm's update formulas to accommodate an infinite number of nesting levels (the resulting designs being called split^k-plot designs), which significantly enhance computational speed. Using this speedup, we make for a comparison against the state-of-the-art MSS (multi stratum-by-stratum) algorithm (Trinca & Gilmour, 2015), which assumes large variance ratios. We demonstrate that our approach yields designs with a similar D-efficiency when variance ratios are large and up to 109% D-efficiency when variance ratios are small. Furthermore, in a practical application involving a Self-Propelled Forage Harvester (SPFH), our algorithm produces a design with a 110% D-efficiency compared to one constructed with commercial software, an improvement equivalent to adding five or six extra runs to the commercially created experiment. While the previous contribution improves the efficiency of structured designs, especially when the variance ratios are small, a more fundamental challenge persists: the initial 'translation step', where practitioners must convert complex, real-world operational constraints into the rigid, abstract parameters required by classical experimental design generation algorithms. In practice, resources are consumed in two primary and often variable ways: the execution cost of each individual run and the transition cost incurred when altering the settings of experimental factors between runs. Since classical design algorithms require a fixed number of runs as input, rather than a total budget that accounts for these variable costs, the practitioner is forced to estimate a feasible number of runs, often based on an assumed average cost, and then verify the total cost of the resulting design against the budget. This translation is a non-trivial task that demands not only considerable statistical expertise but also significant practical experience, often forcing an oversimplification of the experimental reality and leading to designs that are inefficient or impractical. This translation problem is further compounded by a secondary issue: the potential mismatch between the assumptions of the statistical model and the realities of execution. This is particularly evident in designs with fixed reset intervals, like split-plot designs, where the model assumes a reset occurs between each whole plot to correctly estimate different sources of random error. In practice, a technician might skip a redundant reset if a factor's level remains unchanged, altering the experiment's structure and violating the model's assumptions, which leads to a flawed analysis of the data. To address both of these challenges, this thesis introduces its central innovation: the Cost-Optimized Design of Experiments (CODEX) algorithm. The algorithm optimizes a novel 'generalized staggered-level design', a design structure fundamentally defined by the assumption that a statistical reset only occurs when a factor's level is physically changed. By doing so, the design's structure, with its independent and 'staggered' reset points for each factor, emerges as an outcome of the optimization rather than a rigid constraint, albeit at the cost of introducing more random effects. To remove the translation step, the CODEX algorithm, based on the simulated annealing framework, generates these generalized staggered-level designs by operating directly from a total budget and a function computing the resource consumption of a candidate design. This approach allows CODEX to simultaneously optimize the design structure, run order, and number of runs while explicitly incorporating both experimental and transition costs. The algorithm's ability to adapt is clearly demonstrated in a scenario where the transition cost for a factor scales with the magnitude of the level change. Here, CODEX intelligently generated a design that never makes large, costly jumps between the lowest and highest levels, instead always passing through the intermediate zero level to exploit the cost structure. Comparative studies show that this approach generates designs that are substantially more cost-efficient, achieving D-efficiencies of up to 275% and I-efficiencies of up to 207% over the best equivalent split-plot designs when transition costs are factor-dependent. To demonstrate its practical relevance in applications, the CODEX algorithm is extended to handle multiple simultaneous constraints, an approach termed mCODEX. Real-world experiments rarely operate under a single limiting resource. More often, they are bound by a complex interplay of constraints such as time, budget, material availability, and physical capacity. Two case studies showcase the utility of mCODEX. The first involves a mixture experiment with strict limits on ingredient availability. This case provides a direct comparison with the highly specialized Variable Neighborhood Search (VNS) algorithm by Syafitri et al. (2015) and Goos et al. (2020), another algorithm that dynamically allocates runs based on resource consumption. In this domain, mCODEX consistently produces designs with a statistical efficiency within 1% of those generated by the VNS algorithm, proving its competitive performance. While both algorithms perform similarly in this domain, mCODEX is more generic, capable of handling transition costs, and has a lower computational complexity, making it better suited for the large-scale experiments often found in industry. The second, more intricate case study involves planning an agricultural experiment for an SPFH, which is simultaneously constrained by a tight time window (driven by the high transition costs of rebuilding the machine) and a finite amount of available crop field (where consumption depends on the machine's operating speed). In this scenario, where a split-split-plot design is the best traditional alternative, the mCODEX design dramatically outperforms it, achieving a 56.6% improvement in I-optimality and a 67.6% improvement in D-optimality. This improvement can be broken down into two key components. Firstly, the algorithm discovers a more efficient randomization structure, which alone accounts for an 18.3% improvement in I-optimality and a 29.5% improvement in D-optimality. Secondly, by dynamically allocating runs, mCODEX makes more complete use of the available budget, which contributes an additional 31.6% and 29.8% improvement for I- and D-optimality, respectively. To bridge the gap between methodological innovation and practical application, and to enhance the accessibility of these advanced techniques, an open-source Python package, PyOptEx, was developed. This package serves as a practical toolkit, implementing the algorithms for generating not only traditional optimal split-plot designs but also the novel generalized staggered-level designs via the CODEX and mCODEX algorithms. More than just a design generator, PyOptEx provides a comprehensive suite of tools that supports the entire experimental workflow, from initial problem definition to final data analysis. Its high degree of customization is a core feature, allowing researchers to easily define customized cost functions, intricate constraints, and even novel optimization criteria, thereby adapting the methods to the unique and evolving needs of their specific research problems. To lower the entry barrier, the package is accompanied by extensive documentation, where multiple examples demonstrate the seamless workflow from defining factors and models to generating and evaluating a cost-optimized design within the PyOptEx environment. In conclusion, this thesis establishes and validates a new paradigm for experimental design through the CODEX and mCODEX algorithms. By moving beyond traditional, structure-first methodologies to the optimization of designs directly from real-world resource constraints, this approach yields highly cost-efficient plans that consistently outperform conventional methods, especially in complex industrial settings. Complemented by the PyOptEx software, this research significantly enhances DoE performance, making powerful and effective experimentation more economical and accessible.