Edmund K. Burke’s research while affiliated with Bangor University and other places

Routing and scheduling problems with increasingly realistic modelling approaches often entail the consideration of multiple objectives, time constraints, and modelling the system as a multigraph. This detailed modelling approach has increased computational complexity and may also lead to violation of the additivity property of the costs. In the worst scenario, increased complexity makes the problem intractable for exact algorithms. Even when the problem is solvable, exact algorithms may not provide solutions within the given time budget, and the found solutions are not guaranteed to be optimal due to the additivity property violation. Approximate solution methods become more suitable in this case. This paper focuses on one particular real-world application, the Airport Ground Movement Problem, where both time constraints and parallel arcs are involved. We introduce a novel Memetic Algorithm for Routing in Multigraphs with Time constraints (MARMT) and present a comprehensive study of its different variants based on diverse genetic representation methods. We propose a local search operator that enhances search efficiency and effectiveness. MARMT is tested on real data based on two airports of different sizes. Our results show that MARMT does not suffer from the non-additivity property problem as it outperforms the state-of-the-art exact algorithm when allowed to converge. When a time budget of 10 seconds is imposed on MARMT, it is able to provide solutions with quality comparable (within 1-5% degradation) to the ones given by the exact algorithm with respect to the aggregated objective values. MARMT can be adapted for other applications, such as train operations.

Multi-graphs where several edges connect a pair of nodes are an important modelling approach for many real-world optimisation problems. The multi-graph structure is often based on infrastructure and available connections between nodes. In this study, we conduct case studies for a special type of constrained routing and scheduling problems. Using the airport ground movement problem as an example, we analyse how the number of parallel edges and their costs in multi-graph structure influence the quality of obtained solutions found by the routing algorithm. The results show that the number of parallel edges not only affects the computational complexity but also the number of trade-off solutions and the quality of the found solutions. An indicator is further proposed which can estimate when the multi-graph would benefit from a higher number of parallel edges. Furthermore, we show that including edges with dominated costs in the multi-graph can also improve the results in the presence of time window constraints. The findings pave the way to an informed approach to multi-graph creation for similar problems based on multi-graphs.

Industrial software often has many parameters that critically impact performance. Frequently, these are left in a sub-optimal configuration for a given application because searching over possible configurations is costly and, except for developer instinct, the relationships between parameters and performance are often unclear and complex. While there have been significant advances in automated parameter tuning approaches recently, they are typically black-box. The high-quality solutions produced are returned to the user without explanation. The nature of optimisation means that, often, these solutions are far outside the well-established settings for the software, making it difficult to accept and use them. To address the above issue, a systematic approach to software parameter optimization is presented. Several well-established techniques are followed in sequence, each underpinning the next, with rigorous analysis of the search space. This allows the results to be explainable to both end users and developers, improving confidence in the optimal solutions, particularly where they are counter-intuitive. The process comprises statistical analysis of the parameters; single-objective optimization for each target objective; functional ANOVA to explain trends and inter-parameter interactions; and a multi-objective optimization seeded with the results from the single-objective stage. A case study demonstrates application to business-critical software developed by the international airline Air France-KLM for measuring flight schedule robustness. A configuration is found with a run-time of 80% that of the tried-and-tested configuration, with no loss in predictive accuracy. The configuration is supplemented with detailed analysis explaining the importance of each parameter, how they interact with each other, how they influence run-time and accuracy, and how the final configuration was reached. In particular, this explains why the configuration included some parameter settings that were outwith the usually recommended range, greatly increasing developer confidence and encouraging adoption of the new configuration.

The nurse rostering problem is a very important problem to address. Due to the importance of nurses’ jobs, it is vital that all the nurses in a hospital are assigned to the most appropriate shifts and days so as to meet the demands of the hospital as well as to satisfy the requirements and requests of the nurses as much as possible. Nurse rostering is a computationally hard and challenging combinatorial optimisation problem. To solve it, general and efficient methodologies such as selection hyper-heuristics have emerged. To address the multi-stage nurse rostering formulation, posed by the second international nurse rostering competition’s problem, a sequence-based selection hyper-heuristic that utilises a statistical Markov model is developed. The proposed algorithm incorporates a dedicated algorithm for building feasible initial solutions and a series of low-level heuristics with different dynamics that respect the characteristics of the competition’s problem formulation. Empirical results and analysis suggest that the proposed approach has a significant potential on difficult problem instances.

Current integer programming solvers fail to decide whether 12 unit cubes can be packed into a 1x1x11 box within an hour using the natural relaxation of Chen/Padberg. We present an alternative relaxation of the problem of packing boxes into a larger box, which makes it possible to solve much larger instances.