Multi-objective optimisation, a major focus in the thesis, is fundamentally about balancing multiple and often conflicting goals. This multi-objective paradigm is prevalent in fields like engineering, economics, and environmental studies. The challenge arises from the inherent trade-offs between objectives. For example, in manufacturing, enhancing product robustness can increase its cost. In environmental planning, prioritising industrial growth can exacerbate pollution. The goal is to identify Pareto-optimal solutions that navigate these trade-offs.
– My work has been done for GKN Aerospace in Trollhättan, and it was nice to visit the factory and consider possible ways to tackle their resource allocation issues.
Solutions in a reasonable time
While there are mathematically efficient methods for minimising/maximising a single objective (linear) function under (linear) constraints, introducing integer or binary decision variables renders the problem non-convex and hard to solve to optimality. In multi-objective settings, this complexity is compounded. It is not a single optimal solution that is sought, in most cases there does not exist one, but a set of efficient solutions that are Pareto optimal. Thus, there is a pressing need for methods that can address these multi-objective mixed-integer linear programming problems efficiently.
One such application considered in the thesis is allocating machining resources at a factory to products. Each product requires a sequence of operations (routings) that can be performed on a variety of machines. In the beginning two objectives were considered: minimising imbalance in resource loading and minimising one-time set-up cost to qualify a machine for an operation. Later, another objective of minimising the inventory was incorporated. Finally, an algorithm to compute a representative Pareto front with certain guarantees on a performance criterion called coverage gap was suggested. Overall, this will be integrated into a decision-making tool to help GKN Aerospace AB make effective allocation decisions.
– My academic background is in engineering science, but when I did my master’s thesis at the University of Bergen I became interested in mathematical optimisation. I started to look for doctoral positions and could have stayed in Bergen, but when I saw this position at Chalmers’ website I decided to challenge myself a little and not be too comfortable too soon.
Teaching helps to improve scientific communication skills
One of the highlights of Sunney’s doctoral years was the opportunity to teach, an experience he had not encountered before. Given the diverse backgrounds of students in optimisation courses, Sunney honed his ability to articulate complex concepts clearly. This skill not only benefitted the students, but also holds value in communicating with professionals from other fields.
On a personal note, Sunney feels fortunate to have been in Sweden during the early stages of his family life. The societal acknowledgment of the need for family flexibility has been invaluable for him, and he extends his gratitude to both the government and his supervisors. Additionally, Sunney cherishes the natural beauty of Gothenburg, highlighting the expansive forests that offer great running trails.
After the thesis defence, Sunney will take up a postdoc position at another department in Chalmers, where he will continue to work with optimisation but for a different application. Optimisation is a research area that that is useful in a lot of other departments as well.
Sunney Fotedar will defend his PhD thesis Mathematical Multi-Objective Optimization of the Tactical Allocation of Machining Resources in Functional Workshops on September 21 at 10.15 in lecture hall Pascal, Hörsalsvägen 1. Supervisor is Ann-Brith Strömberg, assistant supervisor is Michael Patriksson.