Student: Mariana Bayão Horta Mesquita da Cunha e Silva

Title: “Advancing Multi-Objective Optimization: Representation and Preference inclusion methods”

Date: 28/11/2024

Time: 14h00

Location: Amphitheatre PA-3, Mathematics Building (-1 floor)

Supervisor: Professora Ana Paula Ferreira Dias Barbosa Póvoa (IST)

Co-supervisor: Professor José Rui de Matos Figueira (IST)

Brief description of the research work: When applying multi-objective methods in practice, there are two main challenges. The first is the complexity of computing the Pareto front (PF). The second concerns the interaction with the decision-maker (DM), which must present as few solutions as possible, maintaining the analysis process simple and keeping the DM engaged. This thesis intends to address both challenges through an integrated methodology of different original strategies concerning three stages of the solution of multi-objective problems. The first strategy concerns the generation phase. Instead of computing the PF, we propose methods to calculate only a subset – a representation of the PF. Generating this subset is itself a multi-objective problem since it must: convey the characteristics and trade-offs of the original PF; be uniformly spaced; and minimize cardinality. To that end, three algorithms based on the ϵ-constraint method are put forward, each targeting a different dimension of the representation problem. The second strategy concerns the integration of the DM’s preferences to reduce the feasible region to a smaller space that fits the DM’s interest. This method relies on a priori eliciting the preferences of the DM as a ranking of criteria. Then, based on that ranking, the PF is decomposed in the objective space. Experiments were conducted under three scenarios: the complete order case; hesitation about the least preferred criterion; and hesitation regarding the most preferred criterion. All three scenarios showed significant improvements in PF size and computational time. Furthermore, higher improvements were observed in larger PFs. The third strategy concerns an interactive multi-objective method that during the generation phase includes the DM’s preferences using convex preference cones. In each interaction, the DM is asked to pairwise judge alternatives. The preferences are then incorporated in the model. Additionally, the current literature is extended by deriving the constraints composing the H-representation of the 3-point convex preference cone, allowing the comparison of more alternatives. Results demonstrate the effectiveness of the proposed method and highlight the benefits of increasing the number of alternatives judged per iteration. This thesis presents an innovative framework that combines all three strategies. The framework is applied to the design and planning of pharmaceutical supply chains. This problem is modelled as a multi-objective problem, taking into account economic, social and environmental impacts. The application highlights the relevance and potential impact of this framework.

Research Unit: Centre for Management Studies of IST (CEGIST)