New Multi-objective Partial Optimisation Decomposition Strategies for the Thesis Defence Scheduling Problem
A new multi-objective method for the thesis defence scheduling problem is introduced. The problem involves appointing committees to defences and assigning them to a time slot and room. A multi-objective approach is necessary to provide a better understanding of possible solutions and trade-offs to decision-makers. However, this type of approach is often time-consuming. The new multi-objective optimisation approach decomposes the monolithic problem into a sequence of multi-objective problems. This leads to significant efficiency gains compared to the augmented-e constraint method. The monolithic model is decomposed into two submodels solved sequentially. In the first stage, genetic algorithms find multiple committee configurations. The performance of these solutions is assessed based on committee assignment quality objectives and a proxy objective predicting performance in the next stage. In the second stage, considering multiple partial solutions found previously, an augmented e-constraint method is solved to find non-dominated solutions regarding the assignment of time slots to defences. These solutions consider schedule quality objectives. Finally, non-dominated solutions are presented based on objective function performance for both points of view. For small-size instances, the method takes 8-32% of the time of an augmented e-constraint method but finds non-dominated sets with slightly worse hyper-volume indicator values. For larger instances, times are 6-18% of monolithic resolutions, and hyper-volume indicator values are better. A real-world case study is presented. The experiment with decomposition found 39 non-dominated solutions in 1600 seconds. The augmented e-constraint method found 9 solutions in 2400 seconds. For the three objectives, the new method found a solution improving the best-performing solution with the other method in the time limit.