Genotype Diversity Measures for Escaping Plateau Regions in University Course Timetabling

Abstract

University course timetabling is a well-known problem in combinatorial optimization. When using evolutionary algorithms to solve it as a many-objective problem, measures aimed at encouraging population diversity are commonly applied in the objective value space. Difficulties can arise when the search encounters plateau regions, caused by multiple designs evaluating to a common objective vector. To address this, we propose an enhanced diversity procedure that includes genotype crowding as an additional integrated selection criterion behind dominance and phenotype diversity. We also introduce a standard form encoding to handle solution equivalence and reduce metric entropy. Four metrics and a baseline are tested across problems from the International Timetabling Competition 2007 Track 3 benchmark, using a solver based on NSGA-III. Hyper-volume is the primary performance measure. We find that genotype Hamming distance performs best. This goes against our intuition that the use of metrics closer approximating the Levenshtein distance would lead to superior performance.