A general ontological timetabling-model driven metaheuristics approach based on elite solutions

Abstract

Timetabling is a managerial problem that recurringly appears in various domains such as education, transport, sports, and staff management. The combinatorial nature of this problem poses solution challenges that aggravate with an increase in the problem size. While heuristics and metaheuristics initially offered promise, the progress plateaued as attempts to solve even bigger problems showed exorbitant costs while sampling feasible solutions. This issue is criticized for the lack of exploiting the underlying problem structure and the prevailing fragmentation in modeling and solution approaches. To address these issues, we first propose a novel timetabling ontology that serves as a common modeling basis, resolving the existing heterogeneity across various application domains. This ontology facilitates mapping the anatomy of any real timetabling problem onto its general structure. Second, it offers a unique two-stage solution approach for solving this generalized problem. The first stage of this approach entails generating elite initial solutions by exploiting this general problem structure, while the second stage uses a metaheuristic to improve these solutions at a very low computational cost. Using a university timetabling problem, we demonstrate the applicability of this approach. The numerical results show that the proposed algorithm converges within a fraction of computational costs incurred by other techniques for comparable problem sizes. This research paves the way for consolidating efforts for the development of generalizable cross-domain timetabling approaches.