Decomposition, Reformulation, and Diving in University Course Timetabling
Edmund K. Burke, Jakub Marecek, Andrew J. Parkes, Hana Rudova

TL;DR
This paper introduces a multiphase heuristic approach for complex university course timetabling problems, leveraging decomposition and reformulation techniques to efficiently generate high-quality solutions with bounds on their optimality.
Contribution
It presents a novel multiphase exploitation method combining decomposition, reformulation, and diving strategies for multi-component timetabling problems, with detailed integer programming formulations.
Findings
Effective neighborhood generation reduces soft constraint violations.
Integer programming formulations enable bounds on solution quality.
Approach demonstrates wider applicability beyond the studied problem.
Abstract
In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be…
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