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Decomposition, Reformulation, and Diving in University Course Timetabling
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| Citations: | 9 - 3 self |
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@MISC{Burke_decomposition,reformulation,,
author = {Edmund K. Burke and Jakub Mareček and Andrew J. Parkes and Hana Rudová},
title = {Decomposition, Reformulation, and Diving in University Course Timetabling},
year = {}
}
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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 performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality.
Keyphrases
university course timetabling different measure feasible solution integer programming variable aggregation initial component different component different kind soft constraint multiple objective value-restricted submodels paper study different set many real-life optimisation problem linear combination search space associated subset complete problem multiphase exploitation difficult component first stage soft constraint violation partial solution
