Integer programming techniques for educational timetabling

Abstract

Educational timetabling problems require the assignment of times and resources to events, while sets of required and desirable constraints must be considered. The XHSTT format was adopted in this work because it models the main features of educational timetabling and it is the most used format in recent studies in the eld. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed

A Convex LASSO Framework for Linear Timetabling

“…In this problem, vertices represent events of courses, two vertices are connected if the corresponding events are part of a single curriculum and assignment of events to periods and rooms is represented by assignment of |K| colors to |V | vertices such that connected vertices are assigned different colors and each color is used at most r times, where r represents the number of classrooms available in a single period. Other equality and inequality constraints may be present, like room capacity constraints, precedence/coincidence constraints and exclusion constraints, as explained for example in [13]. The objective is to minimize (1) the number of students left without a seat at an event; (2) the number of deviations from the desired spread of events for each course over distinct week-days; (3) the number of isolated events in daily timetables of individual curricula and (4) the number of rooms allocated for a single course.…”

“…Algorithm 2 was implemented using Matlab CVX [37] with λ = 1 and s th = 0.1. In relation to equation (13), the individual scaling of the groups was γ 1 = 1, γ 2 = 10 and γ 3 = 10. The result of this implementation is shown in Figure ??…”

“…These problems are known to be NP-complete and are difficult to solve for optimality [12]. Heuristics are commonly used to provide feasible solutions without any guarantee on global optimality of the solutions, see for example the recent surveys in [6] and a good summary review of heuristics in [13], [10] and [9]. Alternatively, these problems can be also solved using exact methods, including cutting plane and/or branch and bound techniques that can be terminated with a certifi-cate proving sub-optimality [14].…”

Models and algorithms for high school timetabling problems

“…The strongest formulation for high school timetabling is based on a multi-commodity flow problem. The formulation was first proposed for problems of Brazilian high schools (DORNELES; ARAÚJO; BURIOL, 2017) and adapted later to manage the GHSTP (FONSECA et al, 2017). Extended formulations solved by column generation have also been proposed for high school timetabling problems.…”

“…Stronger formulations have been proposed (DORNELES; BURIOL, 2017;FONSECA et al, 2017). However, they still cannot effectively solve medium and large size instances.…”