Can a Meta-GA solve timetabling problems? Christian Blum, Sebastião Correia, Olivia Rossi-Doria, Marko Snoek, Marco Dorigo (team leader), Ben Paechter (problem leader)

Timetabling, EvoNet Summer School 2001 Contents Introduction The timetabling problem Solution directions Our approach Preliminary results Conclusions and future research directions

Timetabling, EvoNet Summer School 2001 Introduction Background of participants: Christian: mathematics Marko: technology management Olivia: mathematics Sebastião: physics Let’s do timetabling!

Timetabling, EvoNet Summer School 2001 The timetabling problem Goal: assignment of classes to rooms and timeslots, while respecting the hard constraints, and taking into consideration the soft constraints.

Timetabling, EvoNet Summer School 2001 Problem hardness NP-hard problem Problem is highly constrained Difficult to build feasible solutions

Timetabling, EvoNet Summer School 2001 Solution directions Direct representation: genotype is the solution Indirect representation: genotype  phenotype phenotype is the solution

Timetabling, EvoNet Summer School 2001 Solution directions II Characteristics of direct representation: crossover is more likely to be disruptive most solutions are infeasible Characteristics of indirect representation: need timetable builder to construct solution

Timetabling, EvoNet Summer School 2001 Summer School Problem Data: Classes (type of room required) Rooms (type, size) Timeslots (45 in a week) Students (class attendance)

Timetabling, EvoNet Summer School 2001 Summer School Problem Hard constraints: Each class in a suitable room One class per room / timeslot Each student can follow all his / her classes Soft constraints: Students should not have only 1 class / day Students should not have more than 2 classes in a row

Timetabling, EvoNet Summer School 2001 Our approach Indirect representation Toolbox of heuristics is given Use heuristics to build timetable step-by-step Let GA evolve which heuristics to use in every step

Timetabling, EvoNet Summer School 2001 Individual: Our approach II Rules used for insertion of 2 nd event in timetable c1c2… r1r2… t1t2… class rules: room rules: time rules:

Timetabling, EvoNet Summer School 2001 Our approach III Choose next class to insert in timetable: e.g. pick class with most students Choose which room to assign: e.g. pick smallest possible room Choose timeslot: e.g. pick timeslot with most parallel events

Timetabling, EvoNet Summer School 2001 Our approach IV Timetable Problem data Score Fitness Heuristics Timetable builder Meta-GA

Timetabling, EvoNet Summer School 2001 Preliminary results NO RESULTS (yet!)

Timetabling, EvoNet Summer School 2001 Room for improvement Extend set of heuristics Use other assignment orders, e.g. choose timeslot, followed by event, and room Change assignment order during timetable building Apply local search

Timetabling, EvoNet Summer School 2001 Conclusions Advantage of method: adaptation to problem instances Disadvantage of method: phenotype -/-> genotype Presented method is new in the field of timetabling Approach can be improved in various ways