Tree decomposition methods for the periodic event scheduling problem

This paper proposes an algorithm that decomposes the Periodic Event Scheduling Problem (PESP) into trees that can efficiently be solved. By identifying at an early stage which partial solutions can lead to a feasible solution, the decomposed components can be integrated back while maintaining feasibility if possible. If not, the modifications required to regain feasibility can be found efficiently. These techniques integrate dynamic programming into standard search methods. The performance of these heuristics are very satisfying, as the problem using publicly available benchmarks can be solved within a reasonable amount of time, in an alternative way than the currently accepted leading-edge techniques. Furthermore, these heuristics do not necessarily rely on linearity of the objective function, which facilitates the research of timetabling under nonlinear circumstances

A multi-stage IP-based heuristic for class timetabling and trainer rostering

© 2015, Springer Science+Business Media New York. We consider a timetabling and rostering problem involving periodic retraining of large numbers of employees at an Australian electricity distributor. This problem is different from traditional high school and university timetabling problems studied in the literature in several aspects. We propose a three-stage heuristic consisting of timetable generation, timetable improvement, and trainer rostering. Large-scale integer linear programming models for both the timetabling and the rostering components are proposed, and several unique operational constraints are discussed. We show that this solution approach is able to produce good solutions in practically acceptable time

A hybrid meta-heuristic for the generation of feasible large-scale course timetables using instance decomposition

This study introduces a hybrid meta-heuristic for generating feasible course timetables in large-scale scenarios. We conducted tests using our university's instances. The current commercial software often struggles to meet constraints and takes hours to find satisfactory solutions. Our methodology combines adaptive large neighbourhood search, guided local search, variable neighbourhood search, and an innovative instance decomposition technique. Constraint violations from various groups are treated as objective functions to minimize. The search focuses on time slots with the most violations, and if no improvements are observed after a certain number of iterations, the most challenging constraint groups receive new weights to guide the search towards non-dominated solutions, even if the total sum of violations increases. In cases where this approach fails, a shaking phase is employed. The decomposition mechanism works by iteratively introducing curricula to the problem and finding new feasible solutions while considering an expanding set of lectures. Assignments from each iteration can be adjusted in subsequent iterations. Our methodology is tested on real-world instances from our university and random subdivisions. For subdivisions with 400 curricula timetables, decomposition reduced solution times by up to 27%. In real-world instances with 1,288 curricula timetables, the reduction was 18%. Clustering curricula with more common lectures and professors during increments improved solution times by 18% compared to random increments. Using our methodology, viable solutions for real-world instances are found in an average of 21 minutes, whereas the commercial software takes several hours

Network optimization in railway transport planning

This work is dealing with train timetabling problem. In the first chapter, one can find an introduction to network flows which is needed for understanding deeper concepts later on. Namely, basic graph theory definitions are stated as well as core problems like the minimum cost flow and shortest path problem. Furthermore, two equivalent representations of network flows are described, including some useful properties connected to each of them. At the end of the chapter, linear programming and simplex method are introduced into some detail. In the second chapter more complex theory is introduced. At the beginning, multi-commodity flow problem is stated and few solutions approaches are briefly described. Once we settled for one of them, the rest of the chapter is dealing with Lagrangian relaxation and column generation techniques. Since column generation is the main result needed for solving our problem, some finer results, like determining lower and upper bounds, are stated. In the last, third chapter, one can find a model for representing train timetabling problem for a single line network. That model was introduced by Valentina Cacchiani in her Ph.D. thesis. In this work, periodicity of timetable is assumed because it makes computations way quicker, as well as it has some other benefits. At the end, one can find an algorithm based on column generation technique for solving introduced model. That algorithm is based on 6 steps, and after reading this work, one should be able to fully understand each of them.Ovaj rad bavi se problemom rasporeda vožnje u željezničkom prometu. U prvom poglavlju nalazi se uvod u mrežne tokove koji je potreban za razumijevanje naprednijih koncepata. Konkretno, iskazane su osnovne definicije teorije grafova kao i neki temeljni problemi poput problema najjeftinijeg toka i problema najkraćeg puta. Nadalje, opisana su dva ekvivalenta prikaza mrežnih tokova, uključujući neka korisna svojstva za svaki od njih. Na kraju poglavlja, linearno programiranje i simpleks metoda, objašnjeni su na razini razumijevanja. U drugom poglavlju nalazi se naprednija teorija koja se nadovezuje na prvo poglavlje. Na početku poglavlja prikazan je problem više dobara, kao i nekoliko pristupa rješavanju navedenog problema. Nakon što smo se odlučili za jedan od pristupa, ostatak poglavlja bavi se Lagrangeovom relaksacijom i metodom generacije stupaca. Kako je upravo metoda generacije stupaca najvažniji rezultat za rješavanje našega problema, napredniji rezultati vezani uz određivanje donjih i gornjih granica su detaljno objasnjeni. U posljednjem, trećem poglavlju, nalazi se model za prikazivanje problema rasporeda vožnje za mreže s jednom tračnicom. Navedeni model prvi puta je predstavljen u doktorskom radu Valentine Cacchiani. U ovom radu također pretpostavljamo periodičnost rasporeda vožnje kako bismo, između ostalih, ostvarili prednost poput bržeg vremena računanja. Na kraju rada nalazi se algoritam, temeljen na metodi generacije stupaca, za rješavanje predstavljenog modela. Navedeni algoritam sastoji se od 6 koraka, od kojih je svaki detaljno opisan u ovome radu

Scheduling the Australian football league

Generating a schedule for a professional sports league is an extremely demanding task. Good schedules have many benefits for the league, such as higher attendance and TV viewership, lower costs, and increased fairness. The Australian Football League is particularly interesting because of an unusual competition format integrating a single round robin tournament with additional games. Furthermore, several teams have multiple home venues and some venues are shared by multiple teams. This paper presents a 3-phase process to schedule the Australian Football League. The resulting solution outperforms the official schedule with respect to minimizing and balancing travel distance and breaks, while satisfying more requirements