Improving the ILS-TQ technique for the high school timetabling problem

The High School Timetabling Problem is an NP-Complete problem that consists in allocating subjects, that are taught by teachers and assigned to each class, to periods while satisfying constraints. Throughout the years, metaheuristics haven given better results to real-life instances compared to deterministic methods since the search space for timetabling problems are huge and exploring it completely is impossible. The better the schedules are, the better the students and teachers’ performance, and the costs of generating these schedules are reduced. This proposal consists in modifications done separately to the Iterated Local Search (ILS) with the Torque (TQ) operator for the 34 real-life instances of schools of Brazil. These separate modifications change how a schedule is modified and how it is is accepted. Our Simulated Annealing (SA) cooling scheme implementation, with some parameter tuning, gave better results than our other methods, and more consistent solutions than the original method for some instances. Furthermore, to create other instances more easily, a form was created.Tesi

Mining a Small Medical Data Set by Integrating the Decision Tree and t-test

[[abstract]]Although several researchers have used statistical methods to prove that aspiration followed by the injection of 95% ethanol left in situ (retention) is an effective treatment for ovarian endometriomas, very few discuss the different conditions that could generate different recovery rates for the patients. Therefore, this study adopts the statistical method and decision tree techniques together to analyze the postoperative status of ovarian endometriosis patients under different conditions. Since our collected data set is small, containing only 212 records, we use all of these data as the training data. Therefore, instead of using a resultant tree to generate rules directly, we use the value of each node as a cut point to generate all possible rules from the tree first. Then, using t-test, we verify the rules to discover some useful description rules after all possible rules from the tree have been generated. Experimental results show that our approach can find some new interesting knowledge about recurrent ovarian endometriomas under different conditions.[[journaltype]]國外[[incitationindex]]EI[[booktype]]紙本[[countrycodes]]FI

Modeling high school timetabling with bitvectors

High school timetabling (HSTT) is a well known and wide spread problem. The problem consists of coordinating resources (e.g. teachers, rooms), times, and events (e.g. lectures) with respect to various constraints. Unfortunately, HSTT is hard to solve and just finding a feasible solution for simple variants of HSTT has been proven to be NP-complete. We propose a new modeling approach for HSTT using bitvectors in which constraint costs of the general HSTT can be calculated using bit operations. This model allows efficient computation of constraint costs making it useful when implementing HSTT algorithms. Additionally, it can be used to solve HSTT with satisfiability modulo theory (SMT) solvers that support bitvectors. We evaluate the performance for our bitvector modeling approach and compare it to the leading engine KHE when developing local search algorithms such as hill climbing and simulated annealing. The experimental results show that our approach is useful for this problem. Furthermore, experimental results using SMT are given on instances from the ITC 2011 benchmark repository.Austrian Science Fund (FWF

SAT-Based approaches for the general high school timetabling problem

High School Timetabling (HSTT) is a well known and widespread problem. The problem consists of coordinating resources (e.g. teachers, rooms), times, and events (e.g. lectures) with respect to various constraints. Unfortunately, HSTT is hard to solve and just finding a feasible solution for simple variants of HSTT have been proven to be NP-complete. In this work, we consider the general HSTT problem, abbreviated as XHSTT. Despite significant research efforts for XHSTT and other timetabling problems, no \emph{silver bullet} algorithm has been found so far. Many problems have yet to be efficiently and/or optimally solved. The main goal of this thesis is to explore the relation between propositional logic and high school timetabling, as well as related approaches. We model the complex formalism of XHSTT using Boolean variables and basic logical connectives only. We evaluated different cardinality constraint encodings, solvers, and important special cases in order to significantly simplify the modeling in practice. We note that resource assignment constraints have been considered only for special cases, rather than in general. In addition, we investigated a maxSAT-based satisfiability modulo theories (SMT) approach. Another model we studied in this work is based on bitvectors. By using a series of bitvector operations (such as \emph{AND, OR}, and \emph{XOR}) on the set of event bitvectors, we were able to model all constraints, with the exception of resource assignment constraints. The bitvector models serves as an efficient data structure for local search algorithms such as hill climbing and simulated annealing. To integrate maxSAT into a hybrid algorithm, we combined local search with a large neighborhood search algorithm that exploits maxSAT. Furthermore, to the best of our knowledge, it is the first time maxSAT is used within a large neighborhood search scheme. We carried out thorough experimentation on important benchmark instances that can be found in the repository of the third international timetabling competition (ITC 2011) and compared with the state-of-the-art algorithms for XHSTT. Detailed experiments were performed in order to determine the most appropriate maxSAT solvers and cardinality constraint encodings, evaluate our SMT approach, and compare with integer programming and the ITC 2011 results. Computational results demonstrate that we outperform the integer programming approach on numerous benchmarks. We are able to obtain even better results by combining several maxSAT solvers. When compared to the leading KHE engine for XHSTT, the bitvector modeling approach provided significant improvements for local search algorithms such as hill climbing and simulated annealing. Lastly, our large neighborhood search algorithm excelled in situations when limited computational time is allocated, being able to obtain better results than the state-of-the-art solvers and the pure maxSAT approach in many benchmarks.12