Carter Benchmarks Research Articles

A NNIA Scheme for Timetabling Problems

This paper presents a memetic multiobjective optimization algorithm based on NNIA for examination timetabling problems. In this paper, the examination timetabling problem is considered as a two-objective optimization problem while it is modeled as a single-objective optimization problem generally. Within the NNIA framework, the special crossover operator is utilized to search in the solution space; two local search techniques are employed to optimize these two objectives and a diversity-keeping strategy which consists of an elitism group operator and an extension optimization operator to ensure a sufficient number of solutions in the pareto front. The proposed algorithm was tested on the most widely used uncapacitated Carter benchmarks. Experimental results prove that the proposed algorithm is a competitive algorithm.

Incorporating chaos into the developmental approach for solving the examination timetabling problem

The developmental approach DA is a novel methodology which mimics processes from cell biology. Previous work has evaluated different versions of the DA to solve the examination timetabling problem. The DA creates an organism, which represents a solution to the problem, using the processes of cell division, cell interaction and cell migration. A shortcoming of the standard DA algorithm is that is does not incorporate any form of chaos or disorder which is essential for organism development in nature. The paper firstly presents and tests noise operators for this purpose. It then examines the use of an evolutionary algorithm to evolve noise in the DA. The performance of the standard DA, the DA using noise operators DANO and the DA evolving noise DAEN are tested on a set of ten real-world examination timetabling problems from the Carter benchmark set of problems. DAEN was found to outperform both the DA and DANO. Furthermore, the results produced by DAEN were found to be comparative to other methodologies applied to the same set of problems.

Hybrid particle swarm optimization transplanted into a hyper-heuristic structure for solving examination timetabling problem

Examination timetabling is a discrete, multi-objective and combinatorial optimization problem which tends to be solved with a cooperation of stochastic search approaches such as evolutionary algorithms (EAs) and heuristic methods such as sequential graph coloring heuristics. This research investigates the use of discrete particle swarm optimization (DPSO) for solving examination timetabling problem. A combination of mutation, specialist recombination operator and graph coloring heuristics are used to update position of particles in the DPSO. A new local search method, called two staged hill climbing, is proposed and is utilized to hybridize the DPSO algorithm. Three structures for the DPSO and three strategies to hybridize it are proposed. On one hand, since the proposed DPSO algorithms such as hyper-heuristics methods employ a strategy to manage a set of constructive low-level heuristics, they can be classified as hyper-heuristic systems and, on the other hand, the DPSO is a stochastic global optimization method from class of EAs. The proposed algorithms are tested on a set of Carter benchmark problems to set the parameters of algorithms and also to compare different methods. The obtained results demonstrate that the proposed hill climbing local search, in spite of its simplicity, has a better performance than original hill climbing method. Among different graph coloring heuristics, those of algorithms which employ the saturation degree heuristic lead to the better results. Also among different proposed algorithms, the first structure of DPSO and third strategy of hybridizing obtain a better performance than the other structures and strategies. In a later part of the comparative experiment, performance comparisons of the proposed algorithms with some other hyper-heuristic and EA methods are done. The obtained results confirm that the proposed hybrid algorithm has a better, or at least comparable, performance than other hyper-heuristic systems. Also it obtains the best results among hyper-heuristic systems on some problems. Also in comparison of other EAs, it has a completely comparable performance.

A constructive approach to examination timetabling based on adaptive decomposition and ordering

In this study, we investigate an adaptive decomposition and ordering strategy that automatically divides examinations into difficult and easy sets for constructing an examination timetable. The examinations in the difficult set are considered to be hard to place and hence are listed before the ones in the easy set in the construction process. Moreover, the examinations within each set are ordered using different strategies based on graph colouring heuristics. Initially, the examinations are placed into the easy set. During the construction process, examinations that cannot be scheduled are identified as the ones causing infeasibility and are moved forward in the difficult set to ensure earlier assignment in subsequent attempts. On the other hand, the examinations that can be scheduled remain in the easy set. Within the easy set, a new subset called the boundary set is introduced to accommodate shuffling strategies to change the given ordering of examinations. The proposed approach, which incorporates different ordering and shuffling strategies, is explored on the Carter benchmark problems. The empirical results show that the performance of our algorithm is broadly comparable to existing constructive approaches.

A graph coloring constructive hyper-heuristic for examination timetabling problems

In this work we investigate a new graph coloring constructive hyper-heuristic for solving examination timetabling problems. We utilize the hierarchical hybridizations of four low level graph coloring heuristics, these being largest degree, saturation degree, largest colored degree and largest enrollment. These are hybridized to produce four ordered lists. For each list, the difficulty index of scheduling the first exam is calculated by considering its order in all lists to obtain a combined evaluation of its difficulty. The most difficult exam to be scheduled is scheduled first (i.e. the one with the minimum difficulty index). To improve the effectiveness of timeslot selection, a roulette wheel selection mechanism is included in the algorithm to probabilistically select an appropriate timeslot for the chosen exam. We test our proposed approach on the most widely used un-capacitated Carter benchmarks and also on the recently introduced examination timetable dataset from the 2007 International Timetabling Competition. Compared against other methodologies, our results demonstrate that the graph coloring constructive hyper-heuristic produces good results and outperforms other approaches on some of the benchmark instances.

Grasp and Guided Local Search for the examination timetabling problem

Examination timetabling is an optimisation problem, which regards the scheduling of a set of exams to a set of contiguous time slots, satisfying a set of constraints. The problem belongs to the class of NP-Complete problems and is usually tackled using heuristic methods. In this paper, we describe a solution algorithm and its implementation which makes use of the good features of a Greedy Randomised Adaptive Search Procedure (GRASP) and the Guided Local Search (GLS) meta-heuristic. The implementation of the algorithm has been experimented on the popular Carter's benchmarks and compared with the best recent results.

A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem

Research in the domain of examination timetabling is moving towards developing methods that generalise well over a range of problems. This is achieved by implementing hyper-heuristic systems to find the best heuristic or heuristic combination to allocate examinations when constructing a timetable for a problem. Heuristic combinations usually take the form of a list of low-level heuristics that are applied sequentially. This study proposes an alternative representation for heuristic combinations, namely, a hierarchical combination of heuristics. Furthermore, the heuristics in each combination are applied simultaneously rather than sequentially. The study also introduces a new low-level heuristic, namely, highest cost. A set of heuristic combinations of this format have been tested on the 13 Carter benchmarks. The quality of the examination timetables induced using these combinations are comparable to, and in some cases better than, those produced by hyper-heuristic systems combining and applying heuristic combinations sequentially.

An informed genetic algorithm for the examination timetabling problem

This paper presents the results of a study conducted to investigate the use of genetic algorithms (GAs) as a means of inducing solutions to the examination timetabling problem (ETP). This study differs from previous efforts applying genetic algorithms to this domain in that firstly it takes a two-phased approach to the problem which focuses on producing timetables that meet the hard constraints during the first phase, while improvements are made to these timetables in the second phase so as to reduce the soft constraint costs. Secondly, domain specific knowledge in the form of heuristics is used to guide the evolutionary process. The system was tested on a set of 13 real-world problems, namely, the Carter benchmarks. The performance of the system on the benchmarks is comparable to that of other evolutionary techniques and in some cases the system was found to outperform these techniques. Furthermore, the quality of the examination timetables evolved is within range of the best results produced in the field.