A Double Evolutionary Pool Memetic Algorithm for Examination Timetabling Problems


 
 
 
 Abstract:
 Aim: This study is on tackling Examination Timetabling Problem (ETP) of the Faculty of Economics And Administrative Sciences (FEAS) of the Ankara HBV University summer school, where the courses of fall and spring semesters are offered simultaneously and regulations on restricting enrollments in inter-department electives or in-department courses of distinct years are relaxed. Thus, the complexity of the nature of the ETP problem is exacerbated. The direct heuristics based on successive assignments that the university normally adopts was proven inadequate for assuming standard regulations hence, another approach we explain in this paper was needed.
 Design / Research methods: The ETP was formulated as a Linear Mixed-Integer Program (LMIP) and decomposed into three stages; timetabling exams, room assignment, student allocation. To manage the conflict between the stakeholders of the examination procedure, a lexicographic optimization process based on the priority of the parties was undertaken.
 Conclusions / findings: After a recursive timetabling process based on a trial-and-error method a clash-free timetable was generated and, a room assignment plan that minimizes the total number of proctoring duties, usage of higher floor rooms and total crowdedness of rooms respectively was put into action. Therefore no student group experienced any clashing exams, the faculty members saved time that can be spent on research instead, since the room usage was better planned the costs (elevator usage, lighting, air conditioning, the labor of the janitors) were assumed to be decreased.
 Originality / value of the article: Each examination period bares a different ETP due to its problem-specific nature (number of courses offered, structure of student enrollments, availability of rooms, etc.). Summer schools provide a more irregular structure that demands special attention, a trial-and-error reformulation of the ETP in our case. In addition, the traditional formulations of the ETP, to the extent we have been able to scan, do not include the minimization of the crowdedness of the rooms. Thus, in creating a more comfortable environment, easier to monitor exams and, ability in handling unexpected dysfunctionalities (broken classroom equipment, etc.) this study is novel.
 Limitations of the research: The algorithms to solve an ETP formulated as an LMIP are of high complexity therefore, we are not able to assert the optimality of our suggested solutions acquired within time limitations.
 
 
 
 
 Keywords: examination timetabling, group decision making, lexicographic optimization, linear mixed-integer programming
 JEL: C44, C61, M12
 
 
 

Solving a real-world university examination timetabling is an intractable problem. Examination timetabling problems (ETP) can be defined as a problem of assigning a set of final examinations schedules to a given number of timeslots and rooms subject to a set of constraints. These constraints are usually divided into hard and soft constraints. Hard constraints must be satisfied under any circumstances. Whilst, soft constraints are not only essential but also should be satisfied as much as possible. Due to the complexity of the problem, it is usually impossible to have solutions that satisfy all soft constraints. The quality of the timetable is measured based on soft constraints violation. A weighted penalty/value is attached to each violation of the soft constraint and the objective is to minimize the total penalty value of these violations. Although there have been a numerous approaches in solving the ETP, but this paper only focus on Genetic Algorithm (GA) method based on the fact that it is robust and can fits into complex problem space. This paper gives a summary of the GA method on ETP and it aims in helping other researcher to shorten their time in understanding the application of GA in the selected problem.

Hyper-heuristics can be identified as methodologies that search the space generated by a finite set of low level heuristics for solving search problems. An iterative hyper-heuristic framework can be thought of as requiring a single candidate solution and multiple perturbation low level heuristics. An initially generated complete solution goes through two successive processes (heuristic selection and move acceptance) until a set of termination criteria is satisfied. A motivating goal of hyper-heuristic research is to create automated techniques that are applicable to a wide range of problems with different characteristics. Some previous studies show that different combinations of heuristic selection and move acceptance as hyper-heuristic components might yield different performances. This study investigates whether learning heuristic selection can improve the performance of a great deluge based hyper-heuristic using an examination timetabling problem as a case study.

University examination timetabling problem is a complicated, multi-constraint combinatorial optimization problem. The current grouping genetic algorithm could get a better optimistic solution. Although the block encoding technique was applied in, the probabilities of crossover and mutation operation were still based on simple genetic algorithm. So the universality of this algorithm is not very well because the same probabilities of crossover and mutation operation could obtain different effects in different cases of examination arrangements. To find a more general algorithm, an Improved Adaptive Genetic Algorithm (IAGA) for practical applications was presented in this paper. IAGA can reconstruct the probabilities of crossover and mutation operation according to different cases of examination arrangements. To make further improvement of its convergence speed and overcome premature problem, IAGA appropriately adjusts mutation operation by Population's Maturity in addition. Moreover, the Memory Operator was added into the Algorithm to ensure getting the global optimization solution. Finally, IAGA was tested in function optimization and Examination Timetabling problems, and the experiments show that the results are promoted very well.

An informed genetic algorithm for the examination timetabling problem

An examination timetabling problem at a large American university is presented. Although there are some important differences, the solution approach is based on the ITC 2007 winning solver which is integrated in the open source university timetabling system UniTime. In this work, nine real world benchmark data sets are made publicly available and the results on four of them are presented in this paper. A new approach to further decreasing the number of student conflicts by allowing some exams to be split into multiple examination periods is also studied.

The examination timetabling problem involves assigning exams to a specific or limited number of timeslots and rooms with the aim of satisfying all hard constraints (without compromise) and satisfying the soft constraints as far as possible. Most of the techniques reported in the literature have been applied to simplified examination benchmark data sets. In this paper, we bridge the gap between research and practice by investigating a problem taken from the real world. This paper introduces a modified and extended great deluge algorithm (GDA) for the examination timetabling problem that uses a single, easy to understand parameter. We investigate different initial solutions, which are used as a starting point for the GDA, as well as altering the number of iterations. In addition, we carry out statistical analyses to compare the results when using these different parameters. The proposed methodology is able to produce good quality solutions when compared with the solution currently produced by the host organisation, generated in our previous work and from the original GDA.

In general, uncapacitated exam timetabling is conducted manually, which can be time-consuming. Many studies aim to automate and optimize uncapacitated exam timetabling. However, pinpointing the most efficient algorithm is challenging since most studies assert that their algorithms surpass previous ones. To identify the optimal algorithm, this research evaluates the performance of four algorithms: Hill climbing (HC), simulated annealing (SA), great deluge (GD), and tabu search (TS) in addressing the exam timetabling problem. The Kempe chain operator’s influence on optimization solutions is also examined. A simple random method is employed to select the low-level heuristic (LLH). The Carter (Toronto) dataset served as the test material, with each algorithm undergoing 200,000 iterations for comparison. The results indicate that the TS algorithm is superior, providing the best solution in 13 instances. The use of a tabu list enhanced the search process’s efficiency by preventing redundant modifications. The Kempe chain LLH exhibited a tendency towards achieving better solutions.

Hybrid bee colony optimization for examination timetabling problems

At all educational institutions, timetabling is a conventional problem that has always caused numerous difficulties and demands that need to be satisfied. For the examination timetabling problem, those matters can be defined as complexity in scheduling exam events or non-deterministic polynomial hard problems (NP-hard problems). In this study, the latest approach using an ant colony optimisation (ACO) which is the ant system (AS) is presented to find an effective solution for dealing with university exam timetabling problems. This application is believed to be an impressive solution that can be used to eliminate various types of problems for the purpose of optimising the scheduling management system and minimising the number of conflicts. The key of this feature is to simplify and find shorter paths based on index pheromone updating (occurrence matrix). With appropriate algorithm and using efficient techniques, the schedule and assignation allocation can be improved. The approach is applied according to the data set instance that has been gathered. Therefore, performance evaluation and result are used to formulate the proposed approach. This is to determine whether it is reliable and efficient in managing feasible final exam timetables for further use.

In this paper, we present a hybridization of an electromagnetic-like mechanism (EM) and the great deluge (GD) algorithm. This technique can be seen as a dynamic approach as an estimated quality of a new solution and a decay rate are calculated each iteration during the search process. These values are depending on a force value calculated using the EM approach. It is observed that applying these dynamic values help generate high quality solutions. Experimental results on benchmark examination timetabling problems demonstrate the effectiveness of this hybrid EM-GD approach compared with previous available methods. Possible extensions upon this simple approach are also discussed.

Direct heuristic is widely used in scheduling applications, e.g., timeslot selection in school timetabling. Timeslot selection concerns which timeslot, among a number of applicable timeslots, be chosen for a yet-to-assign lesson. In this paper, we propose a timeslot selection heuristic based on the notion of timeslot contention among lessons. Due to the generality of the heuristic, it can be applied to other problem domains that involve disequality constraints such as examination timetabling problem. The new heuristic has been studied both analytically and empirically. Experimental results drawn from a set of real timetabling problem instances have shown that the new heuristic outperformed a variant of small-domain-first heuristic in terms of the timetable completion rate despite the similarity in both heuristics’ computational load.

Examination timetabling is a problem well known to the scheduling community. Its simplest version, which is the uncapacitated examination timetabling problem, is easily described and comprehended. Nevertheless, proof of optimality is notoriously difficult even for moderate size problems. In this paper, we describe the effort that our team exercised in finally proving the optimality of the sta83 instance of Carter’s dataset. The problem was decomposed naturally in three parts and for each part a different approach managed to prove optimality of the currently best known solution. This work also presents optimal solutions to subproblems that exist in various public datasets problems and two best known solutions of such problems.

An investigation of fuzzy multiple heuristic orderings in the construction of university examination timetables

Proteins are cellular macromolecules made up of linear chains of amino acids that adopt a unique three-dimensional structure to carry out specific biological functions. Amongst various computational approaches developed for Protein Structure Prediction (PSP), ab initio methods perform the prediction without prior knowledge of known structures. However, due to huge computational complexity incurred by these methods, simplified hydrophobic-polar (HP) models are often used for the investigations. Despite this simplicity, PSP continues to be a hard combinatorial optimization problem requiring development of efficient heuristic search techniques. Memetic algorithm (MA), with its flexible architecture, encompasses the strength of both local and global search and has shown promise in solving problems with complex search landscape, including PSP. This thesis is focused on developing an effective ab initio technique under a suitable MA framework for solving the PSP problem using low resolution HP models. To enhance the effectiveness of the MA, a mechanism is devised to include knowledge from the problem domain by exploiting the concept of hydrophobic-core (H-core) formation. The size of the maximal possible H-core is estimated and the approximation is validated by our proposed deterministic search technique. Further, a new knowledge-based initial population generation technique ensures generating conformations which are not only valid, but also maintain diversity in the population. This helps to commence the search with good seeds leading towards faster convergence. While solving the PSP problem using MA, the greatest intricacy arises from the complex nature of its multi-modal landscape. Like all the evolutionary algorithms (EAs), MAs have the tendency to get trapped into local minima due to selection pressure and genetic drift induced by the genetic operators, and techniques are necessary to surmount this difficulty. A novel parental selection technique called “Adaptive Strategy for Assortative Mating” is developed that dynamically distributes the re production opportunity among the individuals of the population to boost the effectiveness of cross-over. Further, a new survival selection strategy, namely “Sib-based Survival Selection”, prevents the rapid spread of genetic material from a particular individual to other members in the population, ensuring the concurrent preservation of several potential solutions, and restricting premature convergence. A new diversification mechanism, namely “Memory-based Diversification”, systematically diversifies the population by introducing new genetic material whenever it gets stuck at local peaks and allows it to proceed for further progress. An extensive experimental analysis is also reported on the influence of all three techniques proposed to maintain the diversity of population. Furthermore, in order to carry out the conformational search efficiently, especially with the increase in sequence length, the optimization technique is designed such that it provides an effective balance between exploration and exploitation. A robust Multimodal Memetic Framework has been developed where optimization is accomplished in hierarchical stages. The population of each stage is partitioned into three different states: an Exploratory state to locate promising peaks, an Exploitative state to fine-tune the solutions found in the Exploratory state of the previous stage, and finally, a Central state to carry out the formation of potential solutions to explore the undiscovered regions. Non-identical genetic operators have been implemented in each state to balance the exploration and exploitation by employing necessary selection pressure and diversity. A non-isomorphic encoding based technique has been developed to capture the sub-structures that are representing a particular region. Furthermore, a novel local search technique exploits already explored fit individuals by employing the knowledge of sub-structures. The efficacy of the proposed framework is demonstrated with an adequate number of distinctive data sets and comparison with state-of-the-art methods.