A hybrid genetic algorithm and tabu search approach for post enrolment course timetabling

The post enrolment course timetabling problem (PECTP) is one type of university course timetabling problems, in which a set of events has to be scheduled in time slots and located in suitable rooms according to the student enrolment data. The PECTP is an NP-hard combinatorial optimisation problem and hence is very difficult to solve to optimality. This paper proposes a hybrid approach to solve the PECTP in two phases. In the first phase, a guided search genetic algorithm is applied to solve the PECTP. This guided search genetic algorithm, integrates a guided search strategy and some local search techniques, where the guided search strategy uses a data structure that stores useful information extracted from previous good individuals to guide the generation of offspring into the population and the local search techniques are used to improve the quality of individuals. In the second phase, a tabu search heuristic is further used on the best solution obtained by the first phase to improve the optimality of the solution if possible. The proposed hybrid approach is tested on a set of benchmark PECTPs taken from the international timetabling competition in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed hybrid approach is able to produce promising results for the test PECTPs.     

Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem (CB-CTT), which has been tackled by many researchers and for which there are many available benchmarks.The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Second, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks.A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison.     

Solving a timetabling problem using hybrid genetic algorithms

All over the world, human resources are used on all kinds of different scheduling problems, many of which are time-consuming and tedious. Scheduling tools are thus very welcome. This paper presents a research project, where Genetic Algorithms (GAs) are used as the basis for solving a timetabling problem concerning medical doctors attached to an emergency service. All the doctors express personal preferences, thereby making the scheduling rather difficult. In its natural form, the timetabling problem for the emergency service is stated as a number of constraints to be fulfilled. For this reason, it was decided to compare the strength of a Co-evolutionary Constraint Satisfaction (CCS) technique with that of two other GA approaches. Distributed GAs and a simple special-purpose hill climber were introduced, to improve the performance of the three algorithms. Finally, the performance of the GAs was compared with that of some standard, nonGA approaches. The distributed hybrid GAs were by far the most successful, and one of these hybrid algorithms is currently used for solving the timetabling problem at the emergency service. © 1997 John Wiley & Sons, Ltd.     

A Survey of Automated Timetabling

The timetabling problem consists in scheduling a sequence of lectures between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types. A large number of variants of the timetabling problem have been proposed in the literature, which differ from each other based on the type of institution involved (university or school) and the type of constraints. This problem, that has been traditionally considered in the operational research field, has recently been tackled with techniques belonging also to Artificial Intelligence (e.g., genetic algorithms, tabu search, and constraint satisfaction). In this paper, we survey the various formulations of the problem, and the techniques and algorithms used for its solution.     

Solving the high school timetabling problem using a hybrid cat swarm optimization based algorithm

In this contribution we present the application of a hybrid cat swarm optimization (CSO) based algorithm for solving the school timetabling problem. This easy to use, efficient and fast algorithm is a hybrid variation of the classic CSO algorithm. Its efficiency and performance is demonstrated by conducting experiments with real-world input data. This data, collected from various high schools in Greece, has also been used as test instances by many other researchers in their publications. Results reveal that this hybrid CSO based algorithm, applied to the same school timetabling test instances using the same evaluation criteria, exhibits better performance in less computational time compared to the majority of other existing approaches, such as Genetic Algorithms (GAs), Evolutionary Algorithms (EAs), Simulated Annealing (SA), Particle Swarm Optimization (PSO) and Artificial Fish Swarm (AFS). The algorithm's main process constitutes a variation of the classic CSO algorithm, properly altered so as to be applied for solving the school timetabling problem. This process contains the main algorithmic differences of the proposed approach compared to other algorithms presented in the respective literature.     

Production capacity planning and scheduling in a no-wait environment with controllable processing times: An integrated modeling approach

This paper develops an integrated model between a production capacity planning and an operational scheduling decision making process in which a no-wait job shop (NWJS) scheduling problem is considered incorporating with controllable processing times. The duration of any operations are assumed to be controllable variables based on the amount of capacity allocated to them, whereas in classical NWJS it is assumed that the machine capacity and hence processing times are fixed and known in advance. The suggested problem which is entitled no-wait job shop crashing (NWJSC) problem is decomposed into the crashing, sequencing and timetabling subproblems. To tackle the addressed NWJSC problem, an improved hybrid timetabling procedure is suggested by employing the concept of both non-delay and enhanced algorithms which provides better solution than each one separately. Furthermore, an effective two-phase genetic algorithm approach is devised integrating with hybrid timetabling to deal with the crashing and sequencing components. The results obtained from experimental evaluations support the outstanding performance of the proposed approach.     

Using particle swarm optimization to solve effectively the school timetabling problem

A new hybrid adaptive algorithm based on particle swarm optimization (PSO) is designed, developed and applied to the high school timetabling problem. The proposed PSO algorithm is used to create feasible and efficient timetables for high schools in Greece. Experiments with real-world data coming from different high schools have been conducted to show the efficiency of the proposed PSO algorithm. As well as that, the algorithm has been compared with four other effective techniques found in the literature to demonstrate its efficiency and superior performance. In order to have a fair comparison with these algorithms, we decided to use the exact same input instances used by these algorithms. The proposed PSO algorithm outperforms, in most cases, other existing attempts to solve the same problem as shown by experimental results.     

A greedy gradient-simulated annealing selection hyper-heuristic

Educational timetabling problem is a challenging real world problem which has been of interest to many researchers and practitioners. There are many variants of this problem which mainly require scheduling of events and resources under various constraints. In this study, a curriculum based course timetabling problem at Yeditepe University is described and an iterative selection hyper-heuristic is presented as a solution method. A selection hyper-heuristic as a high level methodology operates on the space formed by a fixed set of low level heuristics which operate directly on the space of solutions. The move acceptance and heuristic selection methods are the main components of a selection hyper-heuristic. The proposed hyper-heuristic in this study combines a simulated annealing move acceptance method with a learning heuristic selection method and manages a set of low level constraint oriented heuristics. A key goal in hyper-heuristic research is to build low cost methods which are general and can be reused on unseen problem instances as well as other problem domains desirably with no additional human expert intervention. Hence, the proposed method is additionally applied to a high school timetabling problem, as well as six other problem domains from a hyper-heuristic benchmark to test its level of generality. The empirical results show that our easy-to-implement hyper-heuristic is effective in solving the Yeditepe course timetabling problem. Moreover, being sufficiently general, it delivers a reasonable performance across different problem domains.     

A hybrid CMA-ES and HDE optimisation algorithm with application to solar energy potential

This paper describes the results of initial experiments to apply computational algorithms to explore a large parameter space containing many variables in the search for an optimal solution for the sustainable design of an urban development using a potentially complicated fitness function. This initial work concentrates on varying the placement of buildings to optimise solar irradiation availability. For this we propose a hybrid of the covariance matrix adaptation evolution strategy (CMA-ES) and hybrid differential evolution (HDE) algorithms coupled with an efficient backwards ray tracing technique. In this paper we concentrate on the formulation of the new hybrid algorithm and its testing using standard benchmarks as well as a solar optimisation problem. The new algorithm outperforms both the standalone CMA-ES and HDE algorithms in benchmark tests and an alternative multi-objective optimisation tool in the case of the solar optimisation problem.     

A genetic algorithm for a university weekly courses timetabling problem

The timetabling problem is concerned with the allocation, subject to constraints, of given resources to objects in space and time in such way as to satisfy as nearly as possible a set of desirable objectives. This problem is known to be NP–complete and as such only combinatorial optimization methods can guarantee an optimal timetable. In this paper we propose a sector–based genetic algorithm for solving a university weekly courses timetabling problem. Preliminary experimental results indicate that the algorithm is promising.     

Course timetabling using evolutionary operators

Timetabling is the problem of scheduling a set of events while satisfying various constraints. In this paper, we develop and study the performance of an evolutionary algorithm, designed to solve a specific variant of the timetabling problem. Our aim here is twofold: to develop a competitive algorithm, but more importantly, to investigate the applicability of evolutionary operators to timetabling. To this end, the introduced algorithm is tested using a benchmark set. Comparison with other algorithms shows that it achieves better results in some, but not all instances, signifying strong and weak points. To further the study, more comprehensive tests are performed in connection with another evolutionary algorithm that uses strictly group-based operators. Our analysis of the empirical results leads us to question single-level selection, proposing, in its place, a multi-level alternative.     

A CAD-based on biological method for designing optimal fatigue life

This paper presents an innovative approach to shape optimisation of three-dimensional, damage-tolerant structures. In this approach, a new and simple method, which we termed Failure Analysis of Structures (FAST), is used to estimate the stress-intensity factor for cracks at a notch. The methodology and software used to automate damage-tolerance calculations are developed using computer-aided design and FAST codes. The worst crack locations are found by modeling many cracks along fractured critical edges of the structure by using FAST. This software is then used to evaluate damage-tolerance objective functions for optimisation algorithms. A particular stress-based biological growth method is employed to study the problem of optimisation with fatigue life as the design objective. This work confirms that a stress-optimised structure does not necessarily give the longest fatigue life by numerical examples.     

Initialization strategies and diversity in evolutionary timetabling

This document seeks to provide a scientific basis by which different initialization algorithms for evolutionary timetabling may be compared. Seeding the initial population may be used to improve initial quality and provide a better starting point for the evolutionary algorithm. This must be tempered against the consideration that if the seeding algorithm produces very similar solutions, then the loss of genetic diversity may well lead to a worse final solution. Diversity, we hope, provides a good indication of how good the final solution will be, although only by running the evolutionary algorithm will the exact result be found. We will investigate the effects of heuristic seeding by taking quality and diversity measures of populations generated by heuristic initialization methods on both random and real-life data, as well as assessing the long-term performance of an evolutionary algorithm (found to work well on the timetabling problem) when using heuristic initialization. This will show how the use of heuristic initialization strategies can substantially improve the performance of evolutionary algorithms for the timetabling problem.     

Measuring instance difficulty for combinatorial optimization problems

Discovering the conditions under which an optimization algorithm or search heuristic will succeed or fail is critical for understanding the strengths and weaknesses of different algorithms, and for automated algorithm selection. Large scale experimental studies - studying the performance of a variety of optimization algorithms across a large collection of diverse problem instances - provide the resources to derive these conditions. Data mining techniques can be used to learn the relationships between the critical features of the instances and the performance of algorithms. This paper discusses how we can adequately characterize the features of a problem instance that have impact on difficulty in terms of algorithmic performance, and how such features can be defined and measured for various optimization problems. We provide a comprehensive survey of the research field with a focus on six combinatorial optimization problems: assignment, traveling salesman, and knapsack problems, bin-packing, graph coloring, and timetabling. For these problems - which are important abstractions of many real-world problems - we review hardness-revealing features as developed over decades of research, and we discuss the suitability of more problem-independent landscape metrics. We discuss how the features developed for one problem may be transferred to study related problems exhibiting similar structures.     

A hybrid particle swarm optimization for a university course scheduling problem with flexible preferences

The timetabling problem at universities is an NP-hard problem concerned with instructor assignments and class scheduling under multiple constraints and limited resources. A novel meta-heuristic algorithm that is based on the principles of particle swarm optimization (PSO) is proposed for course scheduling problem. The algorithm includes some features: designing an ‘absolute position value’ representation for the particle; allowing instructors that they are willing to lecture based on flexible preferences, such as their preferred days and time periods, the maximum number of teaching-free time periods and the lecturing format (consecutive time periods or separated into different time periods); and employing a repair process for all infeasible timetables. Furthermore, in the original PSO algorithm, particles search solutions in a continuous solution space. Since the solution space of the course scheduling problem is discrete, a local search mechanism is incorporated into the proposed PSO in order to explore a better solution improvement. The algorithms were tested using the timetabling data from a typical university in Taiwan. The experimental results demonstrate that the proposed hybrid algorithm yields an efficient solution with an optimal satisfaction of course scheduling for instructors and class scheduling arrangements. This hybrid algorithm also outperforms the genetic algorithm proposed in the literature.     

Train service timetabling in railway open markets by particle swarm optimisation

Railway timetabling is an important process in train service provision as it matches the transportation demand with the infrastructure capacity while customer satisfaction is also considered. It is a multi-objective optimisation problem, in which a feasible solution, rather than the optimal one, is usually taken in practice because of the time constraint. The quality of services may suffer as a result. In a railway open market, timetabling usually involves rounds of negotiations amongst a number of self-interested and independent stakeholders and hence additional objectives and constraints are imposed on the timetabling problem. While the requirements of all stakeholders are taken into consideration simultaneously, the computation demand is inevitably immense. Intelligent solution-searching techniques provide a possible solution. This paper attempts to employ a particle swarm optimisation (PSO) approach to devise a railway timetable in an open market. The suitability and performance of PSO are studied on a multi-agent-based railway open-market negotiation simulation platform.     

A hyperheuristic approach to examination timetabling problems: benchmarks and a new problem from practice

Many researchers studying examination timetabling problems focus on either benchmark problems or problems from practice encountered in their institutions. Hyperheuristics are proposed as generic optimisation methods which explore the search space of heuristics rather than direct solutions. In the present study, the performance of tournament-based hyperheuristics for the exam timetabling problem are investigated. The target instances include both the Toronto and ITC 2007 benchmarks and the examination timetabling problem at KAHO Sint-Lieven (Ghent, Belgium). The Toronto and ITC 2007 benchmarks are post-enrolment-based examination timetabling problems, whereas the KAHO Sint-Lieven case is a curriculum-based examination timetabling problem. We drastically improve the previous (manually created) solution for the KAHO Sint-Lieven problem by generating a timetable that satisfies all the hard and soft constraints. We also make improvements on the best known results in the examination timetabling literature for seven out of thirteen instances for the To ronto benchmarks. The results are competitive with those of the finalists of the examination timetabling track of the International Timetabling Competition.     

A new effective operator for the hybrid algorithm for solving global optimisation problems

Hybrid algorithms have been recently used to solve complex single-objective optimisation problems. The ultimate goal is to find an optimised global solution by using these algorithms. Based on the existing algorithms (HP_CRO, PSO, RCCRO), this study proposes a new hybrid algorithm called MPC (Mean-PSO-CRO), which utilises a new Mean-Search Operator. By employing this new operator, the proposed algorithm improves the search ability on areas of the solution space that the other operators of previous algorithms do not explore. Specifically, the Mean-Search Operator helps find the better solutions in comparison with other algorithms. Moreover, the authors have proposed two parameters for balancing local and global search and between various types of local search, as well. In addition, three versions of this operator, which use different constraints, are introduced. The experimental results on 23 benchmark functions, which are used in previous works, show that our framework can find better optimal or close-to-optimal solutions with faster convergence speed for most of the benchmark functions, especially the high-dimensional functions. Thus, the proposed algorithm is more effective in solving single-objective optimisation problems than the other existing algorithms.     

Integrating employee timetabling with scheduling of machines and transporters in a job-shop environment: A mathematical formulation and an Anarchic Society Optimization algorithm

This paper addresses a ternary-integration scheduling problem that incorporates employee timetabling into the scheduling of machines and transporters in a job-shop environment with a finite number of heterogeneous transporters where the objective is to minimize the completion time of all jobs. The problem is first formulated as a mixed-integer linear programming model. Then, an Anarchic Society Optimization (ASO) algorithm is developed to solve large-sized instances of the problem. The formulation is used to solve small-sized instances and to evaluate the quality of the solutions obtained for instances with larger sizes. A comprehensive numerical study is carried out to assess the performance of the proposed ASO algorithm. The algorithm is compared with three alternative metaheuristic algorithms. It is also compared with several algorithms developed in the literature for the integrated scheduling of machines and transporters. Moreover, the algorithms are tested on a set of adapted benchmark instances for an integrated problem of machine scheduling and employee timetabling. The numerical analysis suggests that the ASO algorithm is both effective and efficient in solving large-sized instances of the proposed integrated job-shop scheduling problem.     

Hybrid algorithms for the twin–screw extrusion configuration problem

The twin-screw configuration problem (TSCP) arises in the context of polymer processing, where twin-screw extruders are used to prepare polymer blends, compounds or composites. The goal of the TSCP is to define the configuration of a screw from a given set of screw elements. The TSCP can be seen as a sequencing problem as the order of the screw elements on the screw axis has to be defined. It is also inherently a multi-objective problem since processing has to optimize various conflicting parameters related to the degree of mixing, shear rate, or mechanical energy input among others. In this article, we develop hybrid algorithms to tackle the bi-objective TSCP. The hybrid algorithms combine different local search procedures, including Pareto local search and two phase local search algorithms, with two different population-based algorithms, namely a multi-objective evolutionary algorithm and a multi-objective ant colony optimization algorithm. The experimental evaluation of these approaches shows that the best hybrid designs, combining Pareto local search with a multi-objective ant colony optimization approach, outperform the best algorithms that have been previously proposed for the TSCP.