A grouping hyper-heuristic framework: application on graph colouring

Grouping problems are hard to solve combinatorial optimisation problems which require partitioning of objects into a minimum number of subsets while a given objective is simultaneously optimised. Selection hyper-heuristics are high level general purpose search methodologies that operate on a space formed by a set of low level heuristics rather than solutions. Most of the recently proposed selection hyper-heuristics are iterative and make use of two key methods which are employed successively; heuristic selection and move acceptance. In this study, we present a novel generic selection hyper-heuristic framework containing a fixed set of reusable grouping low level heuristics and an unconventional move acceptance mechanism for solving grouping problems. This framework deals with one solution at a time at any given decision point during the search process. Also, a set of high quality solutions, capturing the trade-off between the number of groups and the additional objective for the given grouping problem, is maintained. The move acceptance mechanism embeds a local search approach which is capable of progressing improvements on those trade-off solutions. The performance of different selection hyper-heuristics with various components under the proposed framework is investigated on graph colouring as a representative grouping problem. Then, the top performing hyper-heuristics are applied to a benchmark of examination timetabling instances. The empirical results indicate the effectiveness and generality of the proposed framework enabling grouping hyper-heuristics to achieve high quality solutions in both domains. ©2015 Elsevier Ltd. All rights reserved

Exam timetabling using graph colouring approach

Timetabling at large covering many different types of problems which have their own unique characteristics. In education, the three most common academic timetabling problems are school timetable, university timetable and exam timetable. Exam timetable is crucial but difficult to be done manually due to the complexity of the problem. The main problem includes dual academic calendar, increasing student enrolments and limitations of resources. This study presents a solution method for exam timetable problem in centre for foundation studies and extension education (FOSEE), Multimedia University, Malaysia. The method of solution is a heuristic approach that include graph colouring, cluster heuristic and sequential heuristic

Exam Timetabling Using Graph Colouring Approach

Timetabling at large covering many different types of problems which have their own unique characteristics. In education, the three most common academic timetabling problems are school timetable, university timetable and exam timetable. Exam timetable is crucial but difficult to be done manually due to the complexity of the problem. The main problem includes dual academic calendar, increasing student enrolments and limitations of resources. This study presents a solution method for exam timetable problem in centre for foundation studies and extension education (FOSEE), Multimedia University, Malaysia. The method of solution is a heuristic approach that include graph colouring, cluster heuristic and sequential heuristic

Finding feasible timetables using group-based operators.

This paper describes the applicability of the so-called "grouping genetic algorithm" to a well-known version of the university course timetabling problem. We note that there are, in fact, various scaling up issues surrounding this sort of algorithm and, in particular, see that it behaves in quite different ways with different sized problem instances. As a by-product of these investigations, we introduce a method for measuring population diversities and distances between individuals with the grouping representation. We also look at how such an algorithm might be improved: first, through the introduction of a number of different fitness functions and, second, through the use of an additional stochastic local-search operator (making in effect a grouping memetic algorithm). In many cases, we notice that the best results are actually returned when the grouping genetic operators are removed altogether, thus highlighting many of the issues that are raised in the stud

Search with evolutionary ruin and stochastic rebuild: a theoretic framework and a case study on exam timetabling

This paper presents a state transition based formal framework for a new search method, called Evolutionary Ruin and Stochastic Recreate, which tries to learn and adapt to the changing environments during the search process. It improves the performance of the original Ruin and Recreate principle by embedding an additional phase of Evolutionary Ruin to mimic the survival-of-the-fittest mechanism within single solutions. This method executes a cycle of Solution Decomposition, Evolutionary Ruin, Stochastic Recreate and Solution Acceptance until a certain stopping condition is met. The Solution Decomposition phase first uses some problem-specific knowledge to decompose a complete solution into its components and assigns a score to each component. The Evolutionary Ruin phase then employs two evolutionary operators (namely Selection and Mutation) to destroy a certain fraction of the solution, and the next Stochastic Recreate phase repairs the “broken” solution. Last, the Solution Acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution. Hence, optimisation is achieved by an iterative process of component evaluation, solution disruption and stochastic constructive repair. From the state transitions point of view, this paper presents a probabilistic model and implements a Markov chain analysis on some theoretical properties of the approach. Unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments, our model is based on state transitions within the space of partial assignments. The exam timetabling problems are used to test the performance in solving real-world hard problems

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Modifying colourings between time-steps to tackle changes in dynamic random graphs

Many real world operational research problems can be formulated as graph colouring problems. Algorithms for this problem usually operate under the assumption that the size and constraints of a problem are fixed, allowing us to model the problem using a static graph. For many problems however, this is not the case and it would be more appropriate to model such problems using dynamic graphs. In this paper we will explore whether feasible colourings for one graph at time-step t can be modified into a colouring for a similar graph at time-step t+1 in some beneficial manner

Metaheuristics for university course timetabling.

The work presented in this thesis concerns the problem of timetabling at universities – particularly course-timetabling, and examines the various ways in which metaheuristic techniques might be applied to these sorts of problems. Using a popular benchmark version of a university course timetabling problem, we examine the implications of using a “twostaged” algorithmic approach, whereby in stage-one only the mandatory constraints areconsidered for satisfaction, with stage-two then being concerned with satisfying the remaining constraints but without re-breaking any of the mandatory constraints in the process. Consequently, algorithms for each stage of this approach are proposed and analysed in detail.For the first stage we examine the applicability of the so-called Grouping Genetic Algorithm (GGA). In our analysis of this algorithm we discover a number of scaling-upissues surrounding the general GGA approach and discuss various reasons as to why this is so. Two separate ways of enhancing general performance are also explored. Secondly, an Iterated Heuristic Search algorithm is also proposed for the same problem, and in experiments it is shown to outperform the GGA in almost all cases. Similar observations to these are also witnessed in a second set of experiments, where the analogous problem of colouring equipartite graphs is also considered.Two new metaheuristic algorithms are also proposed for the second stage of the twostaged approach: an evolutionary algorithm (with a number of new specialised evolutionaryoperators), and a simulated annealing-based approach. Detailed analyses of both algorithms are presented and reasons for their relative benefits and drawbacks are discussed.Finally, suggestions are also made as to how our best performing algorithms might be modified in order to deal with further “real-world” constraints. In our analyses of these modified algorithms, as well as witnessing promising behaviour in some cases, we are also able to highlight some of the limitations of the two-stage approach in certain cases

Evolutionary Ruin And Stochastic Recreate: A Case Study On The Exam Timetabling Problem

This paper presents a new class of intelligent systems, called Evolutionary Ruin and Stochastic Recreate, that can learn and adapt to the changing enviroment. It improves the original Ruin and Recreate principle’s performance by incorporating an Evolutionary Ruin step which implements evolution within a single solution. In the proposed approach, a cycle of Solution Decomposition, Evolutionary Ruin and Stochastic Recreate continues until stopping conditions are reached. The Solution Decomposition step first uses some domain knowledge to break a solution down into its components and assign a score to each. The Evolutionary Ruin step then applies two operators (namely Selection and Mutation) to destroy a certain fraction of the entire solution. After the above steps, an input solution becomes partial and thus the resulting partial solution needs to be repaired. The repair is carried out by using the Stochastic Recreate step to reintroduce the removed items in a specific way (somewhat stochastic in order to have a better chance to jump out of the local optima), and then ask the underlying improvement heuristic whether this move will be accepted. These three steps are executed in sequence until a specific stopping condition is reached. Therefore, optimisation is achieved by solution disruption, iterative improvement and a stochastic constructive repair process performed within. Encouraging experimental results on exam timetabling problems are reported