Performance Analyses of Graph Heuristics and Selected Trajectory Metaheuristics on Examination Timetable Problem

Examination timetabling problem is hard to solve due to its NP-hard nature, with a large number of constraints having to be accommodated. To deal with the problem effectually, frequently heuristics are used for constructing feasible examination timetable while meta-heuristics are applied for improving the solution quality. This paper presents the performances of graph heuristics and major trajectory metaheuristics or S-metaheuristics for addressing both capacitated and un-capacitated examination timetabling problem. For constructing the feasible solution, six graph heuristics are used. They are largest degree (LD), largest weighted degree (LWD), largest enrolment degree (LE), and three hybrid heuristic with saturation degree (SD) such as SD-LD, SD-LE, and SD-LWD. Five trajectory algorithms comprising of tabu search (TS), simulated annealing (SA), late acceptance hill climbing (LAHC), great deluge algorithm (GDA), and variable neighborhood search (VNS) are employed for improving the solution quality. Experiments have been tested on several instances of un-capacitated and capacitated benchmark datasets, which are Toronto and ITC2007 dataset respectively. Experimental results indicate that, in terms of construction of solution of datasets, hybridizing of SD produces the best initial solutions. The study also reveals that, during improvement, GDA, SA, and LAHC can produce better quality solutions compared to TS and VNS for solving both benchmark examination timetabling datasets

Structure based partial solution search for the examination timetabling problem.

Doctoral Degree. University of KwaZulu-Natal, Pietermaritzburg.The aim of this work is to present a new approach, namely, Structure Based Partial Solution Search (SBPSS) to solve the Examination Timetabling Problem. The success of the Developmental Approach in this problem domain suggested that the strategy of searching the spaces of partial timetables whilst constructing them is promising and worth pursuing. This work adopts a similar strategy. Multiple timetables are incrementally constructed at the same time. The quality of the partial timetables is improved upon by searching their partial solution spaces at every iteration during construction. Another key finding from the literature survey revealed that although timetables may exhibit the same behaviour in terms of their objective values, their structures or exam schedules may be different. The challenge with this finding is to decide on which regions to pursue because some regions may not be worth investigating due to the difficulty in searching them. These problematic areas may have solutions that are not amenable to change which makes it difficult to improve them. Another reason is that the neighbourhoods of solutions in these areas may be less connected than others which may restrict the ability of the search to move to a better solution in that neighbourhood. By moving to these problematic areas of the search space the search may stagnate and waste expensive computational resources. One way to overcome this challenge is to use both structure and behaviour in the search and not only behaviour alone to guide the search. A search that is guided by structure is able to find new regions by considering the structural components of the candidate solutions which indicate which part of the search space the same candidates occupy. Another benefit to making use of a structure-based search is that it has no objective value bias because it is not guided by only the objective value. This statement is consistent with the literature survey where it is suggested that in order to achieve good performance the search should not be guided by only the objective value. The proposed method has been tested on three popular benchmark sets for examination timetabling, namely, the Carter benchmark set; the benchmark set from the International Timetabling competition in 2007 and the Yeditepe benchmark set. The SBPSS found the best solutions for two of the Carter problem instances. The SBPSS found the best solutions for four of the competition problem instances. Lastly, the SBPSS improved on the best results for all the Yeditepe problem instances

A self-adaptive multimeme memetic algorithm co-evolving utility scores to control genetic operators and their parameter settings

Memetic algorithms are a class of well-studied metaheuristics which combine evolutionary algorithms and local search techniques. A meme represents contagious piece of information in an adaptive information sharing system. The canonical memetic algorithm uses a fixed meme, denoting a hill climbing operator, to improve each solution in a population during the evolutionary search process. Given global parameters and multiple parametrised operators, adaptation often becomes a crucial constituent in the design of MAs. In this study, a self-adaptive self-configuring steady-state multimeme memetic algorithm (SSMMA) variant is proposed. Along with the individuals (solutions), SSMMA co-evolves memes, encoding the utility score for each algorithmic component choice and relevant parameter setting option. An individual uses tournament selection to decide which operator and parameter setting to employ at a given step. The performance of the proposed algorithm is evaluated on six combinatorial optimisation problems from a cross-domain heuristic search benchmark. The results indicate the success of SSMMA when compared to the static Mas as well as widely used self-adaptive Multimeme Memetic Algorithm from the scientific literature

An investigation of Monte Carlo tree search and local search for course timetabling problems

The work presented in this thesis focuses on solving course timetabling problems, a variant of education timetabling. Automated timetabling is a popular topic among researchers and practitioners because manual timetable construction is impractical, if not impossible, as it is known to be NP-hard. A two-stage approach is investigated. The first stage involves finding feasible solutions. Monte Carlo Tree Search (MCTS) is utilized in this stage. As far as we are aware, it is used for the first time in addressing the timetabling problem. It is a relatively new search method and has achieved breakthrough in the domain of games particularly Go. Several enhancements are attempted on MCTS such as heuristic based simulations and pruning. We also compare the effectiveness of MCTS with Graph Coloring Heuristic (GCH) and Tabu Search (TS) based methods. Initial findings show that a TS based method is more promising, so we focus on improving TS. We propose an algorithm called Tabu Search with Sampling and Perturbation (TSSP). Among the enhancements that we introduced are event sampling, a novel cost function and perturbation. Furthermore, we hybridize TSSP with Iterated Local Search (ILS). The second stage focuses on improving the quality of feasible solutions. We propose a variant of Simulated Annealing called Simulated Annealing with Reheating (SAR). SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. The rigorous setting of initial and end temperature in conventional SA is bypassed in SAR. Precisely, reheating and cooling were applied at the right time and level, thus saving time allowing the search to be performed efficiently. One drawback of SAR is having to preset the composition of neighborhood structures for the datasets. We present an enhanced variant of the SAR algorithm called Simulated Annealing with Improved Reheating and Learning (SAIRL). We propose a reinforcement learning based method to obtain a suitable neighborhood structure composition for the search to operate effectively. We also propose to incorporate the average cost changes into the reheated temperature function. SAIRL eliminates the need for tuning parameters in conventional SA as well as neighborhood structures composition in SAR. Experiments were tested on four publicly available datasets namely Socha, International Timetabling Competition 2002 (ITC02), International Timetabling Competition 2007 (ITC07) and Hard. Our results are better or competitive when compared with other state of the art methods where new best results are obtained for many instances

A tensor-based selection hyper-heuristic for cross-domain heuristic search

Hyper-heuristics have emerged as automated high level search methodologies that manage a set of low level heuristics for solving computationally hard problems. A generic selection hyper-heuristic combines heuristic selection and move acceptance methods under an iterative single point-based search framework. At each step, the solution in hand is modified after applying a selected heuristic and a decision is made whether the new solution is accepted or not. In this study, we represent the trail of a hyper-heuristic as a third order tensor. Factorization of such a tensor reveals the latent relationships between the low level heuristics and the hyper-heuristic itself. The proposed learning approach partitions the set of low level heuristics into two subsets where heuristics in each subset are associated with a separate move acceptance method. Then a multi-stage hyper-heuristic is formed and while solving a given problem instance, heuristics are allowed to operate only in conjunction with the associated acceptance method at each stage. To the best of our knowledge, this is the first time tensor analysis of the space of heuristics is used as a data science approach to improve the performance of a hyper-heuristic in the prescribed manner. The empirical results across six different problem domains from a benchmark indeed indicate the success of the proposed approach

Modeling and scheduling no-idle hybrid flow shop problems

Although several papers have studied no-idle scheduling problems, they all focus on flow shops, assuming one processor at each working stage. But, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. This paper considers the problem of scheduling no-idle hybrid flow shops. A mixed integer linear programming model is first developed to mathematically formulate the problem. Using commercial software, the model can solve small instances to optimality. Then, two metaheuristics based on variable neighborhood search and genetic algorithms are developed to solve larger instances. Using numerical experiments, the performance of the model and algorithms are evaluated.Although several papers have studied no-idle scheduling problems, they all focus on flow shops, assuming one processor at each working stage. But, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. This paper considers the problem of scheduling no-idle hybrid flow shops. A mixed integer linear programming model is first developed to mathematically formulate the problem. Using commercial software, the model can solve small instances to optimality. Then, two metaheuristics based on variable neighborhood search and genetic algorithms are developed to solve larger instances. Using numerical experiments, the performance of the model and algorithms are evaluated

Developing novel meta-heuristic, hyper-heuristic and cooperative search for course timetabling problems

The research presented in this PhD thesis focuses on the problem of university course timetabling, and examines the various ways in which metaheuristics, hyperheuristics and cooperative heuristic search techniques might be applied to this sort of problem. The university course timetabling problem is an NP-hard and also highly constrained combinatorial problem. Various techniques have been developed in the literature to tackle this problem. The research work presented in this thesis approaches this problem in two stages. For the first stage, the construction of initial solutions or timetables, we propose four hybrid heuristics that combine graph colouring techniques with a well-known local search method, tabu search, to generate initial feasible solutions. Then, in the second stage of the solution process, we explore different methods to improve upon the initial solutions. We investigate techniques such as single-solution metaheuristics, evolutionary algorithms, hyper-heuristics with reinforcement learning, cooperative low-level heuristics and cooperative hyper-heuristics. In the experiments throughout this thesis, we mainly use a popular set of benchmark instances of the university course timetabling problem, proposed by Socha et al. [152], to assess the performance of the methods proposed in this thesis. Then, this research work proposes algorithms for each of the two stages, construction of initial solutions and solution improvement, and analyses the proposed methods in detail. For the first stage, we examine the performance of the hybrid heuristics on constructing feasible solutions. In our analysis of these algorithms we discovered that these hybrid approaches are capable of generating good quality feasible solutions in reasonable computation time for the 11 benchmark instances of Socha et al. [152]. Just for this first stage, we conducted a second set of experiments, testing the proposed hybrid heuristics on another set of benchmark instances corresponding to the international timetabling competition 2002 [91J. Our hybrid construction heuristics were also capable of producing feasible solutions for the 20 instances of the competition in reasonable computation time. It should be noted however, that most of the research presented here was focused on the 11 problem instances of Socha et al. [152]. For the second stage, we propose new metaheuristic algorithms and cooperative hyper-heuristics, namely a non-linear great deluge algorithm, an evolutionary nonlinear great deluge algorithm (with a number of new specialised evolutionary operators), a hyper-heuristic with a learning mechanism approach, an asynchronous cooperative low-level heuristic and an asynchronous cooperative hyper-heuristic. These two last algorithms were inspired by the particle swarm optimisation technique. Detailed analyses of the proposed algorithms are presented and their relative benefits discussed. Finally, we give our suggestions as to how our best performing algorithms might be modified in order to deal with a wide range of problem domains including more real-world constraints. We also discuss the drawbacks of our algorithms in the final section of this thesis

A tensor based hyper-heuristic for nurse rostering

Nurse rostering is a well-known highly constrained scheduling problem requiring assignment of shifts to nurses satisfying a variety of constraints. Exact algorithms may fail to produce high quality solutions, hence (meta)heuristics are commonly preferred as solution methods which are often designed and tuned for specific (group of) problem instances. Hyper-heuristics have emerged as general search methodologies that mix and manage a predefined set of low level heuristics while solving computationally hard problems. In this study, we describe an online learning hyper-heuristic employing a data science technique which is capable of self-improvement via tensor analysis for nurse rostering. The proposed approach is evaluated on a well-known nurse rostering benchmark consisting of a diverse collection of instances obtained from different hospitals across the world. The empirical results indicate the success of the tensor-based hyper-heuristic, improving upon the best-known solutions for four of the instances