Monte Carlo Tree Search in Finding Feasible Solutions for Course Timetabling Problem

We are addressing the course timetabling problem in this work. In a university, students can select their favorite courses each semester. Thus, the general requirement is to allow them to attend lectures without clashing with other lectures. A feasible solution is a solution where this and other conditions are satisfied. Constructing reasonable solutions for course timetabling problem is a hard task. Most of the existing methods failed to generate reasonable solutions for all cases. This is since the problem is heavily constrained and an effective method is required to explore and exploit the search space. We utilize Monte Carlo Tree Search (MCTS) in finding feasible solutions for the first time. In MCTS, we build a tree incrementally in an asymmetric manner by sampling the decision space. It is traversed in the best-first manner. We propose several enhancements to MCTS like simulation and tree pruning based on a heuristic. The performance of MCTS is compared with the methods based on graph coloring heuristics and Tabu search. We test the solution methodologies on the three most studied publicly available datasets. Overall, MCTS performs better than the method based on graph coloring heuristic; however, it is inferior compared to the Tabu based method. Experimental results are discussed

An effective hybrid local search approach for the post enrolment course timetabling problem

We address the post enrolment course timetabling (PE-CTT) problem in this paper. PE-CTT is known as an NP-hard problem that focuses on finding an efficient allocation of courses onto a finite number of time slots and rooms. It is one of the most challenging resources allocation problems faced by universities around the world. This work proposes a two-phase hybrid local search algorithm to address the PE-CTT problem. The first phase focuses on finding a feasible solution, while the second phase tries to minimize the soft constraint violations of the generated feasible solution. For the first phase, we propose a hybrid of Tabu Search with Sampling and Perturbation with Iterated Local Search. We test the proposed methodology on the hardest cases of PE-CTT benchmarks. The hybrid algorithm performs well and our results are superior compared to the recent methods in finding feasible solutions. For the second phase, we propose an algorithm called Simulated Annealing with Reheating (SAR) with two preliminary runs (SAR-2P). The SAR algorithm is used to minimize the soft constraint violations by exploiting information collected from the preliminary runs. We test the proposed methodology on three publicly available datasets. Our algorithm is competitive with the standards set by the recent methods. In total, the algorithm attains new best results for 3 cases and new best mean results for 7 cases. Furthermore, it is scalable when the execution time is extended

A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems

Hyper-heuristics are search methodologies that aim to provide high-quality solutions across a wide variety of problem domains, rather than developing tailor-made methodologies for each problem instance/domain. A traditional hyper-heuristic framework has two levels, namely, the high level strategy (heuristic selection mechanism and the acceptance criterion) and low level heuristics (a set of problem specific heuristics). Due to the different landscape structures of different problem instances, the high level strategy plays an important role in the design of a hyper-heuristic framework. In this paper, we propose a new high level strategy for a hyper-heuristic framework. The proposed high-level strategy utilizes a dynamic multiarmed bandit-extreme value-based reward as an online heuristic selection mechanism to select the appropriate heuristic to be applied at each iteration. In addition, we propose a gene expression programming framework to automatically generate the acceptance criterion for each problem instance, instead of using human-designed criteria. Two well-known, and very different, combinatorial optimization problems, one static (exam timetabling) and one dynamic (dynamic vehicle routing) are used to demonstrate the generality of the proposed framework. Compared with state-of-the-art hyper-heuristics and other bespoke methods, empirical results demonstrate that the proposed framework is able to generalize well across both domains. We obtain competitive, if not better results, when compared to the best known results obtained from other methods that have been presented in the scientific literature. We also compare our approach against the recently released hyper-heuristic competition test suite. We again demonstrate the generality of our approach when we compare against other methods that have utilized the same six benchmark datasets from this test suite

Improved local search approaches to solve the post enrolment course timetabling problem

In this work, we are addressing the post enrollment course timetabling (PE-CTT) problem. We combine different local search algorithms into an iterative two stage procedure. In the first stage, Tabu Search with Sampling and Perturbation (TSSP) is used to generate feasible solutions. In the second stage, we propose an improved variant of Simulated Annealing (SA), which we call Simulated Annealing with Reheating (SAR), to improve the solution quality of feasible solutions. SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. SAR eliminates the need for extensive tuning as is often required in conventional SA. The proposed methodologies are tested on the three most studied datasets from the scientific literature. Our algorithms perform well and our results are competitive, if not better, compared to the benchmarks set by the state of the art methods. New best known results are provided for many instances

Portfolio Optimization Problem: A Taxonomic Review of Solution Methodologies

This survey paper provides an overview of current developments for the Portfolio Optimisation Problem (POP) based on articles published from 2018 to 2022. It reviews the latest solution methodologies utilised in addressing POPs in terms of mechanisms and performance. The methodologies are categorised as Metaheuristic, Mathematical Optimisation, Hybrid Approaches, Matheuristic and Machine Learning. The datasets (benchmark, real-world, and hypothetical) utilised in portfolio optimisation research are provided. The state-of-the-art methodologies for benchmark datasets are presented accordingly. Populationbased metaheuristics are the most preferred techniques among researchers in addressing the POP. Hybrid approaches is an emerging trend (2018 onwards). The OR-Library is the most widely used benchmark dataset for researchers to compare their methodologies in addressing POP. The research challenges and opportunities are discussed. The summarisation of the published papers in this survey provides an insight to researchers in identifying emerging trends and gaps in this research area

Hybrid particle swarm optimization with particle elimination for the high school timetabling problem

In this paper, a PSO-based algorithm that hybridized Particle Swarm Optimization (PSO) and Hill Climbing (HC) is applied to high school timetabling problem. This hybrid has two features, a novel solution transformation and particle elimination. The proposed methodologies are tested on the XHSTT-2014 dataset (which is relatively new for the school timetabling problem) plus other additional instances. The experimental results show that the proposed algorithm is efective in solving small and medium instances compared to standalone HC and better than the conventional PSO for most instances. In a comparison to the state of the art methods, it achieved the lowest mean of soft constraint violations for 7 instances and the lowest mean of hard constraint violations for 1 instance

A Survey of university course timetabling problem: perspectives, trends and opportunities

The timetabling problem is common to academic institutions such as schools, colleges or universities. It is a very hard combinatorial optimisation problem which attracts the interest of many researchers. The university course timetabling problem (UCTTP) is difficult to address due to the size of the problem and several challenging hard and soft constraints. Over the years, various methodologies were proposed to solve UCTTP. The purpose of this survey paper is to provide the most recent scientific review of the methodologies applied to UCTTP. The paper unveils a classification of methodologies proposed in recent years based on chronology and datasets used. Perspectives, trends, challenges and opportunities in UCTTP are also presented. It is observed that meta-heuristic approaches are popular among researchers. This is followed closely by hybrid methodologies. Hyper-heuristic approaches are also able to produce effective results. Another observation is that the state-of-art methodologies in the scientific literature are not fully utilised in a real-world environment perhaps due to the limited flexibility of these methodologies

A harmony search algorithm for nurse rostering problems

Harmony search algorithm (HSA) is a relatively new nature-inspired algorithm. It evolves solutions in the problem search space by mimicking the musical improvisation process in seeking agreeable harmony measured by aesthetic standards. The nurse rostering problem (NRP) is a well-known NP-hard scheduling problem that aims at allocating the required workload to the available staff nurses at healthcare organizations to meet the operational requirements and a range of preferences. This work investigates research issues of the parameter settings in HSA and application of HSA to effectively solve complex NRPs. Due to the well-known fact that most NRPs algorithms are highly problem (or even instance) dependent, the performance of our proposed HSA is evaluated on two sets of very different nurse rostering problems. The first set represents a real world dataset obtained from a large hospital in Malaysia. Experimental results show that our proposed HSA produces better quality rosters for all considered instances than a genetic algorithm (implemented herein). The second is a set of well-known benchmark NRPs which are widely used by researchers in the literature. The proposed HSA obtains good results (and new lower bound for a few instances) when compared to the current state of the art of meta-heuristic algorithms in recent literature

An iterated local search with multiple perturbation operators and time varying perturbation strength for the aircraft landing problem

Landing aircraft safely is an important operation that air traffic controllers have to deal with on a daily basis. For each arriving aircraft a runway and a landing time must be allocated. If these allocations can be done in an efficient way, it could give the airport a competitive advantage. The Aircraft Landing Problem (ALP) aims to minimize the deviation from a preferred target time of each aircraft. It is an NP-hard problem, meaning that we may have to resort to heuristic methods as exact methods may not be suitable, especially as the problem size increases. This paper proposes an iterated local search (ILS) algorithm for the ALP. ILS is a single solution based search methodology that successively invokes a local search procedure to find a local optimum solution. A perturbation operator is used to modify the current solution in order to escape from the local optimum and to provide a new solution for the local search procedure. As different problems and/or instances have different characteristics, the success of the ILS is highly dependent on the local search, the perturbation operator(s) and the perturbation strength. To address these issues, we utilize four perturbation operators and a time varying perturbation strength which changes as the algorithm progresses. A variable neighborhood descent algorithm is used as our local search. The proposed ILS generates high quality solutions for the ALP benchmark instances taken from the scientific literature, demonstrating its efficiency in terms of both solution quality and computational time. Moreover, the proposed ILS produces new best results for some instances

Electromagnetic algorithm for tuning the structure and parameters of neural networks

Electromagnetic algorithm is a population based meta-heuristic which imitates the attraction and repulsion of sample points. In this paper, we propose an electromagnetic algorithm to simultaneously tune the structure and parameter of the feed forward neural network. Each solution in the electromagnetic algorithm contains both the design structure and the parameters values of the neural network. This solution later will be used by the neural network to represents its configuration. The classification accuracy returned by the neural network represents the quality of the solution. The performance of the proposed method is verified by using the well-known classification benchmarks and compared against the latest methodologies in the literature. Empirical results demonstrate that the proposed algorithm is able to obtain competitive results, when compared to the best-known results in the literature