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

Curriculum-based course timetabling with student flow, soft constraints, and smoothing objectives: an application to a real case study

This paper deals with curriculum-based course timetabling. In particular, we describe the results of a real application at the University of Rome “Tor Vergata.” In this regard, we developed a multi-objective mixed-integer model which attempts to optimize (i) the flow produced by the students enrolled in the lectures, (ii) soft conflicts produced by the possible overlap among compulsory and non-compulsory courses, and (iii) the number of lecture hours per curriculum within the weekdays. The model has been implemented and solved by means of a commercial solver and experiments show that the model is able to provide satisfactory solutions as compared with the real scenario under consideration

Move Acceptance in Local Search Metaheuristics for Cross-domain Heuristic Search

Many real-world combinatorial optimisation problems (COPs) are computationally hard problems and search methods are frequently preferred as solution techniques. Traditionally, an expert with domain knowledge designs, and tailors the search method for solving a particular COP. This process is usually expensive, requiring a lot of effort and time and often results in problem specific algorithms that can not be applied to another COP. Then, the domain expert either needs to design a new search method, or reconfigure an existing search method to solve that COP. This prompted interest into developing more general, problem-domain-independent high-level search methods that can be re-used, capable of solving not just a single problem but multiple COPs. The cross-domain search problem is a relatively new concept and represents a high-level issue that involves designing a single solution method for solving a multitude of COPs preferably with the least or no expert intervention. Cross-domain search methods are algorithms designed to tackle the cross-domain search problem. Such methods are of interest to researchers and practitioners worldwide as they offer a single off-the-shelf go-to approach to problem solving. Furthermore, if a cross-domain search method has a good performance, then it can be expected to solve `any' given COP well and in a reasonable time frame. When a practitioner is tasked with solving a new or unknown COP, they are tasked with a decision-making dilemma. This entails the decision of what algorithm they should use, what parameters should be used for that algorithm, and whether any other algorithm can outperform it. A well designed cross-domain search method that performs well and does not require re-tuning can fulfil this dilemma allowing practitioners to find good-enough solutions to such problems. Researchers on the other hand strive to find high-quality solutions to these problems; however, such a cross-domain search method provides them with a good benchmark to which they can compare their solution methods to, and should ultimately aim to outperform. In this work, move acceptance methods, which are a component of traditional search methods, such as metaheuristics and hyper-heuristics, are explored under a cross-domain search framework. A survey of the existing move acceptance methods as a part of local search metaheuristics is conducted based on the hyper-heuristic literature as solution methods to the cross-domain search problem. Furthermore, a taxonomy is provided for classifying them based on their design characteristics. The cross-domain performance of existing move acceptance methods, covering the taxonomy, is compared across a total of 45 problem instances spanning 9 problem domains, and the effects of parameter tuning versus choice of the move acceptance method are explored. A novel move acceptance method (HAMSTA) is proposed to overcome the shortcomings of the existing methods to improve the cross-domain performance of a local search metaheuristic. HAMSTA is capable of outperforming the cross-domain performances of existing methods that are re-tuned for each domain, despite itself using only a single cross-domain parameter configuration derived from tuning experiments that considers 2 instances each from 4 domains; hence, HAMSTA requires no expert intervention to re-configure it to perform well for solving multiple COPs with 37 problem instances unseen by HAMSTA, 25 of which are from unseen domains. HAMSTA is therefore shown to have the potential to fulfil the aforementioned decision-making dilemma

Move Acceptance in Local Search Metaheuristics for Cross-domain Heuristic Search

Many real-world combinatorial optimisation problems (COPs) are computationally hard problems and search methods are frequently preferred as solution techniques. Traditionally, an expert with domain knowledge designs, and tailors the search method for solving a particular COP. This process is usually expensive, requiring a lot of effort and time and often results in problem specific algorithms that can not be applied to another COP. Then, the domain expert either needs to design a new search method, or reconfigure an existing search method to solve that COP. This prompted interest into developing more general, problem-domain-independent high-level search methods that can be re-used, capable of solving not just a single problem but multiple COPs. The cross-domain search problem is a relatively new concept and represents a high-level issue that involves designing a single solution method for solving a multitude of COPs preferably with the least or no expert intervention. Cross-domain search methods are algorithms designed to tackle the cross-domain search problem. Such methods are of interest to researchers and practitioners worldwide as they offer a single off-the-shelf go-to approach to problem solving. Furthermore, if a cross-domain search method has a good performance, then it can be expected to solve `any' given COP well and in a reasonable time frame. When a practitioner is tasked with solving a new or unknown COP, they are tasked with a decision-making dilemma. This entails the decision of what algorithm they should use, what parameters should be used for that algorithm, and whether any other algorithm can outperform it. A well designed cross-domain search method that performs well and does not require re-tuning can fulfil this dilemma allowing practitioners to find good-enough solutions to such problems. Researchers on the other hand strive to find high-quality solutions to these problems; however, such a cross-domain search method provides them with a good benchmark to which they can compare their solution methods to, and should ultimately aim to outperform. In this work, move acceptance methods, which are a component of traditional search methods, such as metaheuristics and hyper-heuristics, are explored under a cross-domain search framework. A survey of the existing move acceptance methods as a part of local search metaheuristics is conducted based on the hyper-heuristic literature as solution methods to the cross-domain search problem. Furthermore, a taxonomy is provided for classifying them based on their design characteristics. The cross-domain performance of existing move acceptance methods, covering the taxonomy, is compared across a total of 45 problem instances spanning 9 problem domains, and the effects of parameter tuning versus choice of the move acceptance method are explored. A novel move acceptance method (HAMSTA) is proposed to overcome the shortcomings of the existing methods to improve the cross-domain performance of a local search metaheuristic. HAMSTA is capable of outperforming the cross-domain performances of existing methods that are re-tuned for each domain, despite itself using only a single cross-domain parameter configuration derived from tuning experiments that considers 2 instances each from 4 domains; hence, HAMSTA requires no expert intervention to re-configure it to perform well for solving multiple COPs with 37 problem instances unseen by HAMSTA, 25 of which are from unseen domains. HAMSTA is therefore shown to have the potential to fulfil the aforementioned decision-making dilemma

Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored

An Ant Colony Optimisation Algorithm for Timetabling Problem

The University Course Timetabling Problem (UCTP) is a combinatorial optimization problem which involves the placement of events into timeslots and assignment of venues to these events. Different institutions have their peculiar problems; therefore there is a need to get an adequate knowledge of the problem especially in the area of constraints before applying an efficient method that will get a feasible solution in a reasonable amount of time. Several methods have been applied to solve this problem; they include evolutionary algorithms, tabu search, local search and swarm optimization methods like the Ant Colony Optimisation (ACO) algorithm. A variant of ACO called the MAX-MIN Ant System (MMAS) is implemented with two local search procedures (one main and one auxiliary) to tackle the UCTP using Covenant University problem instance. The local search design proposed was tailored to suit the problem tackled and was compared with other designs to emphasise the effect of neighbourhood combination pattern on the algorithm performance. From the experimental procedures, it was observed that the local search design proposed significantly bettered the existing one used for the comparison. The results obtained by the implemented algorithm proved that metaheuristics are highly effective when tackling real-world cases of the UCTP and not just generated instances of the problem and can even be better if some tangible modifications are made to it to perfectly suit a problem domain

Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored

Scheduling Problems

Scheduling is defined as the process of assigning operations to resources over time to optimize a criterion. Problems with scheduling comprise both a set of resources and a set of a consumers. As such, managing scheduling problems involves managing the use of resources by several consumers. This book presents some new applications and trends related to task and data scheduling. In particular, chapters focus on data science, big data, high-performance computing, and Cloud computing environments. In addition, this book presents novel algorithms and literature reviews that will guide current and new researchers who work with load balancing, scheduling, and allocation problems