The trade off between diversity and quality for multi-objective workforce scheduling

In this paper we investigate and compare multi-objective and weighted single objective approaches to a real world workforce scheduling problem. For this difficult problem we consider the trade off in solution quality versus population diversity, for different sets of fixed objective weights. Our real-world workforce scheduling problem consists of assigning resources with the appropriate skills to geographically dispersed task locations while satisfying time window constraints. The problem is NP-Hard and contains the Resource Constrained Project Scheduling Problem (RCPSP) as a sub problem. We investigate a genetic algorithm and serial schedule generation scheme together with various multi-objective approaches. We show that multi-objective genetic algorithms can create solutions whose fitness is within 2% of genetic algorithms using weighted sum objectives even though the multi-objective approaches know nothing of the weights. The result is highly significant for complex real-world problems where objective weights are seldom known in advance since it suggests that a multi-objective approach can generate a solution close to the user preferred one without having knowledge of user preferences

ParadisEO-MOEO: A Software Framework for Evolutionary Multi-Objective Optimization

This chapter presents ParadisEO-MOEO, a white-box object-oriented software framework dedicated to the flexible design of metaheuristics for multi-objective optimization. This paradigm-free software proposes a unified view for major evolutionary multi-objective metaheuristics. It embeds some features and techniques for multi-objective resolution and aims to provide a set of classes allowing to ease and speed up the development of computationally efficient programs. It is based on a clear conceptual distinction between the solution methods and the problems they are intended to solve. This separation confers a maximum design and code reuse. This general-purpose framework provides a broad range of fitness assignment strategies, the most common diversity preservation mechanisms, some elitistrelated features as well as statistical tools. Furthermore, a number of state-of-the-art search methods, including NSGA-II, SPEA2 and IBEA, have been implemented in a user-friendly way, based on the fine-grained ParadisEO-MOEO components

Towards Improving the Utilisation of University Teaching Space

There is a perception that teaching space in universities is a rather scarce resource. However, some studies have revealed that in many institutions it is actually chronically under-used. Often, rooms are occupied only half the time, and even when in use they are often only half full. This is usually measured by the ‘utilization' which is defined as the percentage of available ‘seat-hours' that are employed. Within real institutions, studies have shown that this utilization can often take values as low as 20-40%. One consequence of such a low level of utilization is that space managers are under pressure to make more efficient use of the available teaching space. However, better management is hampered because there does not appear to be a good understanding within space management (near-term planning) of why this happens. This is accompanied, within space planning (long-term planning) by a lack of expertise on how best to accommodate the expected low utilizations. This motivates our two main goals: (i) To understand the factors that drive down utilizations, (ii) To set up methods to provide better space planning. Here, we provide quantitative evidence that constraints arising from timetabling and location requirements easily have the potential to explain the low utilizations seen in reality. Furthermore, on considering the decision question ‘Can this given set of courses all be allocated in the available teaching space?' we find that the answer depends on the associated utilization in a way that exhibits threshold behaviour: There is a sharp division between regions in which the answer is ‘almost always yes' and those of ‘almost always no'. Through analysis and understanding of the space of potential solutions, our work suggests that better use of space within universities will come about through an understanding of the effects of timetabling constraints and when it is statistically likely that it will be possible for a set of courses to be allocated to a particular space. The results presented here provide a firm foundation for university managers to take decisions on how space should be managed and planned for more effectively. Our multicriteria approach and new methodology together provide new insight into the interaction between the course timetabling problem and the crucial issue of space planning

Multi-Objective Hyper-Heuristic Approaches For Space Allocation And Timetabling

An important issue in multi-objective optimisation is how to ensure that the obtained non-dominated set covers the Pareto front as widely as possible. A number of techniques (e.g. weight vectors, niching, clustering, cellular structures, etc.) have been proposed in the literature for this purpose. In this paper we propose a new approach to address this issue in multi-objective combinatorial optimisation. We explore hyperheuristics, a research area which has gained increasing interest in recent years. A hyper-heuristic can be thought of as a heuristic method which iteratively attempts to select a good heuristic amongst many. The aim of using a hyper-heuristic is to raise the level of generality so as to be able to apply the same solution method to several problems, perhaps at the expense of reduced but still acceptable solution quality when compared to a tailor-made approach. The key is not to solve the problem directly but rather to (iteratively) recommend a suitable heuristic chosen because of its performance. In this paper we investigate a tabu search hyper-heuristic technique. The idea of our multi-objective hyperheuristic approach is to choose at each iteration during the search, the heuristic that is suitable for the optimisation of a given individual objective. We test the resulting approach on two very di#erent real-world combinatorial optimisation problems: space allocation and timetabling. The results obtained show that the multi-objective hyper-heuristic approach can be successfully developed for these two problems producing solutions of acceptable quality