Decompositions of Grammar Constraints

A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive constraints. We can then, for instance, use state of the art SAT solvers and profit from their advanced features like fast unit propagation, clause learning, and conflict-based search heuristics. This approach holds promise for solving combinatorial problems in scheduling, rostering, and configuration, as well as problems in more diverse areas like bioinformatics, software testing and natural language processing. In addition, decomposition may be an effective method to propagate other global constraints.Comment: Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligenc

An Algorithmic approach to shift structure optimization

Workforce scheduling in organizations often consists of three major phases: workload prediction, shift generation, and staff rostering. Workload prediction involves using historical behaviour of e.g. customers to predict future demand for work. Shift generation is the process of transforming the determined workload into shifts as accurately as possible. In staff rostering, the generated shifts are assigned to employees. In general the problem and even its subproblems are NP-hard, which makes them highly challenging for organizations to solve. Heuristic optimization methods can be used to solve practical instances within reasonable running times, which in turn can result in e.g. improved revenue, improved service, or more satisfied employees for the organizations. This thesis presents some specific subproblems along with practical solution methods--- Työvoiman aikataulutusprosessi koostuu kolmesta päävaiheesta: työtarpeen ennustaminen, työvuorojen muodostus ja työvuorojen miehitys. Tulevaa työtarvetta ennustetaan pääasiassa menneisyyden asiakaskäytöksen perusteella käyttäen esimerkiksi tilastollisia malleja tai koneoppimiseen perustuvia menetelmiä. Työvuorojen muodostuksessa tehdään työvuororakenne, joka noudattaa ennustettua ja ennalta tiedettyä työtarvetta mahdollisimman tarkasti. Työvuorojen miehityksessä määritetään työvuoroille tekijät. Jokainen vaihe itsessään on haasteellinen ratkaistava. Erityisesti työvuorojen miehitys on yleensä NP-kova ongelma. On kuitenkin mahdollista tuottaa käytännöllisiä ratkaisuja järkevässä ajassa käyttäen heuristisia optimointimenetelmiä. Näin on saavutettavissa mitattavia hyötyjä mm. tuottoon, asiakkaiden palvelutasoon sekä työntekijöiden työtyyväisyyteen. Tässä väitöskirjassa esitellään eräitä työvoiman aikataulutuksen aliongelmia sekä niihin sopivia ratkaisumenetelmiä

The General Combinatorial Optimization Problem: Towards Automated Algorithm Design

This paper defines a new combinatorial optimisation problem, namely General Combinatorial Optimisation Problem (GCOP), whose decision variables are a set of parametric algorithmic components, i.e. algorithm design decisions. The solutions of GCOP, i.e. compositions of algorithmic components, thus represent different generic search algorithms. The objective of GCOP is to find the optimal algorithmic compositions for solving the given optimisation problems. Solving the GCOP is thus equivalent to automatically designing the best algorithms for optimisation problems. Despite recent advances, the evolutionary computation and optimisation research communities are yet to embrace formal standards that underpin automated algorithm design. In this position paper, we establish GCOP as a new standard to define different search algorithms within one unified model. We demonstrate the new GCOP model to standardise various search algorithms as well as selection hyper-heuristics. A taxonomy is defined to distinguish several widely used terminologies in automated algorithm design, namely automated algorithm composition, configuration and selection. We would like to encourage a new line of exciting research directions addressing several challenging research issues including algorithm generality, algorithm reusability, and automated algorithm design

Metaheuristics For Solving Real World Employee Rostering and Shift Scheduling Problems

Optimising resources and making considerate decisions are central concerns in any responsible organisation aiming to succeed in efficiently achieving their goals. Careful use of resources can have positive outcomes in the form of fiscal savings, improved service levels, better quality products, improved awareness of diminishing returns and general output efficiency, regardless of field. Operational research techniques are advanced analytical tools used to improve managerial decision-making. There have been a variety of case studies where operational research techniques have been successfully applied to save millions of pounds. Operational research techniques have been successfully applied to a multitude of fields, including agriculture, policing, defence, conservation, air traffic control, and many more. In particular, management of resources in the form of employees is a challenging problem --- but one with the potential for huge improvements in efficiency. The problem this thesis tackles can be divided into two sub-problems; the personalised shift scheduling & employee rostering problem, and the roster pattern problem. The personalised shift scheduling & employee rostering problem involves the direct scheduling of employees to hours and days of week. This allows the creation of schedules which are tailored to individuals and allows a fine level over control over the results, but with at the cost of a large and challenging search space. The roster pattern problem instead takes existing patterns employees currently work, and uses these as a pool of potential schedules to be used. This reduces the search space but minimises the number of changes to existing employee schedules, which is preferable for personnel satisfaction. Existing research has shown that a variety of algorithms suit different problems and hybrid methods are found to typically outperform standalone ones in real-world contexts. Several algorithmic approaches for solving variations of the employee scheduling problem are considered in this thesis. Initially a VNS approach was used with a Metropolis-Hastings acceptance criterion. The second approach utilises ER&SR controlled by the EMCAC, which has only been used in the field of exam timetabling, and has not before been used within the domain of employee scheduling and rostering. ER&SR was then hybridised with our initial approach, producing ER&SR with VNS. Finally, ER&SR was hybridised into a matheuristic with Integer Programming and compared to the hybrid's individual components. A contribution of this thesis is evidence that the algorithm ER&SR has merit outside of the original sub-field of exam scheduling, and can be applied to shift scheduling and employee rostering. Further, ER&SR was hybridised and schedules produced by the hybridisations were found to be of higher quality than the standalone algorithm. In the literature review it was found that hybrid algorithms have become more popular in real-world problems in recent years, and this body of work has explored and continued this trend. Problem formulations in this thesis provide insight into creating constraints which satisfy the need for minimising employee dissatisfaction, particularly in regards to abrupt change. The research presented in this thesis has positively impacted a multinational and multibillion dollar field service operations company. This has been achieved by implementing a variety of techniques, including metaheuristics and a matheuristic, to schedule shifts and roster employees over a period of several months. This thesis showcases the research outputs by this project, and highlights the real-world impact of this research

Novel heuristic and metaheuristic approaches to the automated scheduling of healthcare personnel

This thesis is concerned with automated personnel scheduling in healthcare organisations; in particular, nurse rostering. Over the past forty years the nurse rostering problem has received a large amount of research. This can be mostly attributed to its practical applications and the scientific challenges of solving such a complex problem. The benefits of automating the rostering process include reducing the planner’s workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare. Basically stated, the nurse rostering problem requires the assignment of shifts to personnel to ensure that sufficient employees are present to perform the duties required. There are usually a number of constraints such as working regulations and legal requirements and a number of objectives such as maximising the nurses working preferences. When formulated mathematically this problem can be shown to belong to a class of problems which are considered intractable. The work presented in this thesis expands upon the research that has already been conducted to try and provide higher quality solutions to these challenging problems in shorter computation times. The thesis is broadly structured into three sections. 1) An investigation into a nurse rostering problem provided by an industrial collaborator. 2) A framework to aid research in nurse rostering. 3) The development of a number of advanced algorithms for solving highly complex, real world problems