On Global Warming (Softening Global Constraints)

We describe soft versions of the global cardinality constraint and the regular constraint, with efficient filtering algorithms maintaining domain consistency. For both constraints, the softening is achieved by augmenting the underlying graph. The softened constraints can be used to extend the meta-constraint framework for over-constrained problems proposed by Petit, Regin and Bessiere.Comment: 15 pages, 7 figures. Accepted at the 6th International Workshop on Preferences and Soft Constraint

A Component Based Heuristic Search Method with Evolutionary Eliminations

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with evolutionary eliminations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then to implement two evolutionary elimination strategies mimicking natural selection and natural mutation process on these components respectively to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs an evaluation function which evaluates how well each component contributes towards the final objective. Two elimination steps are then applied: the first elimination eliminates a number of components that are deemed not worthy to stay in the current schedule; the second elimination may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems.Comment: 27 pages, 4 figure

A Component Based Heuristic Search Method with AdaptivePerturbations for Hospital Personnel Scheduling

Nurse rostering is a complex scheduling problem that affects hospital personnel on a daily basis all over the world. This paper presents a new component-based approach with adaptive perturbations, for a nurse scheduling problem arising at a major UK hospital. The main idea behind this technique is to decompose a schedule into its components (i.e. the allocated shift pattern of each nurse), and then mimic a natural evolutionary process on these components to iteratively deliver better schedules. The worthiness of all components in the schedule has to be continuously demonstrated in order for them to remain there. This demonstration employs a dynamic evaluation function which evaluates how well each component contributes towards the final objective. Two perturbation steps are then applied: the first perturbation eliminates a number of components that are deemed not worthy to stay in the current schedule; the second perturbation may also throw out, with a low level of probability, some worthy components. The eliminated components are replenished with new ones using a set of constructive heuristics using local optimality criteria. Computational results using 52 data instances demonstrate the applicability of the proposed approach in solving real-world problems

Fairness aspects in personnel scheduling

In industries like health care, public transport or call centers a shift-based system ensures permanent availability of employees for covering needed services. The resource allocation problem – assigning employees to shifts – is known as personnel scheduling in literature and often aims at minimizing staffing costs. Working in shifts, though, impacts employees’ private lives which adds to the problem of increasing staff shortage in recent years. Therefore, more and more effort is spent on incorporating fairness into scheduling approaches in order to increase employees’ satisfaction. This paper presents a literature review of approaches for personnel scheduling considering fairness aspects. Since fairness is not a quantitative objective, but can be evaluated from different point of views, a large number of fairness measurements exists in the literature. Furthermore, perspective (group vs individual fairness) or time horizon (short-term vs long-term fairness) are often considered very differently. To conclude, we show that a uniform definition and approach for considering fairness in personnel scheduling is challenging and point out gaps for future research

The Second International Nurse Rostering Competition

This paper reports on the Second International Nurse Rostering Competition (INRC-II). Its contributions are (1) a new problem formulation which, differently from INRC-I, is a multi-stage procedure, (2) a competition environment that, as in INRC-I, will continue to serve as a growing testbed for search approaches to the INRC-II problem, and (3) final results of the competition. We discuss also the competition environment, which is an infrastructure including problem and instance definitions, testbeds, validation/simulation tools and rules. The hardness of the competition instances has been evaluated through the behaviour of our own solvers, and confirmed by the solvers of the participants. Finally, we discuss general issues about both nurse rostering problems and optimisation competitions in general.PostprintPeer reviewe

A rostering approach to minimize health risks for workers: An application to a container terminal in the Italian port of Genoa

The evolving safety regulation is pushing seaports to comply with safety measures for workers performing heavy loads handling and repetitive movements. This paper proposes a risk-aware rostering approach in maritime container terminals, i.e., it addresses the rostering problem of minimizing and balancing workers’ risk in such terminals. To this end, a mixed integer mathematical programming model incorporating workforce risks is proposed, considering constraints such as the satisfaction of the workforce demand to perform the terminal operations, the worker-task compatibility and restrictions on the sequence of tasks assigned to the same worker. The model has been successfully applied to plan workforce over a six months horizon in a real container terminal located in Northern Italy, the Southern European Container Hub (SECH) in Genoa. As the workforce demand in SECH terminal is available at most two weeks in advance, a rolling horizon planning approach is devised. Experimental tests on real data provided by SECH terminal over a six months planning horizon highlight the effectiveness of the approach - the maximum monthly risk for workers is reduced by 33.9% compared to the current planning – and suitability to other container terminal contexts. Moreover, the model is applicable to a broad range of port situations, and robust enough to need little adaptation

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

Effective integrations of constraint programming, integer programming and local search for two combinatorial optimisation problems

This thesis focuses on the construction of effective and efficient hybrid methods based on the integrations of Constraint Programming (CP), Integer Programming (IP) and local search (LS) to tackle two combinatorial optimisation problems from different application areas: the nurse rostering problems and the portfolio selection problems. The principle of designing hybrid methods in this thesis can be described as: for the combinatorial problems to be solved, the properties of the problems are investigated firstly and the problems are decomposed accordingly in certain ways; then the suitable solution techniques are integrated to solve the problem based on the properties of substructures/subproblems by taking the advantage of each technique. For the over-constrained nurse rostering problems with a large set of complex constraints, the problems are first decomposed by constraint. That is, only certain selected set of constraints is considered to generate feasible solutions at the first stage. Then the rest of constraints are tackled by a second stage local search method. Therefore, the hybrid methods based on this constraint decomposition can be represented by a two-stage framework “feasible solution + improvement”. Two integration methods are proposed and investigated under this framework. In the first integration method, namely a hybrid CP with Variable Neighourhood Search (VNS) approach, the generation of feasible initial solutions relies on the CP while the improvement of initial solutions is gained by a simple VNS in the second stage. In the second integration method, namely a constraint-directed local search, the local search is enhanced by using the information of constraints. The experimental results demonstrate the effectiveness of these hybrid approaches. Based on another decomposition method, Dantzig-Wolfe decomposition, in the third integration method, a CP based column generation, integrates the feasibility reasoning of CP with the relaxation and optimality reasoning of Linear Programming. The experimental results demonstrate the effectiveness of the methods as well as the knowledge of the quality of the solution. For the portfolio selection problems, two integration methods, which integrate Branch-and-Bound algorithm with heuristic search, are proposed and investigated. In layered Branch-and-Bound algorithm, the problem is decomposed into the subsets of variables which are considered at certain layers in the search tree according to their different features. Node selection heuristics, and branching rules, etc. are tailored to the individual layers, which speed up the search to the optimal solution in a given time limit. In local search branching Branch-and-Bound algorithm, the idea of local search is applied as the branching rule of Branch-and-Bound. The local search branching is applied to generate a sequence of subproblems. The procedure for solving these subproblems is accelerated by means of the solution information reusing. This close integration between local search and Branch-and-Bound improves the efficiency of the Branch-and-Bound algorithm according to the experimental results. The hybrid approaches benefit from each component which is selected according to the properties of the decomposed problems. The effectiveness and efficiency of all the hybrid approaches to the two application problems developed in this thesis are demonstrated. The idea of designing appropriate components in hybrid approach concerning properties of subproblems is a promising methodology with extensive potential applications in other real-world combinatorial optimisation problems