Discrete OptimizationA neutrality-based iterated local search for shift scheduling optimization and interactive reoptimization
Graphical abstract
Introduction
In the design process of an optimization system or optimization-based decision support system, the definition of an adequate optimization model is a key step. The optimization model must reflect the real system to be optimized while being suitable for an optimization procedure. In many situations there are unavoidable discrepancies between the optimization model and the real problem faced by the decision maker.
Some sources of inaccuracies in an optimization model are identified, for instance, in Hillier and Lieberman (2001), do Nascimento and Eades (2005), Roy (2005) and Meignan, Knust, Frayret, Pesant, and Gaud (2015). First, the problem to model may contain objectives or constraints that are difficult to quantify such as risk or tasks’ arduousness. In addition, it may be necessary to simplify the specification of an optimization problem in order to apply a computational optimization approach. Common examples of such a simplification are the combination of several criteria in a single objective function, or the approximation of variable relationships by linear models. Besides these obstacles inherent to the optimization problem, inaccuracies of an optimization model may also be related to the difficulty to obtain a complete specification of the problem for designing the model. Finally, the time and budget for designing and implementing an optimization model are limited. The resulting disparities between an implemented optimization model and the real problem may necessitate an adjustment of the solutions by the decision maker. In this context, interactive reoptimization is an approach that supports the adjustment of candidate solutions and overcomes the limitations of editing solutions only manually.
Interactive reoptimization is an approach that allows the user of an optimization system to correct inaccuracies of the optimization model. It is a semi-automated approach that relies on the problem knowledge of the user for identifying required adjustments on a solution. The interactive process starts with an initial candidate solution provided by an optimization method. The user specifies on this solution the adjustments to be made. Then, a reoptimization procedure is applied to integrate the changes and optimize the rest of the solution accordingly. Since the reoptimization propagates the changes to the rest of the solution, the process may necessitate several iterations in which the user defines additional adjustments on the solution. The process stops when the user considers that a satisfactory solution is obtained.
Interactive reoptimization is an alternative of manual editing when small adjustments have to be made on a candidate solution. In the context of hard optimization problems, a manual modification of an optimized solution may significantly impair the solution. Generally, it is difficult for the user to apprehend all constraints and objectives of an optimization problem. In addition, due to the combinatorial complexity of the underlying problem, it is difficult or even impossible to reflect adequately the modification to the whole solution. The fact that a local modification in a solution implies to adjust other parts of the solution is referred to as the cascading or propagation effect (Pinedo, 2012). In interactive reoptimization this propagation of the modifications requested by the user is performed by a reoptimization procedure. The reoptimization procedure globally optimizes a solution to take into account local modifications requested by the user.
In this paper, a reoptimization approach is proposed and evaluated on a shift scheduling problem. The optimization procedure that provides initial candidate solutions and the reoptimization procedure used to integrate the changes requested by a user are based on a Neutrality-Based Iterated Local Search (NILS) (Marmion, Dhaenens, Jourdan, Liefooghe, & Verel, 2011) which is an extension of the Iterated Local Search method (Lourenço, Martin, & Stützle, 2010). The optimization procedures have been designed to meet the requirements of a decision support system. In this regard, the optimization model of the shift scheduling problem contains realistic constraints. In addition, the reoptimization procedure has been tested with limited computation time of a few seconds in order to reflect the conditions of an interactive use.
The computational experiments are divided into two parts. In the first part, the performance of the NILS for generating initial candidate solutions is evaluated. The results of the proposed NILS procedure are compared to results from the literature on the “International Nurse Rostering Competition” benchmark (INRC2010) (Haspeslagh, Causmaecker, Schaerf, & Stølevik, 2014). The second part of the experiments, concerns the reoptimization of schedules for introducing preferences defined by a decision maker. We modelled these preferences as a set of preferred assignments (e.g., early shift, late shift, no shift) on specific days and employees. For the evaluation of the reoptimization procedure, a set of problem instances has been generated with randomly generated preferences. The NILS procedure is compared to recovery procedures that perform local modifications resembling manual adjustments. The objective of this comparison is to determine the benefit of a global optimization approach for the reoptimization of solutions.
This paper completes a preliminary work on interactive reoptimization presented in Meignan (2014). The additional contribution mainly consists in the proposition of NILS for solving the shift scheduling problem and its reoptimization variant. In Meignan (2014) an ILS procedure was investigated and we show here that NILS provides significantly better results than ILS on the considered benchmark. In addition, this paper presents a more detailed computational study and new results on the reoptimization problem.
The remainder of the paper is organized as follows. In Section 2 the model of the shift scheduling problem investigated throughout this study is presented. Section 3 describes the NILS method implemented for solving the shift scheduling problem and its reoptimization variant. Next, a first part of the computational study is presented in Section 4. This part compares NILS with existing methods on the INRC2010 dataset. The reoptimization variant of the problem is introduced in Section 5, and the second part of the computational study related to the reoptimization is presented in Section 6. Finally, conclusions are given in Section 7.
Section snippets
Shift scheduling problem
The optimization problem considered in this study is a staff shift scheduling problem. In short, the objective of such a problem is to optimize the schedule of employees on a given planning horizon. The criteria used for evaluating a solution, i.e. a schedule, are generally the satisfaction of the demand in term of employees, the satisfaction of the constraints imposed by work regulations, and the optimization of aspects that make a schedule convenient for employees. We refer the reader to
Iterative local search with plateau exploration
For solving the INRC2010 problem presented in the previous section we propose an extension of the Iterative Local Search metaheuristic (ILS) that integrates a phase of plateau exploration. This section first presents the interest of such a metaheuristic and justifies its extension. Next, the optimization procedure is explained and each of its components is detailed.
INRC2010 problem data and experimental setting
The proposed NILS has been evaluated on the INRC2010 benchmark instances (Haspeslagh et al., 2014). This benchmark contains 69 instances divided into three groups of sizes: sprint (33 instances), medium (18 instances) and long (18 instances). Instances are also categorized according to the time of their availability during the INRC2010 competition. The labels used for these categories are early, hint, late and hidden.
All instances in the benchmark are shift scheduling problems with a planning
Interactive reoptimization
In the previous part of this article we showed that NILS provides good results for the studied shift scheduling problem. The second part of the article investigates a reoptimization problem, derived from the INRC2010 model, using the proposed NILS method. This section introduces the reoptimization problem and presents the adaptations of the model that are necessary to use the NILS in a context of interactive reoptimization. Next, Section 6 presents a computational experiment performed on the
Benchmark data
To evaluate NILS on the reoptimization problem we adapted the sprint instances of the INRC2010 benchmark to create a set of reoptimization problem instances. In comparison to INRC2010 instances, the reoptimization instances use the objective function defined in Section 5.2 with the lexicographic order of its components. Moreover, a reoptimization problem instance requires an initial solution and some assignment preferences to be integrated into this initial solution. In a real interactive
Conclusion
In this article we proposed a Neutrality-based Iterated Local Search (NILS) for solving a shift scheduling problem and a reoptimization variant. In comparison to an Iterated Local Search (ILS) procedure, NILS introduces a phase of plateau exploration. This plateau exploration is particularly interesting for the studied problem as the landscape produced by the adopted neighborhood structures contains large plateaus.
The computational study consists of two parts. First, we compared NILS with
Acknowledgments
This work was supported by the Deutsche Forschungsgemeinschaft (DFG), under grant ME 4045/2-1, for the project “Interactive metaheuristics for optimization-based decision support systems”.
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