A hybrid Integer Programming and Variable Neighbourhood Search algorithm to solve Nurse Rostering Problems

Abstract

The Nurse Rostering Problem (NRP) is defined as assigning a number of nurses to different shifts during a specified planning period, considering some regulations and preferences. This is often very difficult to solve in practice particularly by applying a sole approach. In this paper, we propose a novel hybrid algorithm combining the strengths of Integer Programming (IP) and Variable Neighbourhood Search (VNS) algorithms to design a hybrid method for solving the NRP. After generating the initial solution using a greedy heuristic, the solution is further improved by employing a Variable Neighbourhood Descent algorithm. Then IP, deeply embedded in the VNS algorithm, is employed within a ruin-and-recreate framework to assist the search process. Finally, IP is called again to further refine the solution during the remaining time. We utilize the strength of IP not only to diversify the search process, but also to intensify the search efforts. To identify the quality of the current solution, we use a new generic scoring scheme to mark the low-penalty parts of the solution. Based on the computational tests with 24 instances recently introduced in the literature, we obtain better results with our proposed algorithm, where the hybrid algorithm outperforms two state-of-the-art algorithms and Gurobi in most of the instances. Furthermore, we introduce 11 randomly generated instances to further evaluate the efficiency of the hybrid algorithm, and we make these computationally challenging instances publicly available to other researchers for benchmarking purposes.

A hybrid integer and constraint programming approach to solve nurse rostering problems

“…Exact methods mostly include Integer Programming (IP) [19,28,30] and Constraint Programming (CP) [18,42], which are capable of finding the optimal solution, albeit often resulting in unacceptable computational times. In order to address the computational limitations of these methods, many heuristic methods have been proposed in the literature ranging from rather general Variable Neighbourhood Search [27,37] and Genetic Algorithms [8,2] to stochastic approaches [44] and tailor-made heuristics [5]. However, these methods sacrifice the guarantee of an optimal solution (or even any information regarding the solution quality) in order to generate good-quality solutions in acceptable computational times.…”

Two metaheuristic approaches for solving the multi-compartment vehicle routing problem

“…In fact, it chooses a point from the k th neighborhood stochastically, then, it performs a deterministic local search. A deep study of the literature reveals that the VNS is efficient in solving optimization problems (Brimberg et al 2017;Wang et al 2017;Rahimian et al 2017;Wang et al 2017). Moreover, several VNS variants are proposed for solving large problem instances for routing problems (Bula et al 2017;Breunig et al 2016;Li and Tian 2016).…”

A hybrid variable neighbourhood search and dynamic programming approach for the nurse rostering problem

“…In [27], an IP solver was used within a VNS algorithm through a ruin-andrecreate strategy. In their approach, after each iteration of the VNS algorithm, the most contributed parts of the solution to the overall penalty are destroyed and recreated using an IP solver.…”

“…Another comparison with results presented in [27] for a hybrid Integer Programming and Variable Neighbourhood Search (IP-VNS) approach is shown in Table 4. The VNS-DP approach was able to produce better results than the IP-VNS in the largest size instance (instance 24) only and produce the same results also for the first 4 instances.…”