This paper studies a real-life container transportation problem with a wide planning horizon divided into multiple shifts. The trucks in this problem do not return to depot after every single shift but at the end of every two shifts. The mathematical model of the problem is first established, but it is unrealistic to solve this large scale problem with exact search methods. Thus, a Variable Neighbourhood Search algorithm with Reinforcement Learning (VNS-RLS) is thus developed. An urgency level-based insertion heuristic is proposed to construct the initial solution. Reinforcement learning is then used to guide the search in the local search improvement phase. Our study shows that the Sampling scheme in single solution-based algorithms does not significantly improve the solution quality but can greatly reduce the rate of infeasible solutions explored during the search. Compared to the exact search and the state-of-the-art algorithms, the proposed VNS-RLS produces promising results.

An effective and fast hybrid metaheuristic is proposed for solving the pickup and delivery problem with time windows. The proposed approach combines local search, large neighbourhood search and guided ejection search in a novel way to exploit the benefits of each method. The local search component uses a novel neighbourhood operator. A streamlined implementation of large neighbourhood search is used to achieve an effective balance between intensification and diversification. The adaptive ejection chain component perturbs the solution and uses increased or decreased computation time according to the progress of the search. While the local search and large neighbourhood search focus on minimising travel distance, the adaptive ejection chain seeks to reduce the number of routes. The proposed algorithm design results in an effective and fast solution method that finds a large number of new best-known solutions on a well-known benchmark dataset. Experiments are also performed to analyse the benefits of the components and heuristics and their combined use to achieve a better understanding of how to better tackle the subject problem.

University course timetabling problem (UCTP) includes the challenging task of generating an automated timetable for courses under resource limitations. Manual generated timetables might hold some errors and consume a long time to create feasible solutions. Thus, there is a need to find optimal and fast solutions for this problem. The difficulty of the timetabling problem is further increased when tackling faculty-related constraints, according to their requirements, preferences, and availability. Thus, student-related constraints are usually the focus of UCTP generated solutions, in which faculty constraints are limited to their teaching load or preferences. This paper proposes a multi-objective mixed-integer programming model for a preregistration UCTP, combined with faculty-related constraints. The goal is to maximize events assignments and faculty-members preferences satisfaction while balancing the university requirements. At the same time, student learning days and unassigned events are minimized. The model is tested with eight real-world instances. Computational experiments are carried out to show the efficiency of the model. The proposed method can generate optimal timetables for all problem instances that satisfy faculty constraints.

In this paper, a Mixed-Shift Vehicle Routing Problem is proposed based on a real-life container transportation problem. In a long planning horizon of multiple shifts, transport tasks are completed satisfying the time constraints. Due to the different travel distances and time of tasks, there are two types of shifts (long shift and short shift) in this problem. The unit driver cost for long shifts is higher than that of short shifts. A mathematical model of this Mixed-Shift Vehicle Routing Problem with Time Windows (MS-VRPTW) is established in this paper, with two objectives of minimizing the total driver payment and the total travel distance. Due to the large scale and nonlinear constraints, the exact search showed is not suitable to MS-VRPTW. An initial solution construction heuristic (EBIH) and a selective perturbation Hyper-Heuristic (GIHH) are thus developed. In GIHH, five heuristics with different extents of perturbation at the low level are adaptively selected by a high level selection scheme with the Hill Climbing acceptance criterion. Two guidance indicators are devised at the high level to adaptively adjust the selection of the low level heuristics for this bi-objective problem. The two indicators estimate the objective value improvement and the improvement direction over the Pareto Front, respectively. To evaluate the generality of the proposed algorithms, a set of benchmark instances with various features is extracted from real-life historical datasets. The experiment results show that GIHH significantly improves the quality of the final Pareto Solution Set, outperforming the state-of-the-art algorithms for similar problems. Its application on VRPTW also obtains promising results.

We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporate mixed integer programming solvers and heuristics. Home healthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which sub-problems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time.

This article proposes a novel dynamic objective function in a multi-period home health care (HHC) problem, known as the nurse-patient relationship (NPR). The nurse-patient relationship score indicating the trust a patient has for his or her care worker increases when the same people meet regularly and decreases when they are apart. Managing human resources in HHC is a combination of routing and scheduling problems. Due to computational complexity of the HHC problem, a 28-day home health care problem is decomposed into daily subproblems, and solved sequentially with the tabu search. The solutions are then combined to give a solution to the original problem. For problems with less complex constraints, the NPR model can also be solved using exact methods such as CPLEX. For larger scale instances, however, the numerical results show that the NPR model can only be solved in reasonable times using our proposed tabu search approach. The solutions obtained from the NPR models are compared against those from existing models in the literature such as preference and continuity of care. Essentially, the analysis revealed that the proposed NPR models encouraged the search algorithm to assign the same care worker to visit the same patient. In addition, it had a tendency to assign a care worker on consecutive days to each patient, which is one of the key factors in promoting trust between patients and care workers. This leads to the efficacy of monitoring patient’s disease progression and treatment.