A Taxonomic Review of Metaheuristic Algorithms for Solving the Vehicle Routing Problem and Its Variants

In today’s competitive environment, one of the most critical objectives for Home Health Care (HHC) companies is to meet the demand of patients in a timely fashion. According to the feedback from HHC companies, caregivers have to deal with some uncertainties when carrying out a given schedule to visit their patients. However, a majority of the previous work only considers the deterministic models which ignore the uncertainties, and solutions obtained by these deterministic models are usually less robust in case of any possible changes in practical situations. Inspired by this point, in this work, we formulate a model for an HHC Routing and Scheduling Problem with taking into account uncertain travel and service times, from the perspective of Robust Optimization (RO). Specifically, the non-deterministic variables are defined based on the theory of budget uncertainty, and then the arrival time of each caregiver is rewritten as a complicated recursive function. After that, Gurobi Solver, Simulated Annealing, Tabu Search, and Variable Neighborhood Search are adapted to solve the model respectively. Finally, a series of experiments have been performed to validate the proposed models and algorithms. Experimental results from Monte Carlo simulation highlight the strength of considering uncertainties when modeling the problem. Additional, the influences of other characters in instances, like the width of time-window, distributed location have also been empirically analyzed. Finally, the comparison performed between the solutions obtained by the stochastic model and the RO model also demonstrates the advantage of the RO model. This work provides a valuable framework for HHC companies to make a robust schedule when arranging the caregivers.

A robust optimization for a home health care routing and scheduling problem with consideration of uncertain travel and service times

An iterative strategy for task assignment and path planning of distributed multiple unmanned aerial vehicles

Transportation allocates a significant proportion of Gross Domestic Product (GDP) to each country, and it is one of the largest consumers of petroleum products. On the other hand, many efforts have been made recently to reduce Greenhouse Gas (GHG) emissions by vehicles through redesigning and planning transportation processes. This paper proposes a novel Mixed-Integer Linear Programming (MILP) mathematical model for Green Inventory-Routing Problem with Time Windows (GIRP-TW) using a piecewise linearization method. The objective is to minimize the total cost including fuel consumption cost, driver cost, inventory cost and usage cost of vehicles taking into account factors such as the volume of vehicle load, vehicle speed and road slope. To solve the problem, three meta-heuristic algorithms are designed including the original and augmented Tabu Search (TS) algorithms and Differential Evolution (DE) algorithm. In these algorithms, three heuristic methods of improved Clarke-Wright algorithm, improved Push-Forward Insertion Heuristic (PFIH) algorithm and heuristic speed optimization algorithm are also applied to deal with the routing structure of the problem. The performance of the proposed solution techniques is analyzed using some well-known test problems and algorithms in the literature. Furthermore, a statistical test is conducted to efficiently provide the required comparisons for large-sized problems. The obtained results demonstrate that the augmented TS algorithm is the best method to yield high-quality solutions. Finally, a sensitivity analysis is performed to investigate the variability of the objective function.

Paulo Vitor Silvestrin

Papers

An iterated tabu search for the multi-compartment vehicle routing problem