A matheuristic algorithm for the share-a-ride problem

This research studies the Share-a-Ride Problem (SARP) in which a set of taxis is used to serve a set of package and passenger requests at the same time. The goal is to maximize the profit from serving the requests without violating given constraints. We develop a new matheuristic algorithm that combines the simulated annealing with mutation strategy (SAMS) and the set partitioning (SP) approach to improve the reported solutions of SARP benchmark instances. The SAMS consists of a time-slack strategy, neighborhood moves, a mutation strategy that depends on the time-slack strategy, and a penalty mechanism for infeasible solutions. The first phase of the proposed matheuristic uses SAMS to generate a set of feasible candidate routes. A route accumulation mechanism is added to the SAMS to keep the candidate routes in the route pool. The second phase of the matheuristic focuses on solving the set partitioning model to find the best route combination as the final solution. The proposed matheuristic is tested on existing small and large SARP instances, and a set of newly generated large SARP in-stances and then compared with SAMS algorithm. The experimental results show that the proposed matheuristic obtains optimal solutions to all the small SARP benchmark instances. For large instances, the proposed math-euristic outperforms SAMS algorithm as it obtains several new best solutions to SARP. Lastly, our algorithm obtains high-quality solutions to the new large SARP instances generated in this study.