GENVNS-TS-CL-PR: A heuristic approach for solving the vehicle routing problem with simultaneous pickup and delivery

This work addresses the Vehicle Routing Problem with Simultaneous Pickup and Delivery (VRPSPD). Due to its complexity, we propose a heuristic algorithm for solving it, so-called GENVNS-TS-CL-PR. This algorithm combines the heuristic procedures Cheapest Insertion, Cheapest Insertion with multiple routes, GENIUS, Variable Neighborhood Search (VNS), Variable Neighborhood Descent (VND), Tabu Search (TS) and Path Relinking (PR). The first three procedures aim to obtain an good initial solution, and the VND and TS are used as local search methods for VNS. TS is called after some iterations without any improvement through of the VND. The PR procedure is called after each VNS iteration and it connects a local optimum with an elite solution generated during the search. The algorithm uses an strategy based on Candidate List to reduce the number of solutions evaluated in the solution space. The algorithm was tested on benchmark instances taken from the literature and it was able to generate high quality solutions.