Benders/gossip methods for heterogeneous multi-vehicle routing problems

Abstract

In this paper, we propose a logic-based Benders decomposition (LBBD), as well as an LBBD/gossip method to solve the heterogeneous multi-vehicle routing problem (HMVRP). HMVRP is a newly formalized extension of the NP-hard multi-traveling salesman problem (mTSP). First, a hybrid algorithm based on LBBD is formulated that decomposes the HMVRP into an assignment problem and a cluster of sequencing problems. The former is solved by a mixed integer linear programming (MILP) solver, and the latter by a dedicated TSP solver. Then, a gossip algorithm is constructed which utilizes the mentioned LBBD for local optimization to achieve better computational efficiency. The use of LBBD remarkably reduces the CPU time. Furthurmore, integrating the three layers of gossip algorithm, LBBD and the TSP solver, results in a very efficient solution method.

A Gossip Algorithm for Home Healthcare Scheduling and Routing Problems

“…The results of the Centralized method was used as a reference for comparing the results of the other algorithms. Riazi et al [2013] reported that the Centralized method was ineffective for problems with 14 tasks and beyond, mainly due to explosion of the sub-tour elimination constraints (SECs). However, in HHCRSP, we were able to solve instances as large as 35 tasks within a time limit of 2 hours.…”

“…In Riazi et al [2013], Logic-based Benders decomposition was used for the HMVRP to decompose the problem into a task assignment problem (master), and a series of scheduling subproblems in form of traveling salesman problems (TSPs). Integrating the Benders algorithm with a TSP solver for handling the subproblems led to significant speed ups that made the Benders method a viable alternative compared to the Centralized one.…”

“…This is overcome in this paper by employing a heuristic Gossip method to solve the problem. Such an algorithm has been successfully applied to a class of VRPs known as the heterogeneous multi-vehicle routing problem (HMVRP) (see Franceschelli et al [2013], and Riazi et al [2013]). The Gossip algorithm iteratively solves local problems that only consider a subset of caretakers and customers in each iteration.…”

“…Besides using the standard Gossip algorithm, which works on nurses/vehicles in a pairwise fashion, an extended version is also used. The extended algorithm, n-Gossip, presented in Riazi et al [2013], is used to obtain the required flexibility to balance optimality versus computational speed. Finally, Section 5 provides numerical simulations and complexity evaluations of both Gossip algorithms and the Centralized approach.…”

Gossip based asynchronous and randomized distributed task assignment with guaranteed performance on heterogeneous networks

“…Many results followed, for brevity's sake we mention the work by Ravazzi et al in [6] which characterized randomized affine dynamics with several applications to multi-agent systems, social networks and sensor networks and the very popular survey on gossip algorithms by Dimakis et al in [7] and references therein. We also mention applications of gossip algorithms proposed by Riazi et al to the heterogeneous multi-vehicle routing problem in [8] and to home healthcare scheduling problems [9].…”