Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

Capacitated Vehicle Routing with Non-Uniform Speeds

The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple vehicles having non-uniform speeds (that we call Heterogenous CVRP), and present a constant-factor approximation algorithm. The technical heart of our result lies in achieving a constant approximation to the following TSP variant (called Heterogenous TSP). Given a metric denoting distances between vertices, a depot r containing k vehicles with possibly different speeds, the goal is to find a tour for each vehicle (starting and ending at r), so that every vertex is covered in some tour and the maximum completion time is minimized. This problem is precisely Heterogenous CVRP when vehicles are uncapacitated. The presence of non-uniform speeds introduces difficulties for employing standard tour-splitting techniques. In order to get a better understanding of this technique in our context, we appeal to ideas from the 2-approximation for scheduling in parallel machine of Lenstra et al.. This motivates the introduction of a new approximate MST construction called Level-Prim, which is related to Light Approximate Shortest-path Trees. The last component of our algorithm involves partitioning the Level-Prim tree and matching the resulting parts to vehicles. This decomposition is more subtle than usual since now we need to enforce correlation between the size of the parts and their distances to the depot

Industrial and Tramp Ship Routing Problems: Closing the Gap for Real-Scale Instances

Recent studies in maritime logistics have introduced a general ship routing problem and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargo selection, ship-dependent starting locations, travel times and costs, time windows, and incompatibility constraints, among other features. Together, these characteristics pose considerable challenges for exact and heuristic methods, and some cases with as few as 18 cargoes remain unsolved. To face this challenge, we propose an exact branch-and-price (B&P) algorithm and a hybrid metaheuristic. Our exact method generates elementary routes, but exploits decremental state-space relaxation to speed up column generation, heuristic strong branching, as well as advanced preprocessing and route enumeration techniques. Our metaheuristic is a sophisticated extension of the unified hybrid genetic search. It exploits a set-partitioning phase and uses problem-tailored variation operators to efficiently handle all the problem characteristics. As shown in our experimental analyses, the B&P optimally solves 239/240 existing instances within one hour. Scalability experiments on even larger problems demonstrate that it can optimally solve problems with around 60 ships and 200 cargoes (i.e., 400 pickup and delivery services) and find optimality gaps below 1.04% on the largest cases with up to 260 cargoes. The hybrid metaheuristic outperforms all previous heuristics and produces near-optimal solutions within minutes. These results are noteworthy, since these instances are comparable in size with the largest problems routinely solved by shipping companies

Routing Unmanned Vehicles in GPS-Denied Environments

Most of the routing algorithms for unmanned vehicles, that arise in data gathering and monitoring applications in the literature, rely on the Global Positioning System (GPS) information for localization. However, disruption of GPS signals either intentionally or unintentionally could potentially render these algorithms not applicable. In this article, we present a novel method to address this difficulty by combining methods from cooperative localization and routing. In particular, the article formulates a fundamental combinatorial optimization problem to plan routes for an unmanned vehicle in a GPS-restricted environment while enabling localization for the vehicle. We also develop algorithms to compute optimal paths for the vehicle using the proposed formulation. Extensive simulation results are also presented to corroborate the effectiveness and performance of the proposed formulation and algorithms.Comment: Publised in International Conference on Umanned Aerial System