The stochastic vehicle routing problem : a literature review, part II : solution methods

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio

The stochastic vehicle routing problem : a literature review, part I : models

Building on the work of Gendreau et al. (Eur J Oper Res 88(1):3–12; 1996), we review the past 20 years of scientific literature on stochastic vehicle routing problems. The numerous variants of the problem that have been studied in the literature are described and categorized. Keywords: vehicle routing (VRP), stochastic programming, SVRPpublishedVersio

Computational approaches to stochastic vehicle routing problems

"April 18, 1991."Includes bibliographical references (p. 33-34).Supported by the National Science Foundation. DDM-9010332 DDM-9014751 RCD-88-54827 RCD-90-50002Dimitris J. Bertsimas, Philippe Chervi, Michael Peterson

A simheuristic for routing electric vehicles with limited driving ranges and stochastic travel times

Green transportation is becoming relevant in the context of smart cities, where the use of electric vehicles represents a promising strategy to support sustainability policies. However the use of electric vehicles shows some drawbacks as well, such as their limited driving-range capacity. This paper analyses a realistic vehicle routing problem in which both driving-range constraints and stochastic travel times are considered. Thus, the main goal is to minimize the expected time-based cost required to complete the freight distribution plan. In order to design reliable Routing plans, a simheuristic algorithm is proposed. It combines Monte Carlo simulation with a multi-start metaheuristic, which also employs biased-randomization techniques. By including simulation, simheuristics extend the capabilities of metaheuristics to deal with stochastic problems. A series of computational experiments are performed to test our solving approach as well as to analyse the effect of uncertainty on the routing plans.Peer Reviewe

Exact Two-Step Benders Decomposition for Two-Stage Stochastic Mixed-Integer Programs

Many real-life optimization problems belong to the class of two-stage stochastic mixed-integer programming problems with continuous recourse. This paper introduces Two-Step Benders Decomposition with Scenario Clustering (TBDS) as a general exact solution methodology for solving such stochastic programs to optimality. The method combines and generalizes Benders dual decomposition, partial Benders decomposition, and Scenario Clustering techniques and does so within a novel two-step decomposition along the binary and continuous first-stage decisions. We use TBDS to provide the first exact solutions for the so-called Time Window Assignment Traveling Salesperson problem. This is a canonical optimization problem for service-oriented vehicle routing; it considers jointly assigning time windows to customers and routing a vehicle among them while travel times are stochastic. Extensive experiments show that TBDS is superior to state-of-the-art approaches in the literature. It solves instances with up to 25 customers to optimality. It provides better lower and upper bounds that lead to faster convergence than related methods. For example, Benders dual decomposition cannot solve instances of 10 customers to optimality. We use TBDS to analyze the structure of the optimal solutions. By increasing routing costs only slightly, customer service can be improved tremendously, driven by smartly alternating between high- and low-variance travel arcs to reduce the impact of delay propagation throughout the executed vehicle route

Monotone Causality in Opportunistically Stochastic Shortest Path Problems

When traveling through a graph with an accessible deterministic path to a target, is it ever preferable to resort to stochastic node-to-node transitions instead? And if so, what are the conditions guaranteeing that such a stochastic optimal routing policy can be computed efficiently? We aim to answer these questions here by defining a class of Opportunistically Stochastic Shortest Path (OSSP) problems and deriving sufficient conditions for applicability of non-iterative label-setting methods. The usefulness of this framework is demonstrated in two very different contexts: numerical analysis and autonomous vehicle routing. We use OSSPs to derive causality conditions for semi-Lagrangian discretizations of anisotropic Hamilton-Jacobi equations. We also use a Dijkstra-like method to solve OSSPs optimizing the timing and urgency of lane change maneuvers for an autonomous vehicle navigating road networks with a heterogeneous traffic load

Multi-Objective UAV Mission Planning Using Evolutionary Computation

This investigation purports to develop a new model for multiple autonomous aircraft mission routing. Previous research both related and unrelated to this endeavor have used classic combinatoric problems as models for Unmanned Aerial Vehicle (UAV) routing and mission planning. This document presents the concept of the Swarm Routing Problem (SRP) as a new combinatorics problem for use in modeling UAV swarm routing, developed as a variant of the Vehicle Routing Problem with Time Windows (VRPTW). The SRP removes the single vehicle per target restraint and changes the customer satisfaction requirement to one of vehicle on location volume. The impact of these alterations changes the vehicle definitions within the problem model from discrete units to cooperative members within a swarm. This represents a more realistic model for multi-agent routing as a real world mission plan would require the use of all airborne assets across multiple targets, without constraining a single vehicle to a single target. Solutions to the SRP problem model result in route assignments per vehicle that successfully track to all targets, on time, within distance constraints. A complexity analysis and multi-objective formulation of the VRPTW indicates the necessity of a stochastic solution approach leading to the development of a multi-objective evolutionary algorithm. This algorithm design is implemented using C++ and an evolutionary algorithm library called Open Beagle. Benchmark problems applied to the VRPTW show the usefulness of this solution approach. A full problem definition of the SRP as well as a multi-objective formulation parallels that of the VRPTW method. Benchmark problems for the VRPTW are modified in order to create SRP benchmarks. These solutions show the SRP solution is comparable or better than the same VRPTW solutions, while also representing a more realistic UAV swarm routing solution