Local Optima Network Analysis of Multi-Attribute Vehicle Routing Problems

Abstract

Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of Vehicle Routing Problems (VRP) in which, besides the original constraint on vehicle capacity present in Capacitated Vehicle Routing Problem (CVRP), other attributes that model diverse real-life system characteristics are present. Among the most common attributes studied in the literature are vehicle capacity and route duration constraints. The influence of these restrictions on the overall structure of the problem and the performance of local search algorithms used to solve it has yet to be well known. This paper aims to explain the impact of constraints present in different variants of VRP through the alterations of the structure of the underlying search space that they cause. We focus on Local Optima Network Analysis (LONA) for multiple Traveling Salesman Problem (m-TSP) and VRP with vehicle capacity (CVRP), route duration (DVRP), and both (DCVRP) constraints. We present results that indicate that measures obtained for a sample of local optima provide valuable information on the behavior of the landscape under modifications in the problem’s constraints. Additionally, we use the LONA measures to explain the difficulty of VRP instances for solving by local search algorithms.

Optimization Models for the Vehicle Routing Problem under Disruptions

“…Uncertainty in the vehicle routing problem has been studied extensively in the literature (e.g., [3,4]). However, most studies focus on stochastic customers [5], stochastic demands [6], and stochastic travel times [7].…”

“…An example of Property 3 is shown in Figure 2. Although the disruption probabilities in the network are quite extreme, such an instance may also occur when the disruption probabilities on arcs (2, 3) and (3,4) are much larger. Another observation of the VRPMD comes from the fact that a single trip to a node can still be insufficient to satisfy the node demand.…”

An Improved Genetic Algorithm for the Granularity-Based Split Vehicle Routing Problem with Simultaneous Delivery and Pickup

“…Recently, more and more researchers focus on variation VRPs, such as the VRP with time windows [5,6], the VRP with simultaneous delivery and pickup [7,8] and the VRP with heterogeneous fleet [9,10]. These VRPs come from reality and have high practical application values [11][12][13].…”

“…Each customer point is served at least once. Constraints (11) and ( 12) represent the required number of vehicle constraints.…”