Comparison of Randomized Solutions for Constrained Vehicle Routing Problem

In this short paper, we study the capacity-constrained vehicle routing problem (CVRP) and its solution by randomized Monte Carlo methods. For solving CVRP we use some pseudorandom number generators commonly used in practice. We use linear, multiple-recursive, inversive, and explicit inversive congruential generators and obtain random numbers from each to provide a route for CVRP. Then we compare the performance of pseudorandom number generators with respect to the total time the random route takes. We also constructed an open-source library github.com/iedmrc/binary-cws-mcs on solving CVRP by Monte-Carlo based heuristic methods.Comment: 6 pages, 2nd International Conference on Electrical, Communication and Computer Engineering (ICECCE), 12-13 June 2020, Istanbul, Turke

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

Running Genetic Algorithms in the Edge: A First Analysis

Nowadays, the volume of data produced by different kinds of devices is continuously growing, making even more difficult to solve the many optimization problems that impact directly on our living quality. For instance, Cisco projected that by 2019 the volume of data will reach 507.5 zettabytes per year, and the cloud traffic will quadruple. This is not sustainable in the long term, so it is a need to move part of the intelligence from the cloud to a highly decentralized computing model. Considering this, we propose a ubiquitous intelligent system which is composed by different kinds of endpoint devices such as smartphones, tablets, routers, wearables, and any other CPU powered device. We want to use this to solve tasks useful for smart cities. In this paper, we analyze if these devices are suitable for this purpose and how we have to adapt the optimization algorithms to be efficient using heterogeneous hardware. To do this, we perform a set of experiments in which we measure the speed, memory usage, and battery consumption of these devices for a set of binary and combinatorial problems. Our conclusions reveal the strong and weak features of each device to run future algorihms in the border of the cyber-physical system.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish MINECO and FEDER projects TIN2014-57341-R (http://moveon.lcc.uma.es), TIN2016-81766-REDT (http://cirti.es), TIN2017-88213-R (http://6city.lcc.uma.es), the Ministry of Education of Spain (FPU16/02595

On the Transferability of Knowledge among Vehicle Routing Problems by using Cellular Evolutionary Multitasking

Multitasking optimization is a recently introduced paradigm, focused on the simultaneous solving of multiple optimization problem instances (tasks). The goal of multitasking environments is to dynamically exploit existing complementarities and synergies among tasks, helping each other through the transfer of genetic material. More concretely, Evolutionary Multitasking (EM) regards to the resolution of multitasking scenarios using concepts inherited from Evolutionary Computation. EM approaches such as the well-known Multifactorial Evolutionary Algorithm (MFEA) are lately gaining a notable research momentum when facing with multiple optimization problems. This work is focused on the application of the recently proposed Multifactorial Cellular Genetic Algorithm (MFCGA) to the well-known Capacitated Vehicle Routing Problem (CVRP). In overall, 11 different multitasking setups have been built using 12 datasets. The contribution of this research is twofold. On the one hand, it is the first application of the MFCGA to the Vehicle Routing Problem family of problems. On the other hand, equally interesting is the second contribution, which is focused on the quantitative analysis of the positive genetic transferability among the problem instances. To do that, we provide an empirical demonstration of the synergies arisen between the different optimization tasks.Comment: 8 pages, 1 figure, paper accepted for presentation in the 23rd IEEE International Conference on Intelligent Transportation Systems 2020 (IEEE ITSC 2020

Locating Depots for Capacitated Vehicle Routing

We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for this problem. To achieve this result, we reduce to the k-median-forest problem, which generalizes both k-median and minimum spanning tree, and which might be of independent interest. We give a (3+c)-approximation algorithm for k-median-forest, which leads to a (12+c)-approximation algorithm for the above location-routing problem, for any constant c>0. The algorithm for k-median-forest is just t-swap local search, and we prove that it has locality gap 3+2/t; this generalizes the corresponding result known for k-median. Finally we consider the "non-uniform" k-median-forest problem which has different cost functions for the MST and k-median parts. We show that the locality gap for this problem is unbounded even under multi-swaps, which contrasts with the uniform case. Nevertheless, we obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur

The Vehicle Rescheduling Problem

The capacitated vehicle routing problem is to find a routing schedule describing the order in which geographically dispersed customers are visited to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. In many practical applications, a long term routing schedule has to be made for operational purposes, often based on average demand estimates. When demand substantially differs, constructing a new schedule is beneficial. The vehicle rescheduling problem is to find a new schedule that not only minimizes the total traveling costs but also minimizes the costs of deviating from the original schedule. In this paper two mathematical programming formulations of the rescheduling problem are presented as well as two heuristic methods, a two-phase heuristic and a modified savings heuristic. Computational and analytical results show that for sufficiently high deviation costs, the two-phase heuristic generates a schedule that is on average close to optimal or even guaranteed optimal, for all considered problem instances. The modified savings heuristic generates schedules of constant quality, however the two-phase heuristic produces schedules that are on average closer to the optimum.vehicle routing;operational planning;vehicle rescheduling problem