Towards the solution of variants of Vehicle Routing Problem

Some of the problems that are used extensively in -real life are NP complete problems. There is no any algorithm which can give the optimal solution to NP complete problems in the polynomial time in the worst case. So researchers are applying their best efforts to design the approximation algorithms for these NP complete problems. Approximation algorithm gives the solution of a particular problem, which is close to the optimal solution of that problem. In this paper, a study on variants of vehicle routing problem is being done along with the difference in the approximation ratios of different approximation algorithms as being given by researchers and it is found that Researchers are continuously applying their best efforts to design new approximation algorithms which have better approximation ratio as compared to the previously existing algorithms

Several approaches for the traveling salesman problem

We characterize both approaches, mldp and k-mldp, with several methodologies; both a linear and a non-linear mathematical formulation are proposed. Additionally, the design and implementation of an exact methodology to solve both linear formulations is implemented and with it we obtained exact results. Due to the large computation time these formulations take to be solved with the exact methodology proposed, we analyse the complexity each of these approaches and show that both problems are NP-hard. As both problems are NP-hard, we propose three metaheuristic methods to obtain solutions in shorter computation time. Our solution methods are population based metaheuristics which exploit the structure of both problems and give good quality solutions by introducing novel local search procedures which are able to explore more efficiently their search space and to obtain good quality solutions in shorter computation time. Our main contribution is the study and characterization of a bi-objective problematic involving the minimization of two objectives: an economic one which aims to minimize the total travel distance, and a service-quality objective which aims to minimize of the waiting time of the clients to be visited. With this combination of objectives, we aim to characterize the inclusion of the client in the decision-making process to introduce service-quality decisions alongside a classic routing objective.This doctoral dissertation studies and characterizes of a combination of objectives with several logistic applications. This combination aims to pursue not only a company benefit but a benefit to the clients waiting to obtain a service or a product. In classic routing theory, an economic approach is widely studied: the minimization of traveled distance and cost spent to perform the visiting is an economic objective. This dissertation aims to the inclusion of the client in the decision-making process to bring out a certain level of satisfaction in the client set when performing an action. We part from having a set of clients demanding a service to a certain company. Several assumptions are made: when visiting a client, an agent must leave from a known depot and come back to it at the end of the tour assigned to it. All travel times among the clients and the depot are known, as well as all service times on each client. This is to say, the agent knows how long it will take to reach a client and to perform the requested service in the client location. The company is interested in improving two characteristics: an economic objective as well as a servicequality objective by minimizing the total travel distance of the agent while also minimizing the total waiting time of the clients. We study two main approaches: the first one is to fulfill the visits assuming there is a single uncapacitated vehicle, this is to say that such vehicle has infinite capacity to attend all clients. The second one is to fulfill the visits with a fleet of k-uncapacitated vehicles, all of them restricted to an strict constraint of being active and having at least one client to visit. We denominate the single-vehicle approach the minimum latency-distance problem (mldp), and the k-sized fleet the k-minimum latency-distance problem (k-mldp). As previously stated, this company has two options: to fulfil the visits with a single-vehicle or with a fixed-size fleet of k agents to perform the visits

Dynamic Vehicle Routing for Robotic Systems

Recent years have witnessed great advancements in the science and technology of autonomy, robotics, and networking. This paper surveys recent concepts and algorithms for dynamic vehicle routing (DVR), that is, for the automatic planning of optimal multivehicle routes to perform tasks that are generated over time by an exogenous process. We consider a rich variety of scenarios relevant for robotic applications. We begin by reviewing the basic DVR problem: demands for service arrive at random locations at random times and a vehicle travels to provide on-site service while minimizing the expected wait time of the demands. Next, we treat different multivehicle scenarios based on different models for demands (e.g., demands with different priority levels and impatient demands), vehicles (e.g., motion constraints, communication, and sensing capabilities), and tasks. The performance criterion used in these scenarios is either the expected wait time of the demands or the fraction of demands serviced successfully. In each specific DVR scenario, we adopt a rigorous technical approach that relies upon methods from queueing theory, combinatorial optimization, and stochastic geometry. First, we establish fundamental limits on the achievable performance, including limits on stability and quality of service. Second, we design algorithms, and provide provable guarantees on their performance with respect to the fundamental limits.United States. Air Force Office of Scientific Research (Award FA 8650-07-2-3744)United States. Army Research Office. Multidisciplinary University Research Initiative (Award W911NF-05-1-0219)National Science Foundation (U.S.) (Award ECCS-0705451)National Science Foundation (U.S.) (Award CMMI-0705453)United States. Army Research Office (Award W911NF-11-1-0092

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Towards the solution of variants of Vehicle Routing Problem

Some of the problems that are used extensively in -real life are NP complete problems. There is no any algorithm which can give the optimal solution to NP complete problems in the polynomial time in the worst case. So researchers are applying their best efforts to design the approximation algorithms for these NP complete problems. Approximation algorithm gives the solution of a particular problem, which is close to the optimal solution of that problem. In this paper, a study on variants of vehicle routing problem is being done along with the difference in the approximation ratios of different approximation algorithms as being given by researchers and it is found that Researchers are continuously applying their best efforts to design new approximation algorithms which have better approximation ratio as compared to the previously existing algorithms

A robust solving strategy for the vehicle routing problem with multiple depots and multiple objectives

This document presents the development of a robust solving strategy for the Vehicle Routing Problem with Multiple Depots and Multiple Objectives (MO-MDVRP). The problem tackeled in this work is the problem to minimize the total cost and the load imbalance in vehicle routing plan for distribution of goods. This thesis presents a MILP mathematical model and a solution strategy based on a Hybrid Multi- Objective Scatter Search Algorithm. Several experiments using simulated instances were run proving that the proposed method is quite robust, this is shown in execution times (less than 4 minutes for an instance with 8 depots and 300 customers); also, the proposed method showed good results compared to the results found with the MILP model for small instances (up to 20 clients and 2 depots).MaestríaMagister en Ingeniería Industria

Attention, Learn to Solve Routing Problems!

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention layers with benefits over the Pointer Network and we show how to train this model using REINFORCE with a simple baseline based on a deterministic greedy rollout, which we find is more efficient than using a value function. We significantly improve over recent learned heuristics for the Travelling Salesman Problem (TSP), getting close to optimal results for problems up to 100 nodes. With the same hyperparameters, we learn strong heuristics for two variants of the Vehicle Routing Problem (VRP), the Orienteering Problem (OP) and (a stochastic variant of) the Prize Collecting TSP (PCTSP), outperforming a wide range of baselines and getting results close to highly optimized and specialized algorithms.Comment: Accepted at ICLR 2019. 25 pages, 7 figure