A Systematic Review of Approximability Results for Traveling Salesman Problems leveraging the TSP-T3CO Definition Scheme

The traveling salesman (or salesperson) problem, short TSP, is a problem of strong interest to many researchers from mathematics, economics, and computer science. Manifold TSP variants occur in nearly every scientific field and application domain: engineering, physics, biology, life sciences, and manufacturing just to name a few. Several thousand papers are published on theoretical research or application-oriented results each year. This paper provides the first systematic survey on the best currently known approximability and inapproximability results for well-known TSP variants such as the "standard" TSP, Path TSP, Bottleneck TSP, Maximum Scatter TSP, Generalized TSP, Clustered TSP, Traveling Purchaser Problem, Profitable Tour Problem, Quota TSP, Prize-Collecting TSP, Orienteering Problem, Time-dependent TSP, TSP with Time Windows, and the Orienteering Problem with Time Windows. The foundation of our survey is the definition scheme T3CO, which we propose as a uniform, easy-to-use and extensible means for the formal and precise definition of TSP variants. Applying T3CO to formally define the variant studied by a paper reveals subtle differences within the same named variant and also brings out the differences between the variants more clearly. We achieve the first comprehensive, concise, and compact representation of approximability results by using T3CO definitions. This makes it easier to understand the approximability landscape and the assumptions under which certain results hold. Open gaps become more evident and results can be compared more easily

Autonomous golf ball picking robot design and development

The golf ball picking task is a daily that requires human intensive labor. This document presents the hardware developing process of an autonomous golf ball picking robot which aims to efficiently perform this task. It has a maintenance capacity of a 25,000 m2 practice field. Compared to a similar device in the market this robot has twice the maximum speed and three times more container capacity.QREN GOLFmINHO nº1583, FCt - Fundação Ciência e Tecnologia

A new open-source system for strategic freight logistics planning: the SYNCHRO-NET optimization tools

Globalization and e-commerce facilities have yielded in the recent years an incredibly huge increment of freight movements. Consequently, the underlying supply chains have become more and more complex to manage for the shipping companies, in terms of costs, distances, times, and environmental sustainability. SYNCHRO-NET, a H2020 European research project, aims to de-stress the international supply chains by fostering cost-effective and greener transportation alternatives. Besides other important actions, the SYNCHRO-NET framework provides an optimization and simulation toolset to support decision-making in freight logistics planning at a strategic level. The synchronized use of different transportation modes and the exploitation of smart steaming strategies for ship movements are the two main aspects considered in this innovative optimization system. In this paper, we present the optimization toolset developed, its contribution with respect to the existing platforms, and the experimental set-up implemented to evaluate its performance, usability, and effectiveness. The system is, in fact, currently under evaluation by several world-wide leading companies in freight logistics and transportation. However, the toolset potentialities go beyond the SYNCHRO-NET context, being the system an open-source project that makes use of open data formats and technologies

Optimal paths in multi-stage stochastic decision networks

This paper deals with the search of optimal paths in a multi-stage stochastic decision network as a first application of the deterministic approximation approach proposed by Tadei et al. (2019). In the network, the involved utilities are stage-dependent and contain random oscillations with an unknown probability distribution. The problem is modeled as a sequential choice of nodes in a graph layered into stages, in order to find the optimal path value in a recursive fashion. It is also shown that an optimal path solution can be derived by using a Nested Multinomial Logit model, which represents the choice probability at the different stages. The accuracy and efficiency of the proposed method are experimentally proved on a large set of randomly generated instances. Moreover, insights on the calibration of a critical parameter of the deterministic approximation are also provided

A Generalized Bin Packing Problem for parcel delivery in last-mile logistics

Abstract In this paper, we present a new problem arising at a tactical level of setting a last-mile parcel delivery service in a city by considering different Transportation Companies (TC), which differ in cost and service quality. The courier must decide which TCs to select for the service in order to minimize the total cost and maximize the total service quality. We show that the problem can be modeled as a new packing problem, the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), where the items are the parcels to deliver and the bins are the TCs. The aim of the GBPPI is to select the appropriate fleet from TCs and determine the optimal assignment of parcels to vehicles such that the overall net cost is minimized. This cost takes into account both transportation costs and service quality. We provide a Mixed Integer Programming formulation of the problem, which is the starting point for the development of efficient heuristics that can address the GBPPI for instances involving up to 1000 items. Extensive computational tests show the accuracy of the proposed methods. Finally, we present a last-mile logistics case study of an international courier which addresses this problem

The stochastic multi-path traveling salesman problem with dependent random travel costs.

The objective of the stochastic multi-path Traveling Salesman Problem is to determine the expected minimum-cost Hamiltonian tour in a network characterized by the presence of different paths between each pair of nodes, given that a random travel cost with an unknown probability distribution is associated with each of these paths. Previous works have proved that this problem can be deterministically approximated when the path travel costs are independent and identically distributed. Such an approximation has been demonstrated to be of acceptable quality in terms of the estimation of an optimal solution compared to consolidated approaches such as stochastic programming with recourse, completely overcoming the computational burden of solving enormous programs exacerbated by the number of scenarios considered. Nevertheless, the hypothesis regarding the independence among the path travel costs does not hold when considering real settings. It is well known, in fact, that traffic congestion influences travel costs and creates dependence among them. In this paper, we demonstrate that the independence assumption can be relaxed and a deterministic approximation of the stochastic multi-path Traveling Salesman Problem can be derived by assuming just asymptotically independent travel costs. We also demonstrate that this deterministic approximation has strong operational implications because it allows the consideration of realistic traffic models. Computational tests on extensive sets of random and realistic instances indicate the excellent efficiency and accuracy of the deterministic approximation

A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand

The multiple vehicle traveling purchaser problem (MVTPP) consists of simultaneously selecting suppliers and routing a fleet of homogeneous vehicles to purchase different products at the selected suppliers so that all product demands are fulfilled and traveling and purchasing costs are minimized. We consider variants of the MVTPP in which the capacity of the vehicles can become binding and the demand for each product is one unit. Corresponding solution algorithms from the literature are either branch-and-cut or branch-and-price algorithms, where in the latter case the route-generation subproblem is solved on an expanded graph by applying standard dynamic-programming techniques. Our branch-price-and-cut algorithm employs a novel labeling algorithm that works directly on the original network and postpones the purchasing decisions until the route has been completely defined. Moreover, we define a new branching rule generally applicable in case of unitary product demands, introduce a new family of valid inequalities to apply when suppliers can be visited at most once, and show how product incompatibilities can be handled without considering additional resources in the pricing problem. In comprehensive computational experiments with standard benchmark sets we prove that the new branch-price-and-cut approach is highly competitive

Desenvolvimento de uma heurística para a determinação de rotas de recolha e distribuição de produtos considerando múltiplos veículos

Trabalho de projecto de mestrado, Matemática Aplicada à Economia e Gestão, Universidade de Lisboa, Faculdade de Ciências, 2019Neste projeto, apresenta-se um problema de determinação de rotas de recolha e distribuição com escolha seletiva de mercados. Existe uma frota homogénea de veículos e existem pontos onde se faz a recolha de determinados produtos e, posteriormente, faz-se a distribuição pelos clientes, tendo estes uma dada procura que tem que ser satisfeita. Não é obrigatório visitar todos os pontos de recolha disponíveis. O objetivo é construir rotas para os veículos que partam de um depósito, passem por certos mercados para comprar os produtos, entreguem os produtos aos clientes e regressem ao depósito, de modo a minimizar a soma dos custos de aquisição dos produtos e dos custos de deslocação. Neste trabalho, faz-se uma breve referência a alguns problemas de determinação de rotas para veículos e à sua aplicação a casos reais. Apresenta-se, ainda, um modelo matemático em programação linear inteira mista. Desenvolve-se, para obter soluções admissíveis para este problema, uma heurística que é constituída por duas fases. A primeira fase consiste em criar rotas com um único cliente e com os mercados que o servem, tendo como base uma heurística desenvolvida para resolver o Travelling Purchaser Problem. Nesta primeira fase, constrói-se uma solução inicial, a qual é melhorada através de dois procedimentos: Market drop e Market exchange. A segunda fase consiste na fusão das rotas obtidas, juntando vários clientes na mesma rota, de modo a diminuir os custos de viagem. Os resultados computacionais são obtidos para dados gerados aleatoriamente, considerando duas áreas onde estão os clientes, o depósito e os mercados, dois tipos de probabilidade associados à existência de determinado produto em cada mercado e à probabilidade de a procura de determinado produto por parte de um cliente ser superior a zero e diferentes valores para número de mercados e procura. Fazse uma análise dos resultados obtidos em termos de média das melhorias percentuais quando se faz a fusão de rotas e em termos de tempos computacionais, considerando duas capacidades diferentes para os veículos.In this project, a pickup and delivery problem with selective choice of markets is presented. There is a fleet of homogenous vehicles which travels through pickup points to get certain products and then delivers them to the customers who have a certain demand that must be satisfied. It is not necessary to visit every available pickup point. The goal is to find a good, next to optimal, route for the vehicles that leave the depot, stop at certain markets where products are bought, deliver those products to the customers and then return to the depot, in order to minimize the sum of the purchasing costs and the travelling costs. In this project, a brief reference to some vehicle routing problems and some of its applications to the real world is made. A mixed integer linear programming model is presented. A heuristic is built to find feasible solutions for this problem. The heuristic consists of two phases, the first of which, consists of creating routes with a single customer and the markets which satisfy the customer’s demand. This phase is based on a heuristic for the Travelling Purchaser Problem where an initial feasible solution is found and improved upon through two procedures: Market Drop and Market Exchange. The second phase consists of merging the routes obtained beforehand, joining multiple customers in the same route, in order to decrease travelling costs. Some computational results were obtained for randomly generated data, considering two different areas for the depot, customers and markets, two different probabilities for the existence of a certain product in a certain market, two different probabilities for the existence of demand of a certain product for each customer and, lastly, different numbers of customers and markets. The results were analysed in regards to the average percentage improvements for the route merging, as well as regarding the computational time, considering two different maximum vehicle capacities

Comparativo entre o problema do caixeiro viajante e caixeiro viajante com dependência de tempo : estudo de caso de entrega de um produtor rural

Orientador: Prof. Dr. Arinei Carlos Lindbeck da SilvaDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia de Produção. Defesa : Curitiba, 14/10/2022Inclui referênciasResumo: A pesquisa operacional constitui uma área de conhecimento e ode ser utilizada para encontrar soluções em problemas de roteirização de veículos. Um dos problemas conhecidos e estudados em relação à Pesquisa Operacional é o problema do caixeiro viajante, o qual apresenta muitas vertentes, sendo uma delas o problema do caixeiro viajante com dependência de tempo. Visando à eficiência desses problemas em determinar uma rota ótima, decidiu-se utilizá-lo para definir a melhor rota de entrega para um pequeno produtor rural que produz e comercializa morangos. A pesquisa busca fazer um comparativo entre o problema do caixeiro viajante e o problema do caixeiro viajante com dependência de tempo, que considera o momento do dia em que ocorrem as entregas e, assim, elenca-se a melhor rota, para o caso de poucos pontos em uma distância curta. O morango é uma fruta de alta perecibilidade, devendo ser manuseado com cuidado e refrigerado, por isso o tempo de entrega deve ser considerado, e um tempo de transporte muito longo pode afetar a qualidade do produto. Elencaram-se esses problemas para encontrar solução mais adequadas para a entrega do produto, sem elevar o custo da fruta e chegando ao consumidor da forma adequada.Abstract: Operations research is an area of knowledge used to find solutions to vehicle routing problems. One of the known and studied problems in relation to Operations Research is the traveling salesman problem, which has many aspects, one of which is the timedependent traveling salesman problem. Aiming at the efficiency of these problems in determining an optimal route, it was decided to use it to define the ideal delivery path for a small rural producer that produces and sells strawberries. The research seeks to compare the traveling salesman problem and the traveling salesman problem with time dependence, which considers the moment of the day when deliveries occur and, thus, the best route is listed, for the case of a few points within a short distance. Strawberry is a highly perishable fruit and must be handled with care and refrigerated, so the delivery time must be considered. A very long transport time can affect the quality of the product. These problems were listed in order to find an adequate solution for the delivery of the product, without raising the cost of the fruit and reaching the consumer in the appropriate way