Fixed-Parameter Algorithms for Rectilinear Steiner tree and Rectilinear Traveling Salesman Problem in the plane

Given a set $P$ of $n$ points with their pairwise distances, the traveling salesman problem (TSP) asks for a shortest tour that visits each point exactly once. A TSP instance is rectilinear when the points lie in the plane and the distance considered between two points is the $l_1$ distance. In this paper, a fixed-parameter algorithm for the Rectilinear TSP is presented and relies on techniques for solving TSP on bounded-treewidth graphs. It proves that the problem can be solved in $O\left(nh7^h\right)$ where $h \leq n$ denotes the number of horizontal lines containing the points of $P$. The same technique can be directly applied to the problem of finding a shortest rectilinear Steiner tree that interconnects the points of $P$ providing a $O\left(nh5^h\right)$ time complexity. Both bounds improve over the best time bounds known for these problems.Comment: 24 pages, 13 figures, 6 table

DYNAMIC SIMULATION ANALYSIS FOR VARIOUS NUMBERS OF ORDERS IN AN INTEGRATED CAR-MANUFACTURING WAREHOUSE

The order-picking process in a warehouse is critical in managing customer orders, especially in retail stores. It is expensive because fulfilling online orders takes up to 70% of all warehouse activities. Procedures in order picking, including different route selection schemes, can significantly increase yield and reduce costs. The research shows that a suitable routing method can reduce the travel time of the order picker to fulfill the order. However, the number of orders may vary. This paper presented a dynamic simulation analysis based on a real scenario of a various number of orders in an integrated car manufacturing warehouse. The simulation reduced the travel time of the voters by about 44.89%. This simulation model helps to visualize the potential reduction in customer waiting times, leading to increased customer satisfaction

The multi-objective Steiner pollution-routing problem on congested urban road networks

This paper introduces the Steiner Pollution-Routing Problem (SPRP) as a realistic variant of the PRP that can take into account the real operating conditions of urban freight distribution. The SPRP is a multi-objective, time and load dependent, fleet size and mix PRP, with time windows, flexible departure times, and multi-trips on congested urban road networks, that aims at minimising three objective functions pertaining to (i) vehicle hiring cost, (ii) total amount of fuel consumed, and (iii) total makespan (duration) of the routes. The paper focuses on a key complication arising from emissions minimisation in a time and load dependent setting, corresponding to the identification of the full set of the eligible road-paths between consecutive truck visits a priori, and to tackle the issue proposes new combinatorial results leading to the development of an exact Path Elimination Procedure (PEP). A PEP-based Mixed Integer Programming model is further developed for the SPRP and embedded within an efficient mathematical programming technique to generate the full set of the non-dominated points on the Pareto frontier of the SPRP. The proposed model considers truck instantaneous Acceleration/Deceleration (A/D) rates in the fuel consumption estimation, and to address the possible lack of such data at the planning stage, a new model for the construction of reliable synthetic spatiotemporal driving cycles from available macroscopic traffic speed data is introduced. Several analyses are conducted to: (i) demonstrate the added value of the proposed approach, (ii) exhibit the trade-off between the business and environmental objectives on the Pareto front of the SPRP, (iii) show the benefits of using multiple trips, and (iv) verify the reliability of the proposed model for the generation of driving cycles. A real road network based on the Chicago's arterial streets is also used for further experimentation with the proposed PEP algorithm. © 2019 Elsevier Lt

Algoritmos de aproximação para problemas de roteamento e conectividade com múltiplas funções de distância

Orientador: Lehilton Lelis Chaves PedrosaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta dissertação, estudamos algumas generalizações de problemas clássicos de roteamento e conectividade cujas instâncias são compostas por um grafo completo e múltiplas funções de distância. Por exemplo, existe o Problema do Caixeiro Alugador (CaRS), no qual um viajante deseja visitar um conjunto de cidades alugando um ou mais carros disponíveis. Cada carro tem uma função de distância e uma taxa de retorno ao local do aluguel. CaRS é uma generalização do Problema do Caixeiro Viajante (TSP). Nós lidamos com esses problemas usando algoritmos de aproximação, que são algoritmos eficientes que produzem soluções com garantia de qualidade. Neste trabalho, são apresentadas duas abordagens, uma baseada em uma redução linear que preserva o fator de aproximação e outra baseada na construção de instâncias de dois problemas distintos. Os problemas considerados são o Steiner TSP, o Problema do Passeio com Coleta de Prêmios e o Problema da Floresta Restrita. Generalizamos cada um desses problemas considerando múltiplas funções de distância e, para cada um deles, apresentamos um algoritmo de aproximação com fator O(logn), onde n é o número de vértices (cidades). Essas aproximações são assintoticamente ótimas, já que não há algoritmos com fator o(log n), a não ser que P = NPAbstract: In this dissertation, we study some generalizations of classical routing and connectivity problems whose instances are composed of a complete graph and multiple distance functions. As an example, there is the Traveling Car Renter Problem (CaRS) in which a traveler wants to visit a set of cities by renting one or more available cars. Each car is associated to a distance function and a service fee to return to the rental location. CaRS is a generalization of the Traveling Salesman Problem (TSP). We deal with these problems using approximation algorithms which are efficient algorithms that produce solutions with quality guarantee. In this work, two approaches are presented, one based on a linear reduction that preserves the approximation factor and the other based on the construction of instances of two distinct problems. The studied problems are the Steiner TSP, the Profitable Tour Problem, and the Constrained Forest Problem. We generalize these problems by considering multiple distance functions and, for each of them, we present an O(log n)-approximation algorithm, where n is the number of vertices (cities). The factor is asymptotically optimal, since there is no approximation algorithm with factor o(log n) unless P = NPMestradoCiência da ComputaçãoMestra em Ciência da Computação001CAPE

Compact formulations of the Steiner traveling salesman problem and related problems

The Steiner Traveling Salesman Problem (STSP) is a variant of the TSP that is particularly suitable when routing on real-life road networks. The standard integer programming formulations of both the TSP and STSP have an exponential number of constraints. On the other hand, several compact formulations of the TSP, i.e., formulations of polynomial size, are known. In this paper, we adapt some of them to the STSP, and compare them both theoretically and computationally. It turns out that, just by putting the best of the formulations into the CPLEX branch-and-bound solver, one can solve instances with over 200 nodes. We also briefly discuss the adaptation of our formulations to some related problems