A hybrid genetic algorithm for the multi-depot vehicle routing problem

The distribution of finished products from depots to customers is a practical and challenging problem in logistics management. Better routing and scheduling decisions can result in higher level of customer satisfaction because more customers can be served in a shorter time. The distribution problem is generally formulated as the vehicle routing problem (VRP). Nevertheless, there is a rigid assumption that there is only one depot. In cases, for instance, where a logistics company has more than one depot, the VRP is not suitable. To resolve this limitation, this paper focuses on the VRP with multiple depots, or multi-depot VRP (MDVRP). The MDVRP is NP-hard, which means that an efficient algorithm for solving the problem to optimality is unavailable. To deal with the problem efficiently, two hybrid genetic algorithms (HGAs) are developed in this paper. The major difference between the HGAs is that the initial solutions are generated randomly in HGA1. The Clarke and Wright saving method and the nearest neighbor heuristic are incorporated into HGA2 for the initialization procedure. A computational study is carried out to compare the algorithms with different problem sizes. It is proved that the performance of HGA2 is superior to that of HGA1 in terms of the total delivery time.

An integral equation method for a mixed initial boundary value problem for unsteady Stokes system in a doubly-connected domain

We present a novel numerical method for a mixed initial boundary value problem for the unsteady Stokes system in a planar doubly-connected domain. Using a Laguerre transformation the unsteady problem is reduced to a system of boundary value problems for the Stokes resolvent equations. Employing a modied potential approach we obtain a system of boundary integral equations with various singularities and we use a trigonometric quadrature method for their numerical solution. Numerical examples are presented showing that accurate approximations can be obtained with low computational cost.

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delvery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP.

Vehicle routing and location routing problems with minimum latency: algorithms and models

Latency can be defined as the sum of the arrival times at the customers. Minimum latency problems are specially relevant in applications related to humanitarian logistics. This thesis presents algorithms for solving a family of vehicle routing problems with minimum latency. First the latency location routing problem (LLRP) is considered. It consists of determining the subset of depots to be opened, and the routes that a set of homogeneous capacitated vehicles must perform in order to visit a set of customers such that the sum of the demands of the customers assigned to each vehicle does not exceed the capacity of the vehicle. For solving this problem three metaheuristic algorithms combining simulated annealing and variable neighborhood descent, and an iterated local search (ILS) algorithm, are proposed. Furthermore, the multi-depot cumulative capacitated vehicle routing problem (MDCCVRP) and the multi-depot k-traveling repairman problem (MDk-TRP) are solved with the proposed ILS algorithm. The MDCCVRP is a special case of the LLRP in which all the depots can be opened, and the MDk-TRP is a special case of the MDCCVRP in which the capacity constraints are relaxed. Finally, a LLRP with stochastic travel times is studied. A two-stage stochastic programming model and a variable neighborhood search algorithm are proposed for solving the problem. Furthermore a sampling method is developed for tackling instances with an infinite number of scenarios. Extensive computational experiments show that the proposed methods are effective for solving the problems under study.

Étude d'un problème de tournées de véhicules sur les arcs avec contraintes de capacité et coûts de service dépendants du temps

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Premium e-grocery:exploring value in logistics integrated service solutions

E-grocery is gradually becoming viable or a necessity for many families. Yet, most e-supermarkets are seen as providers of low value "staple" and bulky goods mainly. While each store has a large number of SKU available, these products are mainly necessity goods with low marginal value for hedonistic consumption. A need to acquire diverse products (e.g., organic), premium priced products (e.g., wine) for special occasions (e.g., anniversary, birthday), or products just for health related reasons (e.g., allergies, diabetes) are yet to be served via one-stop e-tailers. In this paper, we design a mathematical model that takes into account consumers' geo-demographics and multi-product sourcing capacity for creating critical mass and profit. Our mathematical model is a variant of Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), which we extend by adding intermediate locations for trucks to meet and exchange goods. We illustrate our model for the city of Istanbul using GIS maps, and discuss its various extensions as well as managerial implications.

Determining departure times in dynamic and stochastic maritime routing and scheduling problem

In maritime transportation, decisions are made in a dynamic setting where many aspects of the future are uncertain. However, most academic literature on maritime transportation considers static and deterministic routing and scheduling problems. This work addresses a gap in the literature on dynamic and stochastic maritime routing and scheduling problems, by focusing on the scheduling of departure times. Five simple strategies for setting departure times are considered, as well as a more advanced strategy which involves solving a mixed integer mathematical programming problem. The latter strategy is significantly better than the other methods, while adding only a small computational effort.

Inventory-routing model, for a multi-period problem with stochastic and deterministic demand

The need for integration in the supply chain management leads us to considerthe coordination of two logistic planning functions: transportation andinventory. The coordination of these activities can be an extremely importantsource of competitive advantage in the supply chain management. The battle forcost reduction can pass through the equilibrium of transportation versusinventory managing costs. In this work, we study the specific case of aninventory-routing problem for a week planning period with different types ofdemand. A heuristic methodology, based on the Iterated Local Search, isproposed to solve the Multi-Period Inventory Routing Problem with stochasticand deterministic demand.

Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.

Cooperative routing for collision minimization in wireless sensor networks

Cooperative communication has gained much interest due to its ability to exploit the broadcasting nature of the wireless medium to mitigate multipath fading. There has been considerable amount of research on how cooperative transmission can improve the performance of the network by focusing on the physical layer issues. During the past few years, the researchers have started to take into consideration cooperative transmission in routing and there has been a growing interest in designing and evaluating cooperative routing protocols. Most of the existing cooperative routing algorithms are designed to reduce the energy consumption; however, packet collision minimization using cooperative routing has not been addressed yet. This dissertation presents an optimization framework to minimize collision probability using cooperative routing in wireless sensor networks. More specifically, we develop a mathematical model and formulate the problem as a large-scale Mixed Integer Non-Linear Programming problem. We also propose a solution based on the branch and bound algorithm augmented with reducing the search space (branch and bound space reduction). The proposed strategy builds up the optimal routes from each source to the sink node by providing the best set of hops in each route, the best set of relays, and the optimal power allocation for the cooperative transmission links. To reduce the computational complexity, we propose two near optimal cooperative routing algorithms. In the first near optimal algorithm, we solve the problem by decoupling the optimal power allocation scheme from optimal route selection. Therefore, the problem is formulated by an Integer Non-Linear Programming, which is solved using a branch and bound space reduced method. In the second near optimal algorithm, the cooperative routing problem is solved by decoupling the transmission power and the relay node se- lection from the route selection. After solving the routing problems, the power allocation is applied in the selected route. Simulation results show the algorithms can significantly reduce the collision probability compared with existing cooperative routing schemes.

Exact solutions to the short sea shipping distribution problem

Short sea shipping has several advantages over other means of transportation, recognized by EU members. The maritime transportation could be dealt like a combination of two well-known problems: the container stowage problem and routing planning problem. The integration of these two well-known problems results in a new problem CSSRP (Container stowage and ship routing problem) that is also an hard combinatorial optimization problem. The aim of this work is to solve the CSSRP using a mixed integer programming model. It is proved that regardless the complexity of this problem, optimal solutions could be achieved in a reduced computational time. For testing the mathematical model some problems based on real data were generated and a sensibility analysis was performed.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.

Energy-aware Task Allocation onto Unrelated Heterogeneous Multicore Platform for Mixed Criticality Systems

Presented at Work in Progress Session, IEEE Real-Time Systems Symposium (RTSS 2015). 1 to 4, Dec, 2015. San Antonio, U.S.A..

Multipath inter-domain policy routing

Dissertação submetida para a obtenção do grau de Doutor em Engenharia Electrotécnica e de Computadores