Mathematical Modelling and Methods for Load Balancing and Coordination of Multi-Robot Stations

The automotive industry is moving from mass production towards an individualized production, individualizing parts aims to improve product quality and to reduce costs and material waste. This thesis concerns aspects of load balancing and coordination of multi-robot stations in the automotive manufacturing industry, considering efficient algorithms required by an individualized production. The goal of the load balancing problem is to improve the equipment utilization. Several approaches for solving the load balancing problem are suggested along with details on mathematical tools and subroutines employed.Our contributions to the solution of the load balancing problem are fourfold. First, to circumvent robot coordination we construct disjoint robot programs, which require no coordination schemes, are flexible, admit competitive cycle times for several industrial instances, and may be preferred in an individualized production. Second, since solving the task assignment problem for generating the disjoint robot programs was found to be unreasonably time-consuming, we model it as a generalized unrelated parallel machine problem with set packing constraints and suggest a tailored Lagrangian-based branch-and-bound algorithm. Third, a continuous collision detection method needs to determine whether the sweeps of multiple moving robots are disjoint. We suggest using the maximum velocity of each robot along with distance computations at certain robot configurations to derive a function that provides lower bounds on the minimum distance between the sweeps. The lower bounding function is iteratively minimized and updated with new distance information; our method is substantially faster than previously developed methods. Fourth, to allow for load balancing of complex multi-robot stations we generalize the disjoint robot programs into sequences of such; for some instances this procedure provides a significant equipment utilization improvement in comparison with previous automated methods

Mathematical Modelling for Load Balancing and Minimization of Coordination Losses in Multirobot Stations

The automotive industry is moving from mass production towards an individualized production, in order to improve product quality and reduce costs and material waste. This thesis concerns aspects of load balancing of industrial robots in the automotive manufacturing industry, considering efficient algorithms required by an individualized production. The goal of the load balancing problem is to improve the equipment utilization. Several approaches for solving the load balancing problem are presented along with details on mathematical tools and subroutines employed.Our contributions to the solution of the load balancing problem are manifold. First, to circumvent robot coordination we have constructed disjoint robot programs, which require no coordination schemes, are more flexible, admit competitive cycle times for some industrial instances, and may be preferred in an individualized production. Second, since solving the task assignment problem for generating the disjoint robot programs was found to be unreasonably time-consuming, we modelled it as a generalized unrelated parallel machine problem with set packing constraints and suggested a tighter model formulation, which was proven to be much more tractable for a branch--and--cut solver. Third, within continuous collision detection it needs to be determined whether the sweeps of multiple moving robots are disjoint. Our solution uses the maximum velocity of each robot along with distance computations at certain robot configurations to derive a function that provides lower bounds on the minimum distance between the sweeps. The lower bounding function is iteratively minimized and updated with new distance information; our method is substantially faster than previously developed methods

Mathematical Models and Algorithms for Network Flow Problems Arising in Wireless Sensor Network Applications

We examine multiple variations on two classical network flow problems, the maximum flow and minimum-cost flow problems. These two problems are well-studied within the optimization community, and many models and algorithms have been presented for their solution. Due to the unique characteristics of the problems we consider, existing approaches cannot be directly applied. The problem variations we examine commonly arise in wireless sensor network (WSN) applications. A WSN consists of a set of sensors and collection sinks that gather and analyze environmental conditions. In addition to providing a taxonomy of relevant literature, we present mathematical programming models and algorithms for solving such problems. First, we consider a variation of the maximum flow problem having node-capacity restrictions. As an alternative to solving a single linear programming (LP) model, we present two alternative solution techniques. The first iteratively solves two smaller auxiliary LP models, and the second is a heuristic approach that avoids solving any LP. We also examine a variation of the maximum flow problem having semicontinuous restrictions that requires the flow, if positive, on any path to be greater than or equal to a minimum threshold. To avoid solving a mixed-integer programming (MIP) model, we present a branch-and-price algorithm that significantly improves the computational time required to solve the problem. Finally, we study two dynamic network flow problems that arise in wireless sensor networks under non-simultaneous flow assumptions. We first consider a dynamic maximum flow problem that requires an arc to transmit a minimum amount of flow each time it begins transmission. We present an MIP for solving this problem along with a heuristic algorithm for its solution. Additionally, we study a dynamic minimum-cost flow problem, in which an additional cost is incurred each time an arc begins transmission. In addition to an MIP, we present an exact algorithm that iteratively solves a relaxed version of the MIP until an optimal solution is found

A Matheuristic for Integrated Timetabling and Vehicle Scheduling

Planning a public transportation system is a complex process, which is usually broken down in several phases, performed in sequence. Most often, the trips required to cover a service with the desired frequency (headway) are decided early on, while the vehicles needed to cover these trips are determined at a later stage. This potentially leads to requiring a larger number of vehicles (and, therefore, drivers) that would be possible if the two decisions were performed simultaneously. We propose a multicommodity-flow type model for integrated timetabling and vehicle scheduling. Since the model is large-scale and cannot be solved by off-the-shelf tools with the efficiency required by planners, we propose a diving-type matheuristic approach for the problem. We report on the efficiency and effectiveness of two variants of the proposed approach, differing on how the continuous relaxation of the problem is solved, to tackle real-world instances of bus transport planning problem originating from customers of M.A.I.O.R., a leading company providing services and advanced decision-support systems to public transport authorities and operators. The results show that the approach can be used to aid even experienced planners in either obtaining better solutions, or obtaining them faster and with less effort, or both

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

A generic auction algorithm for the minimum cost network flow problem

Caption title.Includes bibliographical references (p. 40-43).by Dimitri P. Bertsekas and David A. Castanon

Characterization, design and re-optimization on multi-layer optical networks

L'augment de volum de tràfic IP provocat per l'increment de serveis multimèdia com HDTV o vídeo conferència planteja nous reptes als operadors de xarxa per tal de proveir transmissió de dades eficient. Tot i que les xarxes mallades amb multiplexació per divisió de longitud d'ona (DWDM) suporten connexions òptiques de gran velocitat, aquestes xarxes manquen de flexibilitat per suportar tràfic d’inferior granularitat, fet que provoca un pobre ús d'ample de banda. Per fer front al transport d'aquest tràfic heterogeni, les xarxes multicapa representen la millor solució. Les xarxes òptiques multicapa permeten optimitzar la capacitat mitjançant l'empaquetament de connexions de baixa velocitat dins de connexions òptiques de gran velocitat. Durant aquesta operació, es crea i modifica constantment una topologia virtual dinàmica gràcies al pla de control responsable d’aquestes operacions. Donada aquesta dinamicitat, un ús sub-òptim de recursos pot existir a la xarxa en un moment donat. En aquest context, una re-optimizació periòdica dels recursos utilitzats pot ser aplicada, millorant així l'ús de recursos. Aquesta tesi està dedicada a la caracterització, planificació, i re-optimització de xarxes òptiques multicapa de nova generació des d’un punt de vista unificat incloent optimització als nivells de capa física, capa òptica, capa virtual i pla de control. Concretament s'han desenvolupat models estadístics i de programació matemàtica i meta-heurístiques. Aquest objectiu principal s'ha assolit mitjançant cinc objectius concrets cobrint diversos temes oberts de recerca. En primer lloc, proposem una metodologia estadística per millorar el càlcul del factor Q en problemes d'assignació de ruta i longitud d'ona considerant interaccions físiques (IA-RWA). Amb aquest objectiu, proposem dos models estadístics per computar l'efecte XPM (el coll d'ampolla en termes de computació i complexitat) per problemes IA-RWA, demostrant la precisió d’ambdós models en el càlcul del factor Q en escenaris reals de tràfic. En segon lloc i fixant-nos a la capa òptica, presentem un nou particionament del conjunt de longituds d'ona que permet maximitzar, respecte el cas habitual, la quantitat de tràfic extra proveït en entorns de protecció compartida. Concretament, definim diversos models estadístics per estimar la quantitat de tràfic donat un grau de servei objectiu, i diferents models de planificació de xarxa amb l'objectiu de maximitzar els ingressos previstos i el valor actual net de la xarxa. Després de resoldre aquests problemes per xarxes reals, concloem que la nostra proposta maximitza ambdós objectius. En tercer lloc, afrontem el disseny de xarxes multicapa robustes davant de fallida simple a la capa IP/MPLS i als enllaços de fibra. Per resoldre aquest problema eficientment, proposem un enfocament basat en sobre-dimensionar l'equipament de la capa IP/MPLS i recuperar la connectivitat i el comparem amb la solució convencional basada en duplicar la capa IP/MPLS. Després de comparar solucions mitjançant models ILP i heurístiques, concloem que la nostra solució permet obtenir un estalvi significatiu en termes de costos de desplegament. Com a quart objectiu, introduïm un mecanisme adaptatiu per reduir l'ús de ports opto-electrònics (O/E) en xarxes multicapa sota escenaris de tràfic dinàmic. Una formulació ILP i diverses heurístiques són desenvolupades per resoldre aquest problema, que permet reduir significativament l’ús de ports O/E en temps molt curts. Finalment, adrecem el problema de disseny resilient del pla de control GMPLS. Després de proposar un nou model analític per quantificar la resiliència en topologies mallades de pla de control, usem aquest model per proposar un problema de disseny de pla de control. Proposem un procediment iteratiu lineal i una heurística i els usem per resoldre instàncies reals, arribant a la conclusió que es pot reduir significativament la quantitat d'enllaços del pla de control sense afectar la qualitat de servei a la xarxa.The explosion of IP traffic due to the increase of IP-based multimedia services such as HDTV or video conferencing poses new challenges to network operators to provide a cost-effective data transmission. Although Dense Wavelength Division Multiplexing (DWDM) meshed transport networks support high-speed optical connections, these networks lack the flexibility to support sub-wavelength traffic leading to poor bandwidth usage. To cope with the transport of that huge and heterogeneous amount of traffic, multilayer networks represent the most accepted architectural solution. Multilayer optical networks allow optimizing network capacity by means of packing several low-speed traffic streams into higher-speed optical connections (lightpaths). During this operation, a dynamic virtual topology is created and modified the whole time thanks to a control plane responsible for the establishment, maintenance, and release of connections. Because of this dynamicity, a suboptimal allocation of resources may exist at any time. In this context, a periodically resource reallocation could be deployed in the network, thus improving network resource utilization. This thesis is devoted to the characterization, planning, and re-optimization of next-generation multilayer networks from an integral perspective including physical layer, optical layer, virtual layer, and control plane optimization. To this aim, statistical models, mathematical programming models and meta-heuristics are developed. More specifically, this main objective has been attained by developing five goals covering different open issues. First, we provide a statistical methodology to improve the computation of the Q-factor for impairment-aware routing and wavelength assignment problems (IA-RWA). To this aim we propose two statistical models to compute the Cross-Phase Modulation variance (which represents the bottleneck in terms of computation time and complexity) in off-line and on-line IA-RWA problems, proving the accuracy of both models when computing Q-factor values in real traffic scenarios. Second and moving to the optical layer, we present a new wavelength partitioning scheme that allows maximizing the amount of extra traffic provided in shared path protected environments compared with current solutions. Specifically, we define several statistical models to estimate the traffic intensity given a target grade of service, and different network planning problems for maximizing the expected revenues and net present value. After solving these problems for real networks, we conclude that our proposed scheme maximizes both revenues and NPV. Third, we tackle the design of survivable multilayer networks against single failures at the IP/MPLS layer and WSON links. To efficiently solve this problem, we propose a new approach based on over-dimensioning IP/MPLS devices and lightpath connectivity and recovery and we compare it against the conventional solution based on duplicating backbone IP/MPLS nodes. After evaluating both approaches by means of ILP models and heuristic algorithms, we conclude that our proposed approach leads to significant CAPEX savings. Fourth, we introduce an adaptive mechanism to reduce the usage of opto-electronic (O/E) ports of IP/MPLS-over-WSON multilayer networks in dynamic scenarios. A ILP formulation and several heuristics are developed to solve this problem, which allows significantly reducing the usage of O/E ports in very short running times. Finally, we address the design of resilient control plane topologies in GMPLS-enabled transport networks. After proposing a novel analytical model to quantify the resilience in mesh control plane topologies, we use this model to propose a problem to design the control plane topology. An iterative model and a heuristic are proposed and used to solve real instances, concluding that a significant reduction in the number of control plane links can be performed without affecting the quality of service of the network