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We present two algorithms to solve a 3-objective optimization problem arising in telecommunications access network planning, the k-Architecture Connected Facility Location Problem. The methods can also be used to solve any 3-objective integer linear programming model and can be extended to the multiobjective case. We give some exemplary computations using small and medium-sized instances for our problem.
In this paper we study the cost-optimal deployment of optical access networks considering variants of the problem such as fiber to the home (FTTH), fiber to the building (FTTB), fiber to the curb (FTTC), or fiber to the neighborhood (FTTN). We identify the combinatorial structures of the most important sub-problems arising in this area and model these, e.g., as capacitated facility location, concentrator location, or Steiner tree problems. We discuss modeling alternatives as well. We finally construct a “unified” integer programming model that combines all sub-models and provides a global view of all these FTTx problems. We also summarize computational studies of various special cases.
Das vom BMBF geförderte Projekt FTTX-PLAN entwickelt mathematische Modelle und Optimierungsverfahren, um automatisiert kostenoptimierte FTTx-Netze berechnen zu können. Wir zeigen anhand einer Praxisstudie in Zusammenarbeit mit der Regensburger R-KOM, wie ein Planer von diesen Verfahren profitieren kann, um die Auswirkungen bestimmter Entscheidungen auf die Netzstruktur und -kosten zu untersuchen. Wir illustrieren dies am Beispiel eines FTTB/FTTH-Vergleichs, der Variation von Kundenanbindungsraten und der gezielten Ausnutzung existierender Leerrohre, um Tiefbau zu vermeiden.
Network virtualization techniques allow for the coexistence of many virtual networks (VNs) jointly sharing the resources of an underlying substrate network. The Virtual Network Embedding problem (VNE) arises when looking for the most profitable set of VNs to embed onto the substrate. In this paper, we address the offline version of the problem. We propose a Mixed-Integer Linear Programming formulation to solve it to optimality which accounts for acceptance and rejection of virtual network requests, allowing for both splittable and unsplittable (single path) routing schemes. Our formulation also considers a Rent-at-Bulk (RaB) model for the rental of substrate capacities where economies of scale apply. To better emphasize the importance of RaB, we also compare our method to a baseline one which only takes RaB into account a posteriori, once a solution to VNE, oblivious to RaB, has been found. Computational experiments show the viability of our approach, stressing the relevance of addressing RaB directly with an exact formulation.
Energy storages can be of great value when added to power grids. They introduce the possibility to store and release energy whenever this is favorable. This is particularly relevant, for example, if power supply is volatile (as is the case with renewable energy) and the network is small (so that there are few other nodes that might balance fluctuations in consumption or production). We present models and methods from mathematical optimization for computing an optimized storage schedule for this purpose. We look at alternative optimization objectives, such as smallest possible peak load, low energy costs, or the close approximation of a prescribed load curve. The optimization needs to respect general operational and economic constraints as well as limitations in the use of storage, which are imposed by the chosen storage technology. We therefore introduce alternative approaches for modeling the non-linear properties of energy storages and study their impact on the efficiency of the optimization process. Finally, we present a computational study with batteries as storage devices. We use this to highlight the trade-off between solution quality and computational tractability. A version of the model for the purpose of leveling peaks and instabilities has been implemented into a control system for an office-building smart grid scenario.
Energy storages can be of great value when added to power grids. They introduce the possibility to store and release energy whenever this is favorable. This is particularly relevant, for example, if power supply is volatile (as is the case with renewable energy) and the network is small (so that there are few other nodes that might balance fluctuations in consumption or production). We present models and methods from mathematical optimization for computing an optimized storage schedule for this purpose. We look at alternative optimization objectives, such as smallest possible peak load, low energy costs, or the close approximation of a prescribed load curve. The optimization needs to respect general operational and economic constraints as well as limitations in the use of storage, which are imposed by the chosen storage technology. We therefore introduce alternative approaches for modeling the non-linear properties of energy storages and study their impact on the efficiency of the optimization process. Finally, we present a computational study with batteries as storage devices. We use this to highlight the trade-off between solution quality and computational tractability. A version of the model for the purpose of leveling peaks and instabilities has been implemented into a control system for an office-building smart grid scenario.