Branch-and-Cut Techniques for Solving Realistic Two-Layer Network Design Problems (original) (raw)

Two-layer network design by branch-and-cut featuring MIP-based heuristics

2006

This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.

A branch-and-cut approach for minimum cost multi-level network design

Discrete Mathematics, 2002

Network design models with more than one facility type have many applications in communication and distribution problems. Due to their complexity, previous studies have focused on ÿnding good heuristic solutions. In this study, we develop algorithms that solve the multi-level network design problem to optimality. In our approach, the problem is converted to a Steiner tree problem and is solved by a branch-and-cut approach. Our computational study shows that the approach outperforms a dual ascent approach in the literature (Mirchandani, INFORMS J. Comput. 8 (3) (1996) 202) not only on solution times but also on the quality of the solutions.

Capacitated Multi-Layer Network Design with Unsplittable Demands: Polyhedra and Branch-and-Cut

Discrete Optimization, 2019

We consider the Capacitated Multi-Layer Network Design with Unsplittable demands (CMLND-U) problem. Given a two-layer network and a set of traffic demands, this problem consists in installing minimum cost capacities on the upper layer so that each demand is routed along a unique "virtual" path (even using a unique capacity on each link) in this layer, and each installed capacity is in turn associated a "physical" path in the lower layer. This particular hierarchical and unsplittable requirement for routing arises in the design of optical networks, including optical OFDM based networks. In this paper, we give an ILP formulation to the CMLND-U problem and we take advantage of its sub-problems to provide a partial characterization of the CMLND-U polytope including several families of facets. Based on this polyhedral study, we develop a Branch-and-Cut algorithm for the problem and show its effectiveness though a set of experiments, conducted on SNDlib-derived instances and also on real instances.

A node splitting technique for two level network design problems with transition nodes

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2011

The Two Level Network Design (TLND) problem arises when local broadband access networks are planned in areas, where no existing infrastructure can be used, i.e., in the so-called greenfield deployments. Mixed strategies of Fiber-To-The-Home and Fiber-To-The-Curb, i.e., some customers are served by copper cables, some by fiber optic lines, can be modeled by an extension of the TLND. We are given two types of customers (primary and secondary), an additional set of Steiner nodes and fixed costs for installing either a primary or a secondary technology on each edge. The TLND problem seeks a minimum cost connected subgraph obeying a tree-tree topology, i.e., the primary nodes are connected by a rooted primary tree; the secondary nodes can be connected using both primary and secondary technology. In this paper we study an important extension of TLND in which additional transition costs need to be paid for intermediate facilities placed at the transition nodes, i.e., nodes where the change of technology takes place. We call this problem TLNDF. The introduction of transition node costs leads to a problem with a rich structure permitting us to put in evidence reformulation techniques such as modeling in higher dimensional graphs (which in this case are based on a node splitting technique). We first provide a compact way of modeling intermediate facilities. We then present several generalizations of the facility-based inequalities involving an exponential number of constraints. Finally we show how to model the problem in an extended graph based on node splitting. Our main result states that the connectivity constraints on the splitted graph, projected back into the space of the variables of the original model, provide a new family of inequalities that implies, and even strictly dominates, all previously described cuts. We also provide a polynomial time separation algorithm for the more general cuts by calculating maximum flows on the splitted graph. We compare the proposed models both theoretically and computationally.

A Branch-and-Bound Algorithm to Solve a Multi-level Network Optimization Problem

Journal of Mathematical Modelling and Algorithms, 2003

Multi-level network optimization problems arise in many contexts such as telecommunication, transportation, and electric power systems. A model for multi-level network design is formulated as a mixed-integer program. The approach is innovative because it integrates in the same model aspects of discrete facility location, topological network design, and dimensioning. We propose a branch-and-bound algorithm based on Lagrangian relaxation to solve the model. Computational results for randomly generated problems are presented showing the quality of our approach. We also present and discuss a real world problem of designing a two-level local access urban telecommunication network and solving it with the proposed methodology. : 90B10, 68M10.

A Math-Heuristic for Network Slice Design

2021

In this paper, we address the Network Slice Design problem, which arises from blueprinting end-to-end communication networks using fifth-generation (5G) radio access technology. With regard to new sharing policies and radio-access integration, it shows peculiar requirements with respect to conventional function placement and routing problems. To address the underlying optimization problem, we propose an open-access framework based on a math-heuristic that encompasses control-plane and data-plane separation and novel mapping and decomposition dimensions influencing the placement and interconnection of slices. Our framework also incorporates flexible functional splitting, with possibly different splitting for different slices while taking into consideration dependency factors such as varying network latency and data volume throughout the virtual access networks. Numerical results are then presented to assess the efficiency of our approach.

A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems

INFORMS Journal on Computing, 1998

We present a cutting plane algorithm for solving the following telecommunications network design problem: given point-to-point traffic demands in a network, specified survivability requirements and a discrete cost/capacity function for each link, find minimum cost capacity expansions satisfying the given demands. This algorithm is based on the polyhedral study described in . In this paper we describe the underlying problem, the model and the main ingredients in our algorithm. This includes: initial formulation, feasibility test, separation for strong cutting planes and primal heuristics. Computational results for a set of real-world problems are reported.