The congested multicommodity network design problem

This paper studies a version of the fixed-charge multicommodity network design problem where in addition to the traditional costs of flow and design, congestion at nodes is explicitly considered. The problem is initially modeled as a nonlinear integer programming formulation and two solution approaches are proposed: (i) a reformulation of the problem as a mixed integer second order cone program to optimally solve the problem for small to medium scale problem instances, and (ii) an evolutionary algorithm using elements of iterated local search and scatter search to provide upper bounds. Extensive computational results on new benchmark problem instances and on real case data are presented

Parallel metaheuristics for stochastic capacitated multicommodity network design

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

Algorithms for the integer multicommodity network design problem

Cataloged from PDF version of article.In this thesis, we study the problem of logical network design in telecommunication networks. Given a set of nodes and a set of commodities, we aim to locate lightpaths(links) between nodes and route the commodities over these lightpaths. The cost to be minimized is the number of lightpaths used. The problem has capacity, degree and delay constraints. An important characteristic of our problem is that the commodities can not be split, therefore they must be routed on a single path. We present two integer programming formulations of the problem and consider four sets of valid inequalities. Additionally, a relaxation of the problem is presented to obtain a lower bound to the problem. Finally, we propose two algorithms of generating good feasible solutions to the problem. Our results prove to be close to the lower bounds.Kılınç, Mustafa RasimM.S

TS2PACK: A Two-Level Tabu Search for the Three-dimensional Bin Packing Problem

Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing one

A cycle-based evolutionary algorithm for the fixed-charge capacitated multi-commodity network design problem

This paper presents an evolutionary algorithm for the fixed-charge multicommodity network design problem (MCNDP), which concerns routing multiple commodities from origins to destinations by designing a network through selecting arcs, with an objective of minimizing the fixed costs of the selected arcs plus the variable costs of the flows on each arc. The proposed algorithm evolves a pool of solutions using principles of scatter search, interlinked with an iterated local search as an improvement method. New cycle-based neighborhood operators are presented which enable complete or partial re-routing of multiple commodities. An efficient perturbation strategy, inspired by ejection chains, is introduced to perform local compound cycle-based moves to explore different parts of the solution space. The algorithm also allows infeasible solutions violating arc capacities while performing the "ejection cycles", and subsequently restores feasibility by systematically applying correction moves. Computational experiments on benchmark MCNDP instances show that the proposed solution method consistently produces high-quality solutions in reasonable computational times

Network design under uncertainty and demand elasticity

Network design covers a large class of fundamental problems ubiquitous in the fields of transportation and communication. These problems are modelled mathematically using directed graphs and capture the trade-off between initial investment in infrastructure and operational costs. This thesis presents the use of mixed integer programming theory and algorithms to solve network design problems and their extensions. We focus on two types of network design problems, the first is a hub location problem in which the initial investments are in the form of fixed costs for installing infrastructure at nodes for them to be equipped for the transhipment of commodities. The second is a fixed-charge multicommodity network design problem in which investments are in the form of installing infrastructure on arcs so that they may be used to transport commodities. We first present an extension of the hub location problem where both demand and transportation cost uncertainty are considered. We propose mixed integer linear programming formulations and a branch-and-cut algorithm to solve robust counterparts for this problem. Comparing the proposed models' solutions to those obtained from a commensurate stochastic counterpart, we note that their performance is similar in the risk-neutral setting while solutions from the robust counterparts are significantly superior in the risk-averse setting. We next present exact algorithms based on Benders decomposition capable of solving large-scale instances of the classic uncapacitated fixed-charge multicommodity network design problem. The method combines the use of matheuristics, general mixed integer valid inequalities, and a cut-and-solve enumeration scheme. Computational experiments show the proposed approaches to be up to three orders of magnitude faster than the state-of-the-art general purpose mixed integer programming solver. Finally, we extend the classic fixed-charge multicommodity network design problem to a profit-oriented variant that accounts for demand elasticity, commodity selection, and service commitment. An arc-based and a path-based formulation are proposed. The former is a mixed integer non-convex problem solved with a general purpose global optimization solver while the latter is an integer linear formulation with exponentially many variables solved with a hybrid matheuristic. Further analysis shows the impact of considering demand elasticity to be significant in strategic network design

Reducing Power Consumption in Backbone Networks

Abstract—According to several studies, the power consumption of the Internet accounts for up to 10 % of the worldwide energy consumption, and several initiatives are being put into place to reduce the power consumption of the ICT sector in general. To this goal, we propose a novel approach to switch off network nodes and links while still guaranteeing full connectivity and maximum link utilization. After showing that the problem falls in the class of capacitated multi-commodity flow problems, and therefore it is NP-complete, we propose some heuristic algorithms to solve it. Simulation results in a realistic scenario show that it is possible to reduce the number of links and nodes currently used by up to 30 % and 50 % respectively during off-peak hours, while offering the same service quality

Hybrid Statistical Data Mining Framework for Multi-Commodity Fixed Charge Network Flow Problem

This paper presents a new approach to analyze the network structure in multi-commodity fixed charge network flow problems (MCFCNF). This methodology uses historical data produced from repeatedly solving the traditional MCFCNF mathematical model as input for the machine-learning framework. Further, we reshape the problem as a binary classification problem and employ machine-learning algorithms to predict network structure. This predicted network structure is further used as an initial solution for our mathematical model. The quality of the initial solution generated is judged on the basis of predictive accuracy, feasibility and reduction in solving time

An Improved Mathematical Formulation For the Carbon Capture and Storage (CCS) Problem

abstract: Carbon Capture and Storage (CCS) is a climate stabilization strategy that prevents CO2 emissions from entering the atmosphere. Despite its benefits, impactful CCS projects require large investments in infrastructure, which could deter governments from implementing this strategy. In this sense, the development of innovative tools to support large-scale cost-efficient CCS deployment decisions is critical for climate change mitigation. This thesis proposes an improved mathematical formulation for the scalable infrastructure model for CCS (SimCCS), whose main objective is to design a minimum-cost pipe network to capture, transport, and store a target amount of CO2. Model decisions include source, reservoir, and pipe selection, as well as CO2 amounts to capture, store, and transport. By studying the SimCCS optimal solution and the subjacent network topology, new valid inequalities (VI) are proposed to strengthen the existing mathematical formulation. These constraints seek to improve the quality of the linear relaxation solutions in the branch and bound algorithm used to solve SimCCS. Each VI is explained with its intuitive description, mathematical structure and examples of resulting improvements. Further, all VIs are validated by assessing the impact of their elimination from the new formulation. The validated new formulation solves the 72-nodes Alberta problem up to 7 times faster than the original model. The upgraded model reduces the computation time required to solve SimCCS in 72% of randomly generated test instances, solving SimCCS up to 200 times faster. These formulations can be tested and then applied to enhance variants of the SimCCS and general fixed-charge network flow problems. Finally, an experience from testing a Benders decomposition approach for SimCCS is discussed and future scope of probable efficient solution-methods is outlined.Dissertation/ThesisMasters Thesis Industrial Engineering 201