This document presents a genetic algorithm approach to optimize OSPF routing weights. The algorithm aims to minimize maximum and average link utilization directly, unlike previous methods that minimized a convex cost function. It can find weights for both single and multiple shortest path routing. The genetic algorithm uses a chromosome encoding of link weights. It selects parents using rank selection and produces offspring using a reproduction strategy combining crossover and mutation. Additional mutation is applied to offspring not meeting certain conditions. The algorithm is tested on small networks and compared to MIP-based methods, showing results for larger networks with increasing traffic demands.
IMPACT OF PARTIAL DEMAND INCREASE ON THE PERFORMANCE OF IP NETWORKS AND RE-OP...EM Legacy
12th GI/ITG CONFERENCE ON MEASURING, MODELLING AND EVALUATION OF COMPUTER AND COMMUNICATION SYSTEMS 3rd POLISH-GERMAN TELETRAFFIC SYMPOSIUM
PGTS 2004
Eueung Mulyana, Ulrich Killat
This document describes a multi-path routing algorithm for IP networks based on flow optimization. It presents an intra-domain routing algorithm that uses multi-commodity flow optimization to enable load-sensitive forwarding over multiple paths without being constrained by traditional routing protocols like OSPF. The key idea is to aggregate all traffic destined for the same egress node into one commodity during optimization, reducing the number of commodities significantly. This makes the computation tractable and allows forwarding based on destination addresses.
Impact of Partial Demand Increase on the Performance of IP Networks and Re-op...EM Legacy
This document discusses communication networks and the impact of partial demand increases on network performance. It begins by explaining intra-domain IP routing and shortest path routing approaches. It then motivates investigating how partial increases in demand affect network performance metrics and if re-optimization of routing is needed. The document outlines an approach for modeling this problem and evaluating re-optimization methods like partial least squares and simulated annealing to minimize maximum link utilization while limiting routing changes. The results suggest partial least squares performs better at successfully re-optimizing networks in response to demand increases with fewer routing changes.
Energy efficient resources allocations for wireless communication systemsTELKOMNIKA JOURNAL
The energy consumption level of the telecommunication process has become a new
consideration in resource management scheme. It is becoming a new parameter in the resource
management scheme besides throughput, spectral efficiency, and fairness. This work proposes a power
control scheme and user grouping method to keep the rational energy consumption level of the resource
management scheme. Inverse water-filling power allocation is a power allocation scheme that optimizes
the energy efficiency by giving the power to the user which have good channel conditions. The user
grouping method becomes the solution for carrier aggregation (CA) scheme that prevents edge cell user
get the resources from the high-frequency carrier. This can prevent energy wastage in the transmission
process. This power control scheme and user grouping method can optimize the spectral and energy
efficiency without increasing the time complexity of the system.
An Offline Hybrid IGP/MPLS Traffic Engineering Approach under LSP ConstraintsEM Legacy
This document proposes a novel hybrid IGP/MPLS traffic engineering method based on genetic algorithms to handle long or medium-term traffic variations. The method treats the maximum number of hops an LSP may take and the number of LSPs applied solely to improve routing as constraints. Results comparing this hybrid approach to pure IGP routing and full mesh MPLS with and without flow splitting on the German scientific network and other networks are presented.
A PROGRESSIVE MESH METHOD FOR PHYSICAL SIMULATIONS USING LATTICE BOLTZMANN ME...ijdpsjournal
In this paper, a new progressive mesh algorithm is introduced in order to perform fast physical simulations by the use of a lattice Boltzmann method (LBM) on a single-node multi-GPU architecture. This algorithm is able to mesh automatically the simulation domain according to the propagation of fluids. This method can also be useful in order to perform several types of physical simulations. In this paper, we associate this
algorithm with a multiphase and multicomponent lattice Boltzmann model (MPMC–LBM) because it is
able to perform various types of simulations on complex geometries. The use of this algorithm combined
with the massive parallelism of GPUs[5] allows to obtain very good performance in comparison with the
staticmesh method used in literature. Several simulations are shown in order to evaluate the algorithm.
Exploiting 2-Dimensional Source Correlation in Channel Decoding with Paramete...IJECEIAES
The document describes a proposed joint source-channel coding (JSCC) system that exploits 2-dimensional source correlation in channel decoding with parameter estimation. The system uses a modified Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm at the decoder to exploit source correlation on rows and columns of a 2D source. A parameter estimation technique based on the Baum-Welch algorithm is used jointly with the decoder to estimate source correlation parameters at the receiver since these parameters are not always known in practice. Simulation results show that the proposed coding scheme that performs joint decoding and parameter estimation performs very close to an ideal 2D JSCC system with perfect knowledge of source correlation parameters.
IMPACT OF PARTIAL DEMAND INCREASE ON THE PERFORMANCE OF IP NETWORKS AND RE-OP...EM Legacy
12th GI/ITG CONFERENCE ON MEASURING, MODELLING AND EVALUATION OF COMPUTER AND COMMUNICATION SYSTEMS 3rd POLISH-GERMAN TELETRAFFIC SYMPOSIUM
PGTS 2004
Eueung Mulyana, Ulrich Killat
This document describes a multi-path routing algorithm for IP networks based on flow optimization. It presents an intra-domain routing algorithm that uses multi-commodity flow optimization to enable load-sensitive forwarding over multiple paths without being constrained by traditional routing protocols like OSPF. The key idea is to aggregate all traffic destined for the same egress node into one commodity during optimization, reducing the number of commodities significantly. This makes the computation tractable and allows forwarding based on destination addresses.
Impact of Partial Demand Increase on the Performance of IP Networks and Re-op...EM Legacy
This document discusses communication networks and the impact of partial demand increases on network performance. It begins by explaining intra-domain IP routing and shortest path routing approaches. It then motivates investigating how partial increases in demand affect network performance metrics and if re-optimization of routing is needed. The document outlines an approach for modeling this problem and evaluating re-optimization methods like partial least squares and simulated annealing to minimize maximum link utilization while limiting routing changes. The results suggest partial least squares performs better at successfully re-optimizing networks in response to demand increases with fewer routing changes.
Energy efficient resources allocations for wireless communication systemsTELKOMNIKA JOURNAL
The energy consumption level of the telecommunication process has become a new
consideration in resource management scheme. It is becoming a new parameter in the resource
management scheme besides throughput, spectral efficiency, and fairness. This work proposes a power
control scheme and user grouping method to keep the rational energy consumption level of the resource
management scheme. Inverse water-filling power allocation is a power allocation scheme that optimizes
the energy efficiency by giving the power to the user which have good channel conditions. The user
grouping method becomes the solution for carrier aggregation (CA) scheme that prevents edge cell user
get the resources from the high-frequency carrier. This can prevent energy wastage in the transmission
process. This power control scheme and user grouping method can optimize the spectral and energy
efficiency without increasing the time complexity of the system.
An Offline Hybrid IGP/MPLS Traffic Engineering Approach under LSP ConstraintsEM Legacy
This document proposes a novel hybrid IGP/MPLS traffic engineering method based on genetic algorithms to handle long or medium-term traffic variations. The method treats the maximum number of hops an LSP may take and the number of LSPs applied solely to improve routing as constraints. Results comparing this hybrid approach to pure IGP routing and full mesh MPLS with and without flow splitting on the German scientific network and other networks are presented.
A PROGRESSIVE MESH METHOD FOR PHYSICAL SIMULATIONS USING LATTICE BOLTZMANN ME...ijdpsjournal
In this paper, a new progressive mesh algorithm is introduced in order to perform fast physical simulations by the use of a lattice Boltzmann method (LBM) on a single-node multi-GPU architecture. This algorithm is able to mesh automatically the simulation domain according to the propagation of fluids. This method can also be useful in order to perform several types of physical simulations. In this paper, we associate this
algorithm with a multiphase and multicomponent lattice Boltzmann model (MPMC–LBM) because it is
able to perform various types of simulations on complex geometries. The use of this algorithm combined
with the massive parallelism of GPUs[5] allows to obtain very good performance in comparison with the
staticmesh method used in literature. Several simulations are shown in order to evaluate the algorithm.
Exploiting 2-Dimensional Source Correlation in Channel Decoding with Paramete...IJECEIAES
The document describes a proposed joint source-channel coding (JSCC) system that exploits 2-dimensional source correlation in channel decoding with parameter estimation. The system uses a modified Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm at the decoder to exploit source correlation on rows and columns of a 2D source. A parameter estimation technique based on the Baum-Welch algorithm is used jointly with the decoder to estimate source correlation parameters at the receiver since these parameters are not always known in practice. Simulation results show that the proposed coding scheme that performs joint decoding and parameter estimation performs very close to an ideal 2D JSCC system with perfect knowledge of source correlation parameters.
Optimum Network Reconfiguration using Grey Wolf OptimizerTELKOMNIKA JOURNAL
Distribution system Reconfiguration is the process of changing the topology of the distribution
network by opening and closing switches to satisfy a specific objective. It is a complex, combinatorial
optimization problem involving a nonlinear objective function and constraints. Grey Wolf Optimizer (GWO)
is a recently developed metaheuristic search algorithm inspired by the leadership hierarchy and hunting
strategy of grey wolves in nature. The objective of this paper is to determine an optimal network
reconfiguration that presents the minimum power losses, considering network constraints, and using GWO
algorithm. The proposed algorithm was tested using some standard networks (33 bus, 69 bus, 84 bus and
118 bus), and the obtained results reveal the efficiency and effectiveness of the proposed approach.
Optimization of IP Networks in Various Hybrid IGP/MPLS Routing SchemesEM Legacy
This document discusses optimization of IP networks using hybrid IGP/MPLS routing schemes. It proposes a heuristic approach using genetic algorithms to optimize network performance metrics like utilization and hop count while minimizing the number of label switched paths (LSPs). The document presents models for different hybrid routing approaches, a problem formulation, and results from applying the genetic algorithm approach to a case study network.
ENHANCING COMPUTATIONAL EFFORTS WITH CONSIDERATION OF PROBABILISTIC AVAILABL...Raja Larik
This document proposes a Probabilistic Collocation Method (PCM) to improve probabilistic load flow (PLF) computation methods and model network topology uncertainties. PCM uses probability distribution functions to model the impact of uncertainties as a linear function of power injections. It maintains the linear relationship between line flows and power injections. The method is examined using the IEEE 39-bus test system and compared to Monte Carlo simulation, showing significantly reduced computational efforts while maintaining accuracy.
Internet Traffic Engineering for Partially Uncertain DemandsEM Legacy
This document summarizes an academic paper about modeling and solving the problem of routing network traffic with both fixed and uncertain demands. It considers routing strategies that use link metrics to determine shortest paths in IP networks. The proposed model represents uncertain demands using a hose model that specifies maximum aggregate traffic amounts. It calculates link loads by combining loads from fixed demands, maximum outbound uncertain demands, and maximum inbound uncertain demands. Computational results are presented for both multiple and unique shortest path routing strategies to demonstrate the benefits of considering both fixed and uncertain traffic demands.
MODIFIED LLL ALGORITHM WITH SHIFTED START COLUMN FOR COMPLEXITY REDUCTIONijwmn
Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless
communication. The complexity of the different systems models challenge different researches to get a good
complexity to performance balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovàsz (LLL)
algorithm bring more resources to investigate and can contribute to the complexity reduction purposes.
In this paper, we are looking to modify the LLL algorithm to reduce the computation operations by
exploiting the structure of the upper triangular matrix without “big” performance degradation. Basically,
the first columns of the upper triangular matrix contain many zeroes, so the algorithm will perform several
operations with very limited income. We are presenting a performance and complexity study and our
proposal show that we can gain in term of complexity while the performance results remains almost the
same.
Labeled generalized stochastic petri net Based approach for web services Comp...ijcsit
This document proposes an approach for modeling and composing web services using Labeled Generalized Stochastic Petri Nets (LGSPNs). LGSPNs are presented as an expressive way to formally model both the structure and behavior of individual web services. An algebra is then defined to compose existing web services modeled as LGSPNs in order to create new composite services. The composition operators allow incrementally building more complex services through the combination of basic services. The LGSPN modeling approach is argued to provide benefits for understanding, analyzing, and prototyping complex web service compositions.
Mitigating Interference to GPS Operation Using Variable Forgetting Factor Bas...IJCNCJournal
In this paper, an interference method based on signal processing is proposed. The approach is based on
utilizing the maximum likelihood properties of the received signal. The approach is built on maximizing the
probability of the desired data. The GPS data, which is constructed using Binary Phase Shift Keying
(BPSK) modulation, is transmitted as “1’s” and as “0’s.” carried on 1575.42MHz carrier called the L1
frequency. The statistics of the GPS data and interference are utilized in terms of their distribution and
variance. The statistics are used to update (adaptively) the forgetting factor (Lambda) of the Recursive
Least Squares (RLS) filter. The proposed method is called Maximum Likelihood Variable Forgetting Factor
(ML VFF). The adaptive update takes on assigning lambda to the maximum of the probabilities of the
symbols based on the statistics mentioned.
This document summarizes a research paper about realizing complementary Boolean functions in a power-efficient manner using static CMOS logic. The paper proposes a method that algebraically factors Reed-Muller forms to reduce gate count and power consumption. Simulation results show the proposed method achieves on average 26.79% lower power consumption compared to other factored Reed-Muller forms, with reductions of 39.66% in gate count and 12.98% in input literals. However, this approach may decrease the testability of the resulting circuits.
Routing Optimization in IP/MPLS Networks under Per-Class Over-Provisioning Co...EM Legacy
This document describes research on routing optimization in IP/MPLS networks under per-class over-provisioning constraints. It introduces a heuristic approach that iteratively optimizes IGP link metrics to indirectly solve the multi-objective problem of finding routing configurations that efficiently use network resources while satisfying per-class capacity constraints and minimizing the number of explicit label switched paths (LSPs) required. The heuristic calls a traffic engineering procedure based on simulated annealing to optimize routing for aggregate demands and individual traffic classes.
PSO-based Training, Pruning, and Ensembling of Extreme Learning Machine RBF N...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
A PROGRESSIVE MESH METHOD FOR PHYSICAL SIMULATIONS USING LATTICE BOLTZMANN ME...ijdpsjournal
In this paper, a new progressive mesh algorithm is introduced in order to perform fast physical simulations
by the use of a lattice Boltzmann method (LBM) on a single-node multi-GPU architecture. This algorithm is
able to mesh automatically the simulation domain according to the propagation of fluids. This method can
also be useful in order to perform several types of physical simulations. In this paper, we associate this
algorithm with a multiphase and multicomponent lattice Boltzmann model (MPMC–LBM) because it is
able to perform various types of simulations on complex geometries. The use of this algorithm combined
with the massive parallelism of GPUs[5] allows to obtain very good performance in comparison with the
staticmesh method used in literature. Several simulations are shown in order to evaluate the algorithm.
A low complexity partial transmit sequence approach based on hybrid segmentat...journalBEEI
The partial transmit sequences (PTS) is regarded as a promising scheme for inhibiting the high peak-to-average power ratio (PAPR) problem in the orthogonal frequency division multiplexing (OFDM) systems. The PTS scheme relies on partitioning the data sequence into subsets and weighting these subsets by a group of the phase rotation factors. Although the PTS can efficiently reduce the high PAPR value, a great computational complexity (CC) level restricts the utilization of the PTS scheme in practical applications. In PTS, there are three common types of segmentation schemes; interleaving (IL-PTS), pseudo-random (PR-PTS), and adjacent (Ad-PTS) schemes. This paper presents a new algorithm named hybrid pseudo-random and interleaving cosine wave shape (H-PRC-PTS) by combining the PR-PTS scheme and the symmetrical interleaving cosine wave shape (S-IL-C-PTS) scheme which was proposed in our previous work. The results indicate that the suggested algorithms can diminish the PAPR value like the PR-PTS scheme, whereas the CC level is reduced significantly.
ENSURING QOS GUARANTEES IN A HYBRID OCS/OBS NETWORKijngnjournal
The bursting aggregation assembly in edge nodes is one of the key technologies in OBS (Optical Burst Switching) network, which has a direct impact on flow characteristics and packet loss rate. An optical burst assembly technique supporting QoS is presented through this paper, which can automatically adjust the threshold along with the increasing and decreasing volume of business, reduce the operational burst, and generate corresponding BDP (Burst Data Packet) and BCP (Burst Control Packet). In addition to the burst aggregation technique a packet recovery technique by restoration method is also described. The data packet loss due to the physical optical link failure is not currently included in the QoS descriptions. This link failure is also a severe problem which reduces the data throughput of the transmitter node. A mechanism for data recovery from this link failure is vital for guaranteeing the QoS demanded by each user. So this paper will also discusses a specific protocol for reducing the packet loss by utilizing the
features of both optical circuit switching (OCS) and Optical Burst switching (OBS) techniques
Performance Analysis for Parallel MRA in Heterogeneous Wireless NetworksEditor IJCATR
This document analyzes methods for optimal path selection and power allocation in heterogeneous wireless networks where a user can transmit data through multiple radio access technologies (RATs) simultaneously. It formulates the bandwidth and power allocation problem as an optimization problem to maximize total system capacity. The Newton and modified Newton methods are proposed to find the optimal solution. Simulation results show the modified Newton method achieves higher total system capacity compared to the Newton method.
A Weighted Duality based Formulation of MIMO SystemsIJERA Editor
This work is based on the modeling and analysis of multiple-input multiple-output (MIMO) system in downlink communication system. We take into account a recent work on the ratio of quadratic forms to formulate the weight matrices of quadratic norm in a duality structure. This enables us to achieve exact solutions for MIMO system operating under Rayleigh fading channels. We outline couple of scenarios dependent on the structure of eigenvalues to investigate the system behavior. The results obtained are validated by means of Monte Carlo simulations.
A comparative study on synchronization algorithms for various modulation tech...IAEME Publication
This document discusses synchronization algorithms for various modulation techniques used in GSM. It begins with an introduction to GSM and modulation techniques like GMSK. It then reviews previous literature on synchronization algorithms for signals like QPSK and CPM. The document proposes a synchronization algorithm for GMSK modulation that uses a symbol-by-symbol demodulator. It evaluates the proposed algorithm by comparing bit error rate and synchronization parameter estimation against other methods. The results show the proposed algorithm achieves better performance than previous methods in terms of SNR, BER and estimation of timing, frequency and phase offsets for GSM standards.
Aiming at the problem that existing femtocell base station searching the optimal clustering scheme based on the clustering resource allocation algorithm is complex. We propose that building an conflict graph and adjacency matrix before clustering to calculate the number of clusters needed for FBS group by using the adaptive clustering heuristic algorithm. We follow maximization the sum of the FBS distances in the cluster and group the femtocell base stations to narrow the search range to reduce the computational complexity. In order to achieve different business types service, based on the above clustering algorithm, this paper proposes a new method that using the weighted energy efficiency, which including the user interruption and the network spectral efficiency as a fitness function of the power control scheme to solve the problem. The simulation results show that the same rate requirement reduces the complexity, while the same complexity increases the user's average rate.
A CLUSTER BASED STABLE ROUTING PROTOCOL USING BINARY PARTICLE SWARM OPTIMIZAT...ijmnct
The document summarizes a research paper that proposes a new clustering routing protocol called Cluster based Stable Routing protocol (CSR) for mobile ad hoc networks. The protocol uses Binary Particle Swarm Optimization (BPSO) to select cluster heads and determine the optimal number of clusters. The goal is to minimize the number of clusters, efficiently select cluster heads based on remaining battery power, and maximize network lifetime. Experiments showed the proposed method efficiently forms clusters in mobile ad hoc networks.
This document summarizes research on distributed path computation algorithms that aim to prevent routing loops. It introduces the Distributed Path Computation with Intermediate Variables (DIV) algorithm, which can operate with any routing algorithm to guarantee loop-freedom. DIV generalizes previous loop-free algorithms and provably outperforms them by reducing synchronous updates and helping maintain paths during network changes. The document also reviews link-state routing, distance-vector routing, and existing loop-prevention techniques like the Diffusing Update Algorithm and Loop Free Invariance algorithms.
Dimensioning of Multi-Class Over-Provisioned IP NetworksEM Legacy
This document presents an analysis of dimensioning multi-class IP networks to support differentiated services under over-provisioning constraints. It introduces mathematical formulations to represent the problem as mixed integer linear programs that can find optimal solutions for moderate sized networks. A heuristic approach is also proposed to solve the problem for larger networks. The formulations consider different routing schemes (per-class and per-aggregate routing) and over-provisioning constraints (per-class and per-aggregate over-provisioning). Computational results using sample networks are provided to compare the different approaches.
OPTIMIZATION OF IP NETWORKS IN VARIOUS HYBRID IGP/MPLS ROUTING SCHEMESEM Legacy
The document discusses optimization of traffic engineering in hybrid IGP/MPLS networks using a genetic algorithm approach. It formulates the problem and introduces notation for the network topology, link capacities, traffic demands, and label switched paths (LSPs). It then describes three hybrid routing schemes - basic IGP shortcut, IGP shortcut, and overlay - that combine IGP routing with MPLS. The document proposes using a genetic algorithm to solve the optimization problem. It describes encoding potential solutions as chromosomes, where each value represents an LSP assignment for a traffic flow. The algorithm aims to minimize network congestion by evolving populations of chromosomes over iterations to find optimal LSP configurations. Results are presented for the German scientific network topology.
Optimizing IP Networks for Uncertain Demands Using Outbound Traffic ConstraintsEM Legacy
This document discusses various models for optimizing IP networks with uncertain demands using outbound traffic constraints. It introduces several models of increasing complexity: Model A1 specifies maximum outbound traffic per node; Model A2 adds maximum flow constraints; Model A3 groups traffic into destinations; and Model A4 combines grouping with per-group maximum flows. The models are evaluated on a sample network, showing that additional constraints can significantly reduce maximum link utilization at the cost of supporting fewer traffic variations. Overall, the models provide simple ways to characterize traffic uncertainty that can be used with heuristic optimization approaches.
Optimum Network Reconfiguration using Grey Wolf OptimizerTELKOMNIKA JOURNAL
Distribution system Reconfiguration is the process of changing the topology of the distribution
network by opening and closing switches to satisfy a specific objective. It is a complex, combinatorial
optimization problem involving a nonlinear objective function and constraints. Grey Wolf Optimizer (GWO)
is a recently developed metaheuristic search algorithm inspired by the leadership hierarchy and hunting
strategy of grey wolves in nature. The objective of this paper is to determine an optimal network
reconfiguration that presents the minimum power losses, considering network constraints, and using GWO
algorithm. The proposed algorithm was tested using some standard networks (33 bus, 69 bus, 84 bus and
118 bus), and the obtained results reveal the efficiency and effectiveness of the proposed approach.
Optimization of IP Networks in Various Hybrid IGP/MPLS Routing SchemesEM Legacy
This document discusses optimization of IP networks using hybrid IGP/MPLS routing schemes. It proposes a heuristic approach using genetic algorithms to optimize network performance metrics like utilization and hop count while minimizing the number of label switched paths (LSPs). The document presents models for different hybrid routing approaches, a problem formulation, and results from applying the genetic algorithm approach to a case study network.
ENHANCING COMPUTATIONAL EFFORTS WITH CONSIDERATION OF PROBABILISTIC AVAILABL...Raja Larik
This document proposes a Probabilistic Collocation Method (PCM) to improve probabilistic load flow (PLF) computation methods and model network topology uncertainties. PCM uses probability distribution functions to model the impact of uncertainties as a linear function of power injections. It maintains the linear relationship between line flows and power injections. The method is examined using the IEEE 39-bus test system and compared to Monte Carlo simulation, showing significantly reduced computational efforts while maintaining accuracy.
Internet Traffic Engineering for Partially Uncertain DemandsEM Legacy
This document summarizes an academic paper about modeling and solving the problem of routing network traffic with both fixed and uncertain demands. It considers routing strategies that use link metrics to determine shortest paths in IP networks. The proposed model represents uncertain demands using a hose model that specifies maximum aggregate traffic amounts. It calculates link loads by combining loads from fixed demands, maximum outbound uncertain demands, and maximum inbound uncertain demands. Computational results are presented for both multiple and unique shortest path routing strategies to demonstrate the benefits of considering both fixed and uncertain traffic demands.
MODIFIED LLL ALGORITHM WITH SHIFTED START COLUMN FOR COMPLEXITY REDUCTIONijwmn
Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless
communication. The complexity of the different systems models challenge different researches to get a good
complexity to performance balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovàsz (LLL)
algorithm bring more resources to investigate and can contribute to the complexity reduction purposes.
In this paper, we are looking to modify the LLL algorithm to reduce the computation operations by
exploiting the structure of the upper triangular matrix without “big” performance degradation. Basically,
the first columns of the upper triangular matrix contain many zeroes, so the algorithm will perform several
operations with very limited income. We are presenting a performance and complexity study and our
proposal show that we can gain in term of complexity while the performance results remains almost the
same.
Labeled generalized stochastic petri net Based approach for web services Comp...ijcsit
This document proposes an approach for modeling and composing web services using Labeled Generalized Stochastic Petri Nets (LGSPNs). LGSPNs are presented as an expressive way to formally model both the structure and behavior of individual web services. An algebra is then defined to compose existing web services modeled as LGSPNs in order to create new composite services. The composition operators allow incrementally building more complex services through the combination of basic services. The LGSPN modeling approach is argued to provide benefits for understanding, analyzing, and prototyping complex web service compositions.
Mitigating Interference to GPS Operation Using Variable Forgetting Factor Bas...IJCNCJournal
In this paper, an interference method based on signal processing is proposed. The approach is based on
utilizing the maximum likelihood properties of the received signal. The approach is built on maximizing the
probability of the desired data. The GPS data, which is constructed using Binary Phase Shift Keying
(BPSK) modulation, is transmitted as “1’s” and as “0’s.” carried on 1575.42MHz carrier called the L1
frequency. The statistics of the GPS data and interference are utilized in terms of their distribution and
variance. The statistics are used to update (adaptively) the forgetting factor (Lambda) of the Recursive
Least Squares (RLS) filter. The proposed method is called Maximum Likelihood Variable Forgetting Factor
(ML VFF). The adaptive update takes on assigning lambda to the maximum of the probabilities of the
symbols based on the statistics mentioned.
This document summarizes a research paper about realizing complementary Boolean functions in a power-efficient manner using static CMOS logic. The paper proposes a method that algebraically factors Reed-Muller forms to reduce gate count and power consumption. Simulation results show the proposed method achieves on average 26.79% lower power consumption compared to other factored Reed-Muller forms, with reductions of 39.66% in gate count and 12.98% in input literals. However, this approach may decrease the testability of the resulting circuits.
Routing Optimization in IP/MPLS Networks under Per-Class Over-Provisioning Co...EM Legacy
This document describes research on routing optimization in IP/MPLS networks under per-class over-provisioning constraints. It introduces a heuristic approach that iteratively optimizes IGP link metrics to indirectly solve the multi-objective problem of finding routing configurations that efficiently use network resources while satisfying per-class capacity constraints and minimizing the number of explicit label switched paths (LSPs) required. The heuristic calls a traffic engineering procedure based on simulated annealing to optimize routing for aggregate demands and individual traffic classes.
PSO-based Training, Pruning, and Ensembling of Extreme Learning Machine RBF N...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
A PROGRESSIVE MESH METHOD FOR PHYSICAL SIMULATIONS USING LATTICE BOLTZMANN ME...ijdpsjournal
In this paper, a new progressive mesh algorithm is introduced in order to perform fast physical simulations
by the use of a lattice Boltzmann method (LBM) on a single-node multi-GPU architecture. This algorithm is
able to mesh automatically the simulation domain according to the propagation of fluids. This method can
also be useful in order to perform several types of physical simulations. In this paper, we associate this
algorithm with a multiphase and multicomponent lattice Boltzmann model (MPMC–LBM) because it is
able to perform various types of simulations on complex geometries. The use of this algorithm combined
with the massive parallelism of GPUs[5] allows to obtain very good performance in comparison with the
staticmesh method used in literature. Several simulations are shown in order to evaluate the algorithm.
A low complexity partial transmit sequence approach based on hybrid segmentat...journalBEEI
The partial transmit sequences (PTS) is regarded as a promising scheme for inhibiting the high peak-to-average power ratio (PAPR) problem in the orthogonal frequency division multiplexing (OFDM) systems. The PTS scheme relies on partitioning the data sequence into subsets and weighting these subsets by a group of the phase rotation factors. Although the PTS can efficiently reduce the high PAPR value, a great computational complexity (CC) level restricts the utilization of the PTS scheme in practical applications. In PTS, there are three common types of segmentation schemes; interleaving (IL-PTS), pseudo-random (PR-PTS), and adjacent (Ad-PTS) schemes. This paper presents a new algorithm named hybrid pseudo-random and interleaving cosine wave shape (H-PRC-PTS) by combining the PR-PTS scheme and the symmetrical interleaving cosine wave shape (S-IL-C-PTS) scheme which was proposed in our previous work. The results indicate that the suggested algorithms can diminish the PAPR value like the PR-PTS scheme, whereas the CC level is reduced significantly.
ENSURING QOS GUARANTEES IN A HYBRID OCS/OBS NETWORKijngnjournal
The bursting aggregation assembly in edge nodes is one of the key technologies in OBS (Optical Burst Switching) network, which has a direct impact on flow characteristics and packet loss rate. An optical burst assembly technique supporting QoS is presented through this paper, which can automatically adjust the threshold along with the increasing and decreasing volume of business, reduce the operational burst, and generate corresponding BDP (Burst Data Packet) and BCP (Burst Control Packet). In addition to the burst aggregation technique a packet recovery technique by restoration method is also described. The data packet loss due to the physical optical link failure is not currently included in the QoS descriptions. This link failure is also a severe problem which reduces the data throughput of the transmitter node. A mechanism for data recovery from this link failure is vital for guaranteeing the QoS demanded by each user. So this paper will also discusses a specific protocol for reducing the packet loss by utilizing the
features of both optical circuit switching (OCS) and Optical Burst switching (OBS) techniques
Performance Analysis for Parallel MRA in Heterogeneous Wireless NetworksEditor IJCATR
This document analyzes methods for optimal path selection and power allocation in heterogeneous wireless networks where a user can transmit data through multiple radio access technologies (RATs) simultaneously. It formulates the bandwidth and power allocation problem as an optimization problem to maximize total system capacity. The Newton and modified Newton methods are proposed to find the optimal solution. Simulation results show the modified Newton method achieves higher total system capacity compared to the Newton method.
A Weighted Duality based Formulation of MIMO SystemsIJERA Editor
This work is based on the modeling and analysis of multiple-input multiple-output (MIMO) system in downlink communication system. We take into account a recent work on the ratio of quadratic forms to formulate the weight matrices of quadratic norm in a duality structure. This enables us to achieve exact solutions for MIMO system operating under Rayleigh fading channels. We outline couple of scenarios dependent on the structure of eigenvalues to investigate the system behavior. The results obtained are validated by means of Monte Carlo simulations.
A comparative study on synchronization algorithms for various modulation tech...IAEME Publication
This document discusses synchronization algorithms for various modulation techniques used in GSM. It begins with an introduction to GSM and modulation techniques like GMSK. It then reviews previous literature on synchronization algorithms for signals like QPSK and CPM. The document proposes a synchronization algorithm for GMSK modulation that uses a symbol-by-symbol demodulator. It evaluates the proposed algorithm by comparing bit error rate and synchronization parameter estimation against other methods. The results show the proposed algorithm achieves better performance than previous methods in terms of SNR, BER and estimation of timing, frequency and phase offsets for GSM standards.
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An Alternative Genetic Algorithm to Optimize OSPF Weights
1. An Alternative Genetic Algorithm to Optimize OSPF Weights
Eueung Mulyana, Ulrich Killat
Department of Communication Networks, Technical University Hamburg-Harburg
Denickestrasse 17, D-21073 Hamburg, Germany
phone: (+49) 40-42878-2925, fax: (+49) 40-42878-2941
email: mulyana@tu-harburg.de
Abstract
In this paper, a method based on genetic algorithm (GA),
is presented to optimize administrative weights for OSPF
routing. This method can be seen as an alternative to the
local-search method in [1] or another GA-based method
in [11]. However, the GA as well as the objective func-
tion we use are different. Instead of minimizing a con-
vex cost function we prefer to minimize the maximum
and average utilization directly. This objective function is
similar as one proposed in [7, 8]. In addition we imple-
ment a method to search weights for both single and mul-
tiple shortest paths routing and propose an enhancement
to the objective function to minimize weight changes for
an existing operational network. We will demonstrate
our method in a case of small networks and compare
the results with MIP-based (Mixed Integer Programming)
method from [7, 8, 10]. Afterwards we will show the re-
sults for a bigger network with increasing traffic demands,
compared with the results of some conventional weight
settings as well as with the lower bound of general opti-
mal routing (linear program / LP solution).
Keywords: OSPF, genetic algorithm, traffic engineering,
routing optimization
1 Introduction
Routing protocols in IP networks are usually classified
as Interior Gateway Protocols (IGP) and Exterior Gate-
way Protocols (EGP). OSPF (Open Shortest Path First) is
the most popular IGP used in today’s IP networks. OSPF
calculates routes as follows. Each link is assigned a di-
mensionless metric, called cost or weight. This cost is an
integer ranging from 1 to 65535 (= 216
− 1). The cost
of a path is the sum of link costs. Paths are selected us-
ing Dijkstra’s shortest path algorithm. Given a network
topology and predicted traffic demands, the OSPF weight
setting (OSPFWS [11]) problem is to find a set of OSPF
weights that optimizes network performance. The chosen
arc weights determine the shortest paths, which in turn de-
termine the routing of traffic flows, the loads on the arcs
and the value of the cost function.
In the case of multiple shortest paths, some vendors
have implemented OSPF with ECMP (Equal Cost Multi-
Path) so that it will use load balancing and split the traffic
flow over several shortest paths roughly evenly. The even
splitting is a nice tool for balancing the flows in order
to avoid congestion in the network, but it is considered
harmful for several reasons [2]. First, the exact details of
the splitting method depend on the individual router, and
may not be released by the vendor. Secondly, the split-
ting is typically not exactly even. The possibility of un-
even splitting makes it difficult to predict link loads even
with a given demand matrix. The question whether sin-
gle shortest path routing is better than multiple shortest
paths routing or not, is beyond the scope of this paper.
Here we simply implement both of single and multiple
shortest paths to see the results and compare them. In our
implementation we use an exact even-splitting in case of
multiple shortest paths and use the method proposed by
Thorup [2] to get a single shortest path routing.
In the following we first present a mathematical model
of the objective function and some related constraints for
the general routing problem. In Section 3, OSPF routing
mechanism will be shortly discussed. After that (in Sec-
tion 4) we will refer to a MIP-based (Mixed Integer Pro-
gramming) approach as published in [7, 8, 10]. In Sec-
tion 5 we present an enhancement of the objective func-
tion to minimize weight changes in a dynamic scenario.
In Section 6 we explain the genetic algorithm (GA) we
used to solve the problem. Finally, the results of some
test-networks will be presented.
2 General Routing Problem
In the general routing problem, there are no limitations
on how flows can be distributed along the paths from
source to destination, and the problem can be formulated
and solved in polynomial time as a multi commodity flow
problem [1, 11]. A directed network G(V, E) is given,
where V is the set of vertices (nodes) representing the
network’s routers and E is the set of edges (arcs) repre-
senting the network’s links. Each link (i, j) ∈ E has a ca-
pacity cij . Furthermore, we have a demand fuv for each
pair (u, v) ∈ V ×V , giving the demand to be carried from
2. source u to destination v. A real variable luv
ij is associated
with the load on link (i, j) resulting from flow demand
fuv. Thus, the general routing problem optimization can
be formulated as follows:
min {(at · t) +
1
|E| ij uv
luv
ij
cij
}
∀(i, j) ∈ E, ∀(u, v) ∈ V × V (1)
δunfuv +
m∈V
luv
mn = δnvfuv +
m∈V
luv
nm
∀(u, v) ∈ V × V, ∀n, m ∈ V (2)
uv
luv
ij
cij
≤ t ∀(i, j) ∈ E (3)
luv
ij ≥ 0 ∀(i, j) ∈ E, ∀(u, v) ∈ V × V (4)
Equation 1 is the objective function to minimize uti-
lization t on the most utilized link (Eq. 3) and average
utilization. A constant at is used to trade between these
two components. Eq. 2 describes flow conservation con-
straints that ensure the desired traffic flow to be routed
from source to destination.
3 OSPF Weight Setting (OSPFWS)
Problem
As mentioned in section 1, in OSPF routing we choose a
weight wk for each arc. The routing of the demands is
determined by the shortest paths computed by Dijkstra’s
algorithm, which is in turn determined by the weights
we assign to the arcs. Thus for each source destina-
tion pair (u, v) and link (i, j), the variable luv
ij = 0 if
link (i, j) is not on a shortest path from u to v and be-
cause of even-splitting luv
im = luv
in if both (i, m) and (i, n)
are on shortest paths from u to v. For a given demand
fuv, ∀(u, v) ∈ V × V and a given set of weights we
can compute the load distribution in the network. Note
that this load distribution is not dependent on link capac-
ities i.e. some weight configurations may cause a con-
gestion as the total traffic to be routed on a certain link
may exceed its capacity. In this case for the link uti-
lization uv
luv
ij
cij
> 1 holds. We apply no constraints
to force a solution to have a utilization below 1, but sim-
ply minimize a certain cost function, which in our case is
equation (1). The desired result then is a set of weights
which corresponds to the minimized cost function. An-
other technique to get this result is based on Mixed Inte-
ger Programming (MIP). Fortz and Thorup [1] used a lo-
cal search heuristic and a convex cost function as a func-
tion of link utilizations in the network, which was derived
from their experimental study.
4 MIP-based Optimization
Mixed Integer Programming (MIP) as a method to op-
timize routing within a specific network is already well
known [7, 8, 13, 14, 15]. In [7, 8, 13, 14] two formula-
tions are needed. The first formulation is to optimize the
maximum and average utilization and the second formu-
lation is to compute the link weights. The approach in
[7, 8] uses no load balancing so that the result obtained
by this method is always a single path routing pattern.
So far, the usage of MIP on routing optimization is re-
stricted to small or at most medium-sized networks, de-
pending on the associated link structure. An exact solu-
tion will not always be possible in reasonable computa-
tional time because some problems are NP-hard [15] and
as the network grows the resulting integer program is too
complex to be solved. In such cases heuristics have to
be deployed. A heuristic is more flexible in terms of op-
timization criterion (constraints) and scalability problem.
Recent work such as [9] tries to utilize MIP on large net-
works by using a decomposition method and optimize the
parts of the network independently. Such an approach can
be seen as a form of heuristic as well. We will dispense
with a detailed explanation of MIP-based method and use
only the results from [7, 10] to verify our method.
5 Minimizing Weight Changes
Weight changes should be avoided as much as possible
[2] for an operational network. The weight change has
to be flooded in the network. As the routers learn about
the change, they recompute their shortest paths to update
their routing tables, and it may take seconds before all
routers agree on the new shortest paths. The more weight
changes we try to flood simultaneously, the more chaos
we introduce in the network with packets being sent back
and forth between routers.
Thus a modification of administrative metric values
used by OSPF or generally IGP is not desirable too often
and should be confined to a medium or long term basis
[15]. Also, if we want to modify the metric values to op-
timize network performance, it is worth to change only
an amount as small as possible. In the following we in-
troduce a different version of the objective function in Eq.
(1) in order to minimize the changes to be performed.
(at · t) + (
1
|E|
·
ij uv
luv
ij
cij
) + (
ay
|E|
·
k∈E
yk) (5)
yk =
1 if wk = wr
k
0 else
(6)
The last term in Eq. (5) measures similarities
between current weights’ configuration as reference
wr
1, wr
2, · · · , wr
k, · · · , wr
|E| and a new configuration to
3. be evaluated w1, w2, · · · , wk, · · · , w|E| . The constants
at and ay can be used to trade between the different com-
ponents in Eq. (5). Note that k is a vectorized version of
matrix index ij where i = j and cij = 0.
6 An Alternative GA for OSPFWS
Problem
As mentioned earlier, in [11] a GA for optimizing OSPF
weights is proposed. However the GA that we propose
in this paper is different. It is based on earlier work by
Beckmann [3, 4, 5] with several modifications to adapt to
the problem.
Exit Condition Selection
Add new
population
Mutation
Selection
population
Start
yes
no
Reproduction
Figure 1: A GA proposed
Figure 1 shows a block diagram from our GA imple-
mentation. We begin with a randomly generated initial
population of 50 chromosomes. In contrast to [11] we
make no partitions and all chromosomes belong to the
population. After this, the population goes to the evo-
lution loop. The exit condition is ideal if the best fitness
found matches the global optimum of the fitness value.
As for most cases we do not know this global optimum,
the program will terminate based on a predefined number
of iterations (exit condition). At the beginning of each
iteration some vectors of high quality are selected to pro-
duce new, hopefully better solutions. After this selection
process there follow two genetic mechanisms ”reproduc-
tion” and ”mutation” to form some new chromosomes.
Afterwards we construct the next population by substitut-
ing the least successful chromosomes of the previous it-
eration by the new ones. In the following we will discuss
the method in more detail.
6.1 Encoding
In order to apply a genetic algorithm, generally a suit-
able encoding of possible solutions in a vector (i.e.
chromosome) representation is needed. In our case a
chromosome is represented by a set of link weights
w1, w2, · · · , wk, · · · , w|E| where wk ∈ [1, MAX] for
each edge k = 1, ..., |E| and the maximum value for
MAX is 65535. Each chromosome has a fitness value
according to Eq. (1) and corresponds to a certain link
utilization resulting from a load distribution computed by
Dijkstra’s shortest path algorithm.
6.2 Selection
All chromosomes will be selected according to their fit-
ness. In our case we want a fitness value as small as pos-
sible. There are two selection mechanisms i.e. to select
parent chromosomes for a new generation and to remove
some of bad chromosomes from the current population.
For the first task we implement so called ”rank selection”
to make the probability to be selected a little bit more bal-
anced for all chromosomes in the population. We first
rank the population and then every chromosome receives
a probability value from this ranking. The probability
value is measured relative to the probability value of the
last (worst) chromosome i.e. the last but one will have
twice that probability etc. For the second task we simply
sort the chromosomes according to their fitness from good
to bad and then remove some of the last chromosomes.
6.3 Reproduction
The reproduction strategy used is similar to the one used
in [11], however with different parameters. We have a
good convergence for const1 = 0.03 and const2 = 0.53.
With an assumption that the random numbers generated
are uniformly distributed in the interval [0, 1], these pa-
rameters mean that the chance for gen’s mutation is 3%
and the chance for gen’s inheritation from the two parent
chromosomes is 50% and 47%. In the following is the
pseudocode for this strategy.
for all genes k ∈ [1, |E|]
generate r = random [0,1]
if r < const1 then
wO1
k , wO2
k = random [1,MAX]
else if r < const2 then
wO1
k = wP 1
k , wO2
k = wP 2
k
else
wO1
k = wP 2
k , wO2
k = wP 1
k
end if
end for
This process combines both crossover and mutation di-
rectly. For all genes we generate a random real number in
the interval [0, 1]. If this number is less than const1, the
offsprings’ genes wO1
k and wO2
k will be mutated by choos-
ing a random integer number in the interval [1, MAX]. If
the number is between const1 and const2, wO1
k will be
inherited from the gene wP 1
k of parent 1 and wO2
k from
the gene wP 2
k of parent 2. If the number is more than
const2, wO1
k will be inherited from wP 2
k and wO2
k from
wP 1
k . From this reproduction process we obtain two new
chromosomes O1 and O2 (Figure 2).
4. P1 P2
O1 O2
Reproduction
O3O4
MutationMutation
(a) Forming a new generation
¡ ¡ ¡ ¡
¢¡¢¢¡¢¢¡¢¢¡¢
£¡££¡££¡££¡£
¤¡¤¤¡¤¤¡¤¤¡¤
Population
50 Chromosomes
Population
45 Chromosomes
Reproduction
Mutation
8 Chromosomes
Selection (parents)
Selection
(remove 10%)
Population
61 Chromosomes
Offsprings
16 Chromosomes
(best 50 chromosomes)
Selection
(b) Population dynamics
Figure 2: Forming a new generation and population dy-
namics
6.4 Additional Mutation
In addition to the reproduction process one type of mu-
tation is additionally implemented. We apply a heuristic
to mutate some genes from offsprings 1 and 2 that do not
satisfy a particular condition. We simply add (substract)
a random number to the weight wk if the link utilization
from an arc k is bigger (lower) than a particular treshold
because we know that the bigger the weight, the lower
the chance that traffic will get routed on that link and vice
versa. With this type of mutation we hope, that the off-
springs O3 and O4 have a better link utilization at k, and
hopefully also a better maximum and average utilization.
This can be seen as a ”targeted” mutation proposed for
other problems in [3]. The process to form a new genera-
tion and the population dynamics are depicted in Figure 2.
c2
c3c1
c4
av0 s1 s2 s3 s4 Link Utilization
Figure 3: A mutation heuristic
Figure 3 shows an example of this heuristic in more
detail. If the current link utilization is larger than s4, we
increase the link cost for that arc by a factor c4. If the cur-
rent link utilization is lower than s1, we decrease the link
cost for that arc by a factor c1 etc. The constants ci are
actually implemented as upper bounds for these weight
changes i.e. the actual constants are thus randomly gen-
erated with these ci as upper bounds. Therefore we do not
”disturb” the randomness of the GA.
7 Results
Weight settings and link utilization. First we tested
our method with two small networks from [7, 8] con-
sisting of only 6 and 10 routers, respectively, in order to
compare our results to those from MIP optimization. We
present here only the results and for the capacities and
traffic matrices we refer to the above mentioned papers.
Figure 4: Simulation result of 6 routers network
For the 6 routers network the MAX value was set to
6 and we got the optimum value of maximum utilization
of 35.7% and average utilization of 22.7% about 95 times
from 100 independent program runs and for each run we
used 100 iterations (Figure 4). For the 10 routers network
the MAX value was set to 30 and we got the optimum
value of maximum utilization of 96.7% and average uti-
lization of 82.9% about 32 times from 100 times indepen-
dent program runs and for each run we used 300 iterations
(Figure 5). The chance to find the global optimum can be
increased by increasing the number of iterations executed
5. in the GA.
Figure 5: Simulation result of 10 routers network
To give a fair comparison with [7, 8] which used no
load balancing: the ”penalty factor” of Thorup’s method
[12] was set quite high, so that the resulting weight set-
tings yield a single shortest path routing.
Minimizing changes. Figure 6 shows the results with
the modified cost function (Eq. 5). The figures at the
top show the ”current” network, in terms of the weight
configurations (left) based on inverse capacities and the
resulting link utilization (right). With this configuration
we have an average utilization of 22.4% and a maximum
utilization of 42.9%. The figures at the bottom show the
optimized network configuration, with an average utiliza-
tion of 22.7% and a maximum utilization of 35.7%; this is
identical to the results found in connection with Figure 5.
But in this case we only need to change 4 link costs (or
28.6% of all) namely (2, 1), (3, 4), (4, 5) and (5, 6). By
contrast, the solution depicted in Figure 5 was obtained
without any considerations to the ”current” weight set-
tings.
Convergence. In the following figures we will demon-
strate the convergence characteristic of the proposed GA.
Figure 7 shows the convergence of average fitness in the
population. Figure 8 shows the fitness convergence of
best chromosome found in the population. The network
used for this simulation is the AT&T network adopted
from [16] and consisting of 29 nodes and 100 directed
arcs with randomly generated traffic demand. Curves
(1) result from 10 independent program runs, using only
the reproduction strategy mentioned in Section 6.3 and
curves (2) are from a GA using both reproduction and ad-
ditional mutations described in Section 6.4. The average
fitness from additionally mutated population converges
faster than the other one. And of course if the average
fitness in a population is better, then the chance that we
have a better solution is also bigger. But adding additional
Figure 6: Result of minimizing changes
new chromosomes means an increase in computation time
for determining the fitness. Thus we must trade speed for
quality. In our case the additional mutation results in a
doubling of the run time for one iteration.
10
0
10
1
10
2
0
5
10
15
20
25
Evolution Loop
Fitness
LP lower bound
population average fitness (1)
population average fitness (2)
Figure 7: Average population fitness
Increasing traffic. Finally we present the results of our
method for the case of increasing traffic demands. In
Figure 9 and Figure 10 we compare maximum utiliza-
tion based on some common metrics to our results and
to a lower bound resulting from a linear programming
result for the general routing problem. In Figure 9 we
used Eq. 1 as objective function. In Figure 10 we used
the modified objective function (Eq. 5). For compar-
ison we considered hop count metric (denoted by Uni-
tOSPF) and inverse capacities metric (denoted by InvCa-
pOSPF). GA1OSPF denotes the result of our method with
load balancing and GA2OSPF denotes one without load
balancing (single shortest path routing). For both types
of calculations, the value of MAX was set to 99. Fig-
6. 10
0
10
1
10
2
0
1
2
3
4
5
6
7
8
Evolution Loop
Fitness
LP lower bound
best chromosome fitness (1)
best chromosome fitness (2)
Figure 8: Best chromosome fitness
ure 9 shows that in comparison with InvCapOSPF and
UnitOSPF, we can increase the network capacity by fac-
tors of at least 35% and 450% respectively, before the
network becomes congested. In order to use Eq. 5 a
reference set of weights is needed. Here we used ran-
domly generated weights representing a solution a little
bit better than one resulting from hop count metric. Nev-
ertheless we can find solutions that outperform than the
performance of InvCapOSPF and UnitOSPF by factors
of at least 20% and 400%, respectively. The numbers in
percent on the figures show the relative changes to be per-
formed from reference weight settings i.e. the last term of
Eq. (5). Note that the term ”maximum utilization” used
here is the theoretical link utilization as discussed in Sec-
tion 3.
0.5 1 1.5 2 2.5 3 3.5
x 10
4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Traffic Volume
MaxUtilization
UnitOSPF
InvCapOSPF
GA1OSPF
GA2OSPF
LP lower bound
Figure 9: Increasing traffic (AT&T model network con-
sisting of 29 nodes and 100 arcs with Eq. (1) as objective
function)
0.5 1 1.5 2 2.5 3 3.5
x 10
4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Traffic Volume
MaxUtilization
5%
34% 17%
12% 19%
59%
30%
59%
31%
29% 45%
29%
37%
59%
41%
13%
39%
39%
53%
86%
UnitOSPF
InvCapOSPF
GA1OSPF
GA2OSPF
LP lower bound
Reference Setting
Figure 10: Increasing traffic and minimizing changes
(AT&T model network consisting of 29 nodes and 100
arcs with Eq. (5) as objective function)
8 Conclusions
We have considered the problem of OSPF or generally
IGP link costs setting with an alternative genetic algo-
rithm, using the objective function from [7, 8] and en-
hancing it in order to minimize changes to be made for
an operational network. We proposed in addition a mu-
tation heuristic to improve solution quality and to speed
up convergence. The program is written in C++ with STL
(Standard Template Library) and all calculations are done
on an unloaded PC (800 MHz) running Linux operating
system. A single run for the AT&T model network con-
sisting of 29 nodes and 100 arcs needs about 10 minutes
for 300 iterations. The application of our method to big-
ger networks as reported on in [1, 11] is subject of our
future research.
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