12 research outputs found
A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique
This paper continues our effort initiated in [9] to study Multicast
Communication Networks, modeled as bilevel hierarchical clustering problems, by
using mathematical optimization techniques. Given a finite number of nodes, we
consider two different models of multicast networks by identifying a certain
number of nodes as cluster centers, and at the same time, locating a particular
node that serves as a total center so as to minimize the total transportation
cost through the network. The fact that the cluster centers and the total
center have to be among the given nodes makes this problem a discrete
optimization problem. Our approach is to reformulate the discrete problem as a
continuous one and to apply Nesterov smoothing approximation technique on the
Minkowski gauges that are used as distance measures. This approach enables us
to propose two implementable DCA-based algorithms for solving the problems.
Numerical results and practical applications are provided to illustrate our
approach
Local Search Heuristics For The Multidimensional Assignment Problem
The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case
of s dimensions) is an extension of the well-known assignment problem. The most
studied case of MAP is 3-AP, though the problems with larger values of s also
have a large number of applications. We consider several known neighborhoods,
generalize them and propose some new ones. The heuristics are evaluated both
theoretically and experimentally and dominating algorithms are selected. We
also demonstrate a combination of two neighborhoods may yield a heuristics
which is superior to both of its components.Comment: 30 pages. A preliminary version is published in volume 5420 of
Lecture Notes Comp. Sci., pages 100-115, 200
A DC Programming Approach for Solving Multicast Network Design Problems via the Nesterov Smoothing Technique
This paper continues our effort initiated in [19] to study Multicast Communication Networks, modeled as bilevel hierarchical clustering problems, by using mathematical optimization techniques. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost through the network. The fact that the cluster centers and the total center have to be among the given nodes makes this problem a discrete optimization problem. Our approach is to reformulate the discrete problem as a continuous one and to apply Nesterov smoothing approximation technique on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach
A Dc Programming Approach For Solving Multicast Network Design Problems Via The Nesterov Smoothing Technique
This paper continues our recent effort in applying continuous optimization techniques to study optimal multicast communication networks modeled as bilevel hierarchical clustering problems. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost throughout the network. The fact that the cluster centers and the total center have to be among the given nodes makes these problems discrete optimization problems. Our approach is to reformulate the discrete problems as continuous ones and to apply Nesterov’s smoothing approximation techniques on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach
Asymptotic Synchronization of a Leader-Follower Network of Uncertain Euler-Lagrange Systems
Abstract-This paper investigates the synchronization of a network of Euler-Lagrange systems with leader tracking. The EulerLagrange systems are heterogeneous and uncertain and contain bounded, exogenous disturbances. The network leader has a timevarying trajectory which is known to only a subset of the follower agents. A robust integral sign of the error-based decentralized control law is developed to yield semiglobal asymptotic agent synchronization and leader tracking