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Locating network monitors: Complexity, heuristics and coverage
 in Proceedings of IEEE Infocom
, 2005
"... Abstract — There is increasing interest in concurrent passive monitoring of IP flows at multiple locations within an IP network. The common objective of such a distributed monitoring system is to sample packets belonging to a large fraction of IP flows in a costeffective manner by carefully placing ..."
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Cited by 41 (0 self)
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Abstract — There is increasing interest in concurrent passive monitoring of IP flows at multiple locations within an IP network. The common objective of such a distributed monitoring system is to sample packets belonging to a large fraction of IP flows in a costeffective manner by carefully placing monitors and controlling their sampling rates. In this paper, we consider the problem of where to place monitors within the network and how to control their sampling. To address the tradeoff between monitoring cost and monitoring coverage, we consider minimum cost and maximum coverage problems under various budget constraints. We show that all of the defined problems are NPhard. We propose greedy heuristics, and show that the heuristics provide solutions quite close to the optimal solutions through experiments using synthetic and real network topologies. In addition, our experiments show that a small number of monitors is often enough to monitor most of the traffic in an entire IP network. I.
Reformulation and Convex Relaxation Techniques for Global Optimization
 4OR
, 2004
"... Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested i ..."
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Cited by 9 (7 self)
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Many engineering optimization problems can be formulated as nonconvex nonlinear programming problems (NLPs) involving a nonlinear objective function subject to nonlinear constraints. Such problems may exhibit more than one locally optimal point. However, one is often solely or primarily interested in determining the globally optimal point. This thesis is concerned with techniques for establishing such global optima using spatial BranchandBound (sBB) algorithms.
Decomposition of mixedinteger optimal control problems using branch and bound and sparse direct collocation
 IN PROCEEDINGS OF ADPM 2000 – AUTOMATION OF MIXED PROCESSES: HYBRID DYNAMIC SYSTEMS
, 2000
"... A large class of optimal control problems for hybrid dynamic systems can be formulated as mixedinteger optimal control problems (MIOCPs). It is the intrinsic combinatorial complexity, in addition to the nonlinearity of the continuous, multiphase optimal control problems that is largely responsible ..."
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Cited by 8 (3 self)
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A large class of optimal control problems for hybrid dynamic systems can be formulated as mixedinteger optimal control problems (MIOCPs). It is the intrinsic combinatorial complexity, in addition to the nonlinearity of the continuous, multiphase optimal control problems that is largely responsible for the challenges in the theoretical and numerical solution of MIOCPs. We present a new decomposition approach to numerically solving fairly general MICOPs with binary control variables. A Branch and Bound (B&B) technique is applied to efficiently search the entire discrete solution space performing a truncated binary tree search for the discrete variables maintaining upper and lower bounds on the performance index. The partially relaxed binary variables at an inner node define an optimal control problem with dynamic equations defined in multiple phases. Its global solution provides a lower bound on the performance index for all nodes of the subtree. If the lower bound for a given subtree is greater than the current global upper bound then that entire subtree need no longer be searched. The many optimal control problems with nonlinear, continuous state dynamics defined in multiple phases subject to nonlinear constraints are solved most efficiently by a sparse direct collocation transcription. Hereby, the multiphase optimal control problem is transcribed to a sparse, largescale nonlinear programming problem being solved efficiently by a tailored SQP method. Despite the high efficiency of the sparse direct collocation method, the efficiency of the decomposition technique for MIOCPs strongly depends on
Nonlinear hybrid dynamical systems: modeling, optimal control, and applications
 in Modelling, Analysis and Design of Hybrid Systems, ser. Lecture Notes in Control and Information
, 2002
"... Abstract. Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are ..."
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Cited by 8 (7 self)
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Abstract. Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are presented. Hybrid dynamical systems are characterized by discrete event and continuous dynamics which have an interconnected structure and can thus represent an extremely wide range of systems of practical interest. Consequently, many modeling and control methods have surfaced for these problems. This work is particularly focused on systems for which the degree of discrete/continuous interconnection is comparatively strong and the continuous portion of the dynamics may be highly nonlinear and of high dimension. The hybrid optimal control problem is defined and two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation for continuous dynamic optimization): one fixes interior point constraints on a grid, another uses branchandbound. These are applied to a robotic multiarm transport task, an underactuated robot arm, and a benchmark motorized traveling salesman problem. 1
Towards Hybrid Optimal Control
, 2000
"... In this article a general class of hybrid optimal control problems with continuous and discrete state variables and control inputs is defined. After a brief review of conventional optimal control, major novel challenges resulting from the hybrid nature are discussed. Some application problems are co ..."
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Cited by 4 (3 self)
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In this article a general class of hybrid optimal control problems with continuous and discrete state variables and control inputs is defined. After a brief review of conventional optimal control, major novel challenges resulting from the hybrid nature are discussed. Some application problems are comparatively easy to solve because of the fixed or known sequence of discrete events; however, if the number and the sequence of discrete phases is not known a priori, the solution must then be found among a combinatorial number of possible sequence candidates. The article presents several preliminary approaches to the (numerical) solution of hybrid optimal control problems by hybrid dynamic programming, by decomposition using branchandbound, or fixing transversality conditions to obtain suboptimal solutions. The last two methods rely on the capabilities of the direct collocation method DIRCOL to solving multiphase optimal control problems robustly and efficiently. Results obtained by the proposed methods are presented in two examples: an underactuated robotic system with a holding brake as the discrete component, and a hybrid, motorized traveling salesman problem.
SOME MINLP SOLUTION ALGORITHMS
"... Abstract. This document describes several methods to solve MixedInteger Nonlinear Programming (MINLP) problems within a GAMS environment. We demonstrate Generalized Benders Decomposition (GDB), Outer Approximation (OA) and Branchandbound (BB) using algorithms compactly implemented in the GAMS lan ..."
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Cited by 1 (0 self)
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Abstract. This document describes several methods to solve MixedInteger Nonlinear Programming (MINLP) problems within a GAMS environment. We demonstrate Generalized Benders Decomposition (GDB), Outer Approximation (OA) and Branchandbound (BB) using algorithms compactly implemented in the GAMS language.