Abstract We develop a stochastic programming approach to solving an intra-ring Synchronous Optica... more Abstract We develop a stochastic programming approach to solving an intra-ring Synchronous Optical Network (SONET) design problem. This research diers,from pioneering SONET design studies in two fundamental ways. First, while traditional approaches to solving this problem assume that all data are deterministic, we observe that for practical planning situations, network demand levels are stochastic. Second, while most models disallow demand,shortages and focus only on the minimization of capital Add-Drop Multiplexer (ADM) equipment expenditure, our model minimizes a mix of ADM installations and expected penalties arising from the failure to satisfy some or all of the actual telecommunication demand. We propose an L-shaped algorithm to solve this design problem, and demonstrate how a nonlinear reformulation of the problem may improve the strength of the generated optimality cuts. We next enhance the ba- sic algorithm by implementing powerful lower and upper bounding techniques via an assortment of modeling, valid inequality, and heuristic strategies. Our computational results conclusively demonstrate the ecacy,of our proposed algorithm as opposed to standard L-shaped and extensive form approaches to solving the problem.
We consider an interdiction problem that involves an operator (or defender) whose goal is to maxi... more We consider an interdiction problem that involves an operator (or defender) whose goal is to maximize flow from a source node to a sink node in some network that resides in Euclidean space. The problem we examine takes the perspective of an interdictor, who seeks to minimize the defender's maximum flow by locating a set of attacks that diminish arc capacities in accordance with the distance from the arc to the attack. Attacks are not restricted to node or arc locations, and can occur anywhere on the region in which the network is located. We refer to this problem as the Euclidean maximum flow network interdiction problem (E-MFNIP). We show that E-MFNIP is NP-hard, as it generalizes the maximum flow interdiction problem studied by Wood [47]. This article contributes two approaches to solving E-MFNIP based on solving a sequence of lower-bounding integer programs from which upper bounds can be readily obtained, and shows that these bounds are convergent. Computations on a set of te...
ABSTRACT In this paper, we introduce a new class of algorithms for solving the mixed-integer bile... more ABSTRACT In this paper, we introduce a new class of algorithms for solving the mixed-integer bilevel min-max optimization problem. This problem involves two players, a leader and a follower, who play a Stackelberg game. In particular, the leader seeks to minimize over a set of discrete variables the maximum objective that the follower can achieve. The complicating features of our problem are that a subset of the follower’s decisions are restricted to be integer-valued, and that the follower’s decisions are constrained by the leader’s decisions. We first describe several bilevel min-max programs that can be used to obtain lower and upper bounds on the optimal objective value of the problem. We then present algorithms for this problem that finitely terminate with an optimal solution when the leader variables are restricted to take binary values. Finally, we report the results of a computational study aimed at evaluating the quality of our algorithms on two families of randomly generated problems.
... 1 Department of Industrial and Systems Engineering, The University of Florida, Gainesville, F... more ... 1 Department of Industrial and Systems Engineering, The University of Florida, Gainesville, Florida, USA cole@ise.ufl.edu 2 Systems Engineering ... The interdiction problem is thus to deploy a (limited) set of sensors such that the smugger's maximum-reliability path is minimized. ...
ABSTRACT We consider a version of the stochastic network interdiction problem modeled by Morton e... more ABSTRACT We consider a version of the stochastic network interdiction problem modeled by Morton et al. (IIE Trans 39:3–14, 2007) in which an interdictor attempts to minimize a potential smuggler’s chance of evasion via discrete deployment of sensors on arcs in a bipartite network. The smuggler reacts to sensor deployments by solving a maximum-reliability path problem on the resulting network. In this paper, we develop the (minimal) convex hull representation for the polytope linking the interdictor’s decision variables with the smuggler’s for the case in which the smuggler’s origin and destination are known and interdictions are cardinality-constrained. In the process, we propose an exponential class of easily-separable inequalities that generalize all of those developed so far for the bipartite version of this problem. We show how these cuts may be employed in a cutting-plane fashion when solving the more difficult problem in which the smuggler’s origin and destination are stochastic, and argue that some instances of the stochastic model have facets corresponding to the solution of NP-hard problems. Our computational results show that the cutting planes developed in this paper may strengthen the linear programming relaxation of the stochastic model by as much as 25 %.
The objective of this study was to quantify the network complexity, information flow, and effect ... more The objective of this study was to quantify the network complexity, information flow, and effect of critical-node failures on a prototypical regional anesthesia and perioperative pain medicine (RAPPM) service using social network analysis. Pilot cross-sectional investigation. This study was conducted at a prototypical single-center, multi-location academic anesthesiology department with an active RAPPM service. We constructed an empirically derived prototypical social network representative of a large academic RAPPM service. The primary objective was measurement of network complexity via network size, structure, and information flow metrics. The secondary objective identified, via network simulation, those nodes whose deletion via single, two-level, or three-level node failures would result in the greatest network fragmentation. Exploratory analyses measured the impact of nodal failures on the resulting network complexity. The baseline network consisted of 84 nodes and 208 edges with a low density of 0.03 and high Krackhardt hierarchy of 0.787. Nodes exhibited low average total degree centrality (mean ± standard deviation [SD]) of 0.03 ± 0.034 and mean eigenvector centrality of 0.164 ± 0.182. The RAPPM resident-on-call was identified as the critical node in a single-node failure, with the resulting network fragmentation increasing from 0 to 0.52 upon node failure. A two-level failure involved both the RAPPM resident-on-call as well as the RAPPM attending-on-call, with the resulting fragmentation expanding to 0.772. A three-level node failure included the RAPPM resident-on-call, the main block-room attending, and block room fellow with fragmentation increasing to 0.814. The RAPPM service entails considerable network complexity and increased hierarchy, but low centrality. The network is at considerable fragmentation risk from even single-node failure.
We present a heuristic technique for solving a parameter estimation problem that arises in modeli... more We present a heuristic technique for solving a parameter estimation problem that arises in modeling the thermal behavior of electronic chip packages. Compact Thermal Models (CTMs) are network models of steady state thermal behavior, which show promise in augmenting the use of more detailed and computationally expensive models. The CTM parameter optimization problem that we examine is a nonconvex optimization problem in which we seek a set of CTM parameters that best predicts, under general conditions, the thermal response of a particular chip package geometry that has been tested under a small number of conditions. We begin by developing a nonlinear programming formulation for this parameter optimization problem, and then develop an algorithm that uses special characteristics of the optimization problem to quickly generate heuristic solutions. Our algorithm descends along a series of solutions to one-dimensional nonconvex optimization problems, obtaining a locally optimal set of model parameters at modest computational cost. Finally, we provide some experimental results and recommendations for extending this research.
Abstract We develop a stochastic programming approach to solving an intra-ring Synchronous Optica... more Abstract We develop a stochastic programming approach to solving an intra-ring Synchronous Optical Network (SONET) design problem. This research diers,from pioneering SONET design studies in two fundamental ways. First, while traditional approaches to solving this problem assume that all data are deterministic, we observe that for practical planning situations, network demand levels are stochastic. Second, while most models disallow demand,shortages and focus only on the minimization of capital Add-Drop Multiplexer (ADM) equipment expenditure, our model minimizes a mix of ADM installations and expected penalties arising from the failure to satisfy some or all of the actual telecommunication demand. We propose an L-shaped algorithm to solve this design problem, and demonstrate how a nonlinear reformulation of the problem may improve the strength of the generated optimality cuts. We next enhance the ba- sic algorithm by implementing powerful lower and upper bounding techniques via an assortment of modeling, valid inequality, and heuristic strategies. Our computational results conclusively demonstrate the ecacy,of our proposed algorithm as opposed to standard L-shaped and extensive form approaches to solving the problem.
We consider an interdiction problem that involves an operator (or defender) whose goal is to maxi... more We consider an interdiction problem that involves an operator (or defender) whose goal is to maximize flow from a source node to a sink node in some network that resides in Euclidean space. The problem we examine takes the perspective of an interdictor, who seeks to minimize the defender's maximum flow by locating a set of attacks that diminish arc capacities in accordance with the distance from the arc to the attack. Attacks are not restricted to node or arc locations, and can occur anywhere on the region in which the network is located. We refer to this problem as the Euclidean maximum flow network interdiction problem (E-MFNIP). We show that E-MFNIP is NP-hard, as it generalizes the maximum flow interdiction problem studied by Wood [47]. This article contributes two approaches to solving E-MFNIP based on solving a sequence of lower-bounding integer programs from which upper bounds can be readily obtained, and shows that these bounds are convergent. Computations on a set of te...
ABSTRACT In this paper, we introduce a new class of algorithms for solving the mixed-integer bile... more ABSTRACT In this paper, we introduce a new class of algorithms for solving the mixed-integer bilevel min-max optimization problem. This problem involves two players, a leader and a follower, who play a Stackelberg game. In particular, the leader seeks to minimize over a set of discrete variables the maximum objective that the follower can achieve. The complicating features of our problem are that a subset of the follower’s decisions are restricted to be integer-valued, and that the follower’s decisions are constrained by the leader’s decisions. We first describe several bilevel min-max programs that can be used to obtain lower and upper bounds on the optimal objective value of the problem. We then present algorithms for this problem that finitely terminate with an optimal solution when the leader variables are restricted to take binary values. Finally, we report the results of a computational study aimed at evaluating the quality of our algorithms on two families of randomly generated problems.
... 1 Department of Industrial and Systems Engineering, The University of Florida, Gainesville, F... more ... 1 Department of Industrial and Systems Engineering, The University of Florida, Gainesville, Florida, USA cole@ise.ufl.edu 2 Systems Engineering ... The interdiction problem is thus to deploy a (limited) set of sensors such that the smugger's maximum-reliability path is minimized. ...
ABSTRACT We consider a version of the stochastic network interdiction problem modeled by Morton e... more ABSTRACT We consider a version of the stochastic network interdiction problem modeled by Morton et al. (IIE Trans 39:3–14, 2007) in which an interdictor attempts to minimize a potential smuggler’s chance of evasion via discrete deployment of sensors on arcs in a bipartite network. The smuggler reacts to sensor deployments by solving a maximum-reliability path problem on the resulting network. In this paper, we develop the (minimal) convex hull representation for the polytope linking the interdictor’s decision variables with the smuggler’s for the case in which the smuggler’s origin and destination are known and interdictions are cardinality-constrained. In the process, we propose an exponential class of easily-separable inequalities that generalize all of those developed so far for the bipartite version of this problem. We show how these cuts may be employed in a cutting-plane fashion when solving the more difficult problem in which the smuggler’s origin and destination are stochastic, and argue that some instances of the stochastic model have facets corresponding to the solution of NP-hard problems. Our computational results show that the cutting planes developed in this paper may strengthen the linear programming relaxation of the stochastic model by as much as 25 %.
The objective of this study was to quantify the network complexity, information flow, and effect ... more The objective of this study was to quantify the network complexity, information flow, and effect of critical-node failures on a prototypical regional anesthesia and perioperative pain medicine (RAPPM) service using social network analysis. Pilot cross-sectional investigation. This study was conducted at a prototypical single-center, multi-location academic anesthesiology department with an active RAPPM service. We constructed an empirically derived prototypical social network representative of a large academic RAPPM service. The primary objective was measurement of network complexity via network size, structure, and information flow metrics. The secondary objective identified, via network simulation, those nodes whose deletion via single, two-level, or three-level node failures would result in the greatest network fragmentation. Exploratory analyses measured the impact of nodal failures on the resulting network complexity. The baseline network consisted of 84 nodes and 208 edges with a low density of 0.03 and high Krackhardt hierarchy of 0.787. Nodes exhibited low average total degree centrality (mean ± standard deviation [SD]) of 0.03 ± 0.034 and mean eigenvector centrality of 0.164 ± 0.182. The RAPPM resident-on-call was identified as the critical node in a single-node failure, with the resulting network fragmentation increasing from 0 to 0.52 upon node failure. A two-level failure involved both the RAPPM resident-on-call as well as the RAPPM attending-on-call, with the resulting fragmentation expanding to 0.772. A three-level node failure included the RAPPM resident-on-call, the main block-room attending, and block room fellow with fragmentation increasing to 0.814. The RAPPM service entails considerable network complexity and increased hierarchy, but low centrality. The network is at considerable fragmentation risk from even single-node failure.
We present a heuristic technique for solving a parameter estimation problem that arises in modeli... more We present a heuristic technique for solving a parameter estimation problem that arises in modeling the thermal behavior of electronic chip packages. Compact Thermal Models (CTMs) are network models of steady state thermal behavior, which show promise in augmenting the use of more detailed and computationally expensive models. The CTM parameter optimization problem that we examine is a nonconvex optimization problem in which we seek a set of CTM parameters that best predicts, under general conditions, the thermal response of a particular chip package geometry that has been tested under a small number of conditions. We begin by developing a nonlinear programming formulation for this parameter optimization problem, and then develop an algorithm that uses special characteristics of the optimization problem to quickly generate heuristic solutions. Our algorithm descends along a series of solutions to one-dimensional nonconvex optimization problems, obtaining a locally optimal set of model parameters at modest computational cost. Finally, we provide some experimental results and recommendations for extending this research.
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