This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary... more This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system. Computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications. For the nonconvex case an s-approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function.
DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1995
Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling,... more Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Often, a DOP is formulated in terms of nding a (minimum cost) solution path in a graph from an initial node to a goal node and solved by graph/tree search methods such as branch-and-bound and dynamic programming. Availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete optimization problems. This article provides an overview of parallel search algorithms for solving discrete optimization problems. 1 Introduction. Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Formally, a DOP can be stated as follows : Given a nite discrete set X and a function f(x) de ned on the elements of X, nd an optimal element x opt , such that, f(x opt ) = minff(x)=x Xg. In
Informatica (lithuanian Academy of Sciences), 1992
In this paper, we present a new local search algorithm for solving the Quadratic Assignment Probl... more In this paper, we present a new local search algorithm for solving the Quadratic Assignment Problem based on the Kernighan.Lin heuristic for the. Graph Partitioning Problem. We also prove that finding a local optimum for the Quadratic Assignment Problem, with the neighborhood.structure defined in the algorithm, is PLi·complete. The greatest advantages of the algorithm are its simplicity and sPfed in generating high quality solutions. Tlie algorithm has been implemented alnd tested on an IBM 3090 computer with a variety of test" problems of dimensions up to 100, including many test problems available in the literature and a newi set of test problems with known optimal permuta.tions. Subject classifications: analysis of algorithms: computational com· plexity, suboptimal algorithms; facilities/equipment planning: discrete location. Other key words: combinatorial optimization, graph partitioning, poly· nomial·time local search. Introduction. The Quadratic Assignment Problem(QAP) be...
Traditionally, networks have been studied in an independent fashion. With the emergence of novel ... more Traditionally, networks have been studied in an independent fashion. With the emergence of novel smart city technologies, coupling among networks has been strengthened. To capture the ever-increasing coupling, we explain the notion of interdependent networks, i.e., multi-layered networks with shared decision-making entities, and shared sensing infrastructures with interdisciplinary applications. The main challenge is how to develop data analytics solutions that are capable of enabling interdependent decision making. One of the emerging solutions is agent-based distributed decision making among heterogeneous agents and entities when their decisions are affected by multiple networks. We first provide a big picture of real-world interdependent networks in the context of smart city infrastructures. We then provide an outline of potential challenges and solutions from a data science perspective. We discuss potential hindrances to ensure reliable communication among intelligent agents from different networks. We explore future research directions at the intersection of network science and data science. Concept: Basic principles of a new data science output observed and reported
We present computational experience with an interior-point algorithm for large-scale quadratic pr... more We present computational experience with an interior-point algorithm for large-scale quadratic programming problems with box constraints. The algorithm requires a total of O (√ nL) number of iterations, where L is the size of the input data of the problem, and O (n 3) arithmetic operations per iteration. The algorithm has been implemented using vectorization and tested on an IBM 3090-600S computer with vector facilities. The computational results suggest that the efficiency of the algorithm depends on an appropriate choice of ...
Functional Magnetic Resonance (fMRI) data can be used to depict functional connectivity of the br... more Functional Magnetic Resonance (fMRI) data can be used to depict functional connectivity of the brain. Standard techniques have been developed to construct brain networks from this data; typically nodes are considered as voxels or sets of voxels with weighted edges between them representing measures of correlation. Identifying cognitive states based on fMRI data is connected with recording voxel activity over a certain time interval. Using this information, network and machine learning techniques can be applied to discriminate the cognitive states of the subjects by exploring different features of data. In this work we wish to describe and understand the organization of brain connectivity networks under cognitive tasks. In particular, we use a regularity partitioning algorithm that finds clusters of vertices such that they all behave with each other almost like random bipartite graphs. Based on the random approximation of the graph, we calculate a lower bound on the number of triangles as well as the expectation of the distribution of the edges in each subject and state. We investigate the results by comparing them to the state of the art algorithms for exploring connectivity and we argue that during epochs that the subject is exposed to stimulus, the inspected part of the brain is organized in an efficient way that enables enhanced functionality.
With the surge of the global energy demand, natural gas plays an increasingly important role in t... more With the surge of the global energy demand, natural gas plays an increasingly important role in the global energy market. To meet the demand, optimization techniques have been widely used in the natural gas industry, and yielded a lot of promising results. In this chapter, we give a detailed discussion of optimization models in the natural gas industry with the focus on the natural gas production, transportation, and market.
We consider the problem of maximizing the total connectivity for a set of wireless agents in a mo... more We consider the problem of maximizing the total connectivity for a set of wireless agents in a mobile ad hoc network. That is, given a set of wireless units each having a start point and a destination point, our goal is to determine a set of routes for the units which maximizes the overall connection time between them. Known as the cooperative communication problem in mobile ad hoc networks (ccpm), this problem has several military applications including coordination of rescue groups, path planning for unmanned air vehicles, and geographical exploration and target recognition. The ccpm is N P-hard; therefore heuristic development has been the major focus of research. In this work, we survey the ccpm examining first some early combinatorial formulations and solution techniques. Then we introduce new continuous formulations and compare the results of several case studies. By removing the underlying graph structure, we are able to create a more realistic model of the problem as supported by the numerical evidence. W. Chaovalitwongse et al. (eds.), Optimization and Logistics Challenges 411 in the Enterprise, Springer Optimization and Its Applications 30,
Since Karmarkar proposed the first interior-point algorithm for linear programming, many variatio... more Since Karmarkar proposed the first interior-point algorithm for linear programming, many variations have been discovered. In particular, they can be extended to semidefinite programming We will study some of them in this chapter.
The graph partitioning problem consists of partitioning the vertex set of a graph into several di... more The graph partitioning problem consists of partitioning the vertex set of a graph into several disjoint subsets so that the sum of weights of the edges between the disjoint subsets is minimized. In this paper, robust optimization models with two decomposition algorithms are introduced to solve the graph partitioning problem with interval uncertain weights of edges. The bipartite graph partitioning problem with edge uncertainty is also presented. Throughout this paper, we make no assumption regarding the probability of the uncertain weights.
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary... more This paper gives an O(n) algorithm for a singly constrained convex quadratic program using binary search to solve the Kuhn-Tucker system. Computational results indicate that a randomized version of this algorithm runs in expected linear time and is suitable for practical applications. For the nonconvex case an s-approximate algorithm is proposed which is based on convex and piecewise linear approximations of the objective function.
DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1995
Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling,... more Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Often, a DOP is formulated in terms of nding a (minimum cost) solution path in a graph from an initial node to a goal node and solved by graph/tree search methods such as branch-and-bound and dynamic programming. Availability of parallel computers has created substantial interest in exploring the use of parallel processing for solving discrete optimization problems. This article provides an overview of parallel search algorithms for solving discrete optimization problems. 1 Introduction. Discrete optimization problems (DOPs) arise in various applications such as planning, scheduling, computer aided design, robotics, game playing and constraint directed reasoning. Formally, a DOP can be stated as follows : Given a nite discrete set X and a function f(x) de ned on the elements of X, nd an optimal element x opt , such that, f(x opt ) = minff(x)=x Xg. In
Informatica (lithuanian Academy of Sciences), 1992
In this paper, we present a new local search algorithm for solving the Quadratic Assignment Probl... more In this paper, we present a new local search algorithm for solving the Quadratic Assignment Problem based on the Kernighan.Lin heuristic for the. Graph Partitioning Problem. We also prove that finding a local optimum for the Quadratic Assignment Problem, with the neighborhood.structure defined in the algorithm, is PLi·complete. The greatest advantages of the algorithm are its simplicity and sPfed in generating high quality solutions. Tlie algorithm has been implemented alnd tested on an IBM 3090 computer with a variety of test" problems of dimensions up to 100, including many test problems available in the literature and a newi set of test problems with known optimal permuta.tions. Subject classifications: analysis of algorithms: computational com· plexity, suboptimal algorithms; facilities/equipment planning: discrete location. Other key words: combinatorial optimization, graph partitioning, poly· nomial·time local search. Introduction. The Quadratic Assignment Problem(QAP) be...
Traditionally, networks have been studied in an independent fashion. With the emergence of novel ... more Traditionally, networks have been studied in an independent fashion. With the emergence of novel smart city technologies, coupling among networks has been strengthened. To capture the ever-increasing coupling, we explain the notion of interdependent networks, i.e., multi-layered networks with shared decision-making entities, and shared sensing infrastructures with interdisciplinary applications. The main challenge is how to develop data analytics solutions that are capable of enabling interdependent decision making. One of the emerging solutions is agent-based distributed decision making among heterogeneous agents and entities when their decisions are affected by multiple networks. We first provide a big picture of real-world interdependent networks in the context of smart city infrastructures. We then provide an outline of potential challenges and solutions from a data science perspective. We discuss potential hindrances to ensure reliable communication among intelligent agents from different networks. We explore future research directions at the intersection of network science and data science. Concept: Basic principles of a new data science output observed and reported
We present computational experience with an interior-point algorithm for large-scale quadratic pr... more We present computational experience with an interior-point algorithm for large-scale quadratic programming problems with box constraints. The algorithm requires a total of O (√ nL) number of iterations, where L is the size of the input data of the problem, and O (n 3) arithmetic operations per iteration. The algorithm has been implemented using vectorization and tested on an IBM 3090-600S computer with vector facilities. The computational results suggest that the efficiency of the algorithm depends on an appropriate choice of ...
Functional Magnetic Resonance (fMRI) data can be used to depict functional connectivity of the br... more Functional Magnetic Resonance (fMRI) data can be used to depict functional connectivity of the brain. Standard techniques have been developed to construct brain networks from this data; typically nodes are considered as voxels or sets of voxels with weighted edges between them representing measures of correlation. Identifying cognitive states based on fMRI data is connected with recording voxel activity over a certain time interval. Using this information, network and machine learning techniques can be applied to discriminate the cognitive states of the subjects by exploring different features of data. In this work we wish to describe and understand the organization of brain connectivity networks under cognitive tasks. In particular, we use a regularity partitioning algorithm that finds clusters of vertices such that they all behave with each other almost like random bipartite graphs. Based on the random approximation of the graph, we calculate a lower bound on the number of triangles as well as the expectation of the distribution of the edges in each subject and state. We investigate the results by comparing them to the state of the art algorithms for exploring connectivity and we argue that during epochs that the subject is exposed to stimulus, the inspected part of the brain is organized in an efficient way that enables enhanced functionality.
With the surge of the global energy demand, natural gas plays an increasingly important role in t... more With the surge of the global energy demand, natural gas plays an increasingly important role in the global energy market. To meet the demand, optimization techniques have been widely used in the natural gas industry, and yielded a lot of promising results. In this chapter, we give a detailed discussion of optimization models in the natural gas industry with the focus on the natural gas production, transportation, and market.
We consider the problem of maximizing the total connectivity for a set of wireless agents in a mo... more We consider the problem of maximizing the total connectivity for a set of wireless agents in a mobile ad hoc network. That is, given a set of wireless units each having a start point and a destination point, our goal is to determine a set of routes for the units which maximizes the overall connection time between them. Known as the cooperative communication problem in mobile ad hoc networks (ccpm), this problem has several military applications including coordination of rescue groups, path planning for unmanned air vehicles, and geographical exploration and target recognition. The ccpm is N P-hard; therefore heuristic development has been the major focus of research. In this work, we survey the ccpm examining first some early combinatorial formulations and solution techniques. Then we introduce new continuous formulations and compare the results of several case studies. By removing the underlying graph structure, we are able to create a more realistic model of the problem as supported by the numerical evidence. W. Chaovalitwongse et al. (eds.), Optimization and Logistics Challenges 411 in the Enterprise, Springer Optimization and Its Applications 30,
Since Karmarkar proposed the first interior-point algorithm for linear programming, many variatio... more Since Karmarkar proposed the first interior-point algorithm for linear programming, many variations have been discovered. In particular, they can be extended to semidefinite programming We will study some of them in this chapter.
The graph partitioning problem consists of partitioning the vertex set of a graph into several di... more The graph partitioning problem consists of partitioning the vertex set of a graph into several disjoint subsets so that the sum of weights of the edges between the disjoint subsets is minimized. In this paper, robust optimization models with two decomposition algorithms are introduced to solve the graph partitioning problem with interval uncertain weights of edges. The bipartite graph partitioning problem with edge uncertainty is also presented. Throughout this paper, we make no assumption regarding the probability of the uncertain weights.
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
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