Neng Fan

Solving the Connected Dominating Set Problem and Power Dominating Set Problem by Integer Programming

In this paper, we propose several integer programming approaches with a polynomial number of constraints to formulate and solve the minimum connected dominating set problem. Further, we consider both the power dominating set problem – a special dominating set problem for sensor placement in power systems – and its connected version. We propose formulations and algorithms to solve these integer programs, and report results for several power system graphs.

Linear and quadratic programming approaches for the general graph partitioning problem

The graph partitioning problem is to partition the vertex set of a graph into a number of nonempty subsets so that the total weight of edges connecting distinct subsets is minimized. Previous research requires the input of cardinalities of subsets or the number of subsets for equipartition. In this paper, the problem is formulated as a zero-one quadratic programming problem without the input of cardinalities. We also present three equivalent zero-one linear integer programming reformulations. Because of its importance in data biclustering, the bipartite graph partitioning is also studied. Several new methods to determine the number of subsets and the cardinalities are presented for practical applications. In addition, hierarchy partitioning and partitioning of bipartite graphs without reordering one vertex set, are studied.

Contingency-Risk Informed Power System Design

We consider the problem of designing (or augmenting) an electric power system at a minimum cost such that it satisfies the N-k-ε survivability criterion. This survivability criterion is a generalization of the well-known N-k criterion, and it requires that at least (1-εj) fraction of the steady-state demand be met after failures of j components, for j=0,1,...,k. The network design problem adds another level of complexity to the notoriously hard contingency analysis problem, since the contingency analysis is only one of the requirements for the design optimization problem. We present a mixed-integer programming formulation of this problem that takes into account both transmission and generation expansion. We propose an algorithm that can avoid combinatorial explosion in the number of contingencies, by seeking vulnerabilities in intermediary solutions and constraining the design space accordingly. Our approach is built on our ability to identify such system vulnerabilities quickly. Our empirical studies on modified instances of the IEEE 30-bus and IEEE 57-bus systems show the effectiveness of our methods. We were able to solve the transmission and generation expansion problems for k=4 in approximately 30 min, while other approaches failed to provide a solution at the end of 2 h.

Robust optimization of graph partitioning and critical node detection in analyzing networks

The graph partitioning problem (GPP) 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 isminimized. The critical node problem (CNP) is to detect a set of vertices in a graph whose deletion results in the graph having the minimum pairwise connectivity between the remaining vertices. Both GPP and CNP find many applications in identification of community structures or influential individuals in social networks, telecommunication networks, and supply chain networks. In this paper, we use integer programming to formulate GPP and CNP. In several practice cases, we have networks with uncertain weights of links. Some times, these uncertainties have no information of probability distribution. We use robust optimization models of GPP and CNP to formulate the community structures or influential individuals in such networks.

Recent Advances of Data Biclustering with Application in Computational Neuroscience

Clustering and biclustering are important techniques arising in data mining. Different from clustering, biclustering simultaneously groups the objects and features according their expression levels. In this review, the backgrounds, motivation, data input, objective tasks, and history of data biclustering are carefully studied. The bicluster types and biclustering structures of data matrix are defined mathematically. Most recent algorithms, including OREO, nsNMF, BBC, cMonkey, etc., are reviewed with formal mathematical models. Additionally, a match score between biclusters is defined to compare algorithms. The application of biclustering in computational neuroscience is also reviewed in this chapter.

Multi-way clustering and biclustering by the Ratio cut and Normalized cut in graphs

In this paper, we consider the multi-way clustering problem based on graph partitioning models by the Ratio cut and Normalized cut. We formulate the problem using new quadratic models. Spectral relaxations, new semidefinite programming relaxations and linearization techniques are used to solve these problems. It has been shown that our proposed methods can obtain improved solutions. We also adapt our proposed techniques to the bipartite graph partitioning problem for biclustering.

Robust chance-constrained support vector machines with second-order moment information

Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper studies SVM when the data points are uncertain. With some properties known for the distributions, chance-constrained SVM is used to ensure the small probability of misclassification for the uncertain data. As infinite number of distributions could have the known properties, the robust chance-constrained SVM requires efficient transformations of the chance constraints to make the problem solvable. In this paper, robust chance-constrained SVM with second-order moment information is studied and we obtain equivalent semidefinite programming and second order cone programming reformulations. The geometric interpretation is presented and numerical experiments are conducted. Three types of estimation errors for mean and covariance information are studied in this paper and the corresponding formulations and techniques to handle these types of errors are presented.

N-1-1 contingency-constrained optimal power flow by interdiction methods

N-1-1 contingency analysis considers the consecutive loss of two elements in a power system, with intervening time for operator adjustments; the associated reliability criterion was recently included in the NERC Standard TPL-001-1. In this paper, we introduce optimization models for N-1-1 contingency analysis, based on DC optimal power flow considerations. We use mixed-integer programming approaches to optimally model the system adjustments required to avoid potential cascading outages during the primary and secondary contingencies. Contingencies are determined via worst-case interdiction analysis. To facilitate operation during the secondary contingency, line overloads and load shedding are allowed. We test our models and algorithms on several IEEE test systems. Our computational experiments indicate potential for the models to augment comprehensive system operations models, such as unit commitment.

Robust optimization of graph partitioning involving interval uncertainty

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.

Contingency-constrained unit commitment with post-contingency corrective recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an