Papers by Panos M Pardalos
Algorithmica, 1999
The isotonic regression problem has applications in statistics, operations research, and image pr... more The isotonic regression problem has applications in statistics, operations research, and image processing. In this paper a general framework for the isotonic regression algorithm is proposed. Under this framework, we discuss the isotonic regression problem in the case where the directed graph specifying the order restriction is a directed tree with n vertices. A new algorithm is presented for this case, which can be regarded as a generalization of the PAV algorithm of Ayer et al. Using a simple tree structure such as the binomial heap, the algorithm can be implemented in O(n log n) time, improving the previously best known O(n 2 ) time algorithm. We also present linear time algorithms for special cases where the directed graph is a path or a star.
Springer Optimization and Its Applications, 2009
New Computer Methods for Global Optimization (H. Ratschek and J. Rokne)
SIAM Review, 1991
Interval analysis is the mathematical treatment of an interval of real numbers (represented by an... more Interval analysis is the mathematical treatment of an interval of real numbers (represented by an ordered pair) as a new kind of" interval number." Working with interval numbers facilitates the analysis oferror bounds in digital computation [5]. Already, several computer languages and software packages implement interval arithmetic (eg, ALGOL-60, PASCAL-SC, FORTRAN-SC, and ACRITH). With such a concept, it becomes pos-sible to determine lower and upper bounds on the exact solutions of certain problems in a computationally efficient ...
Combinatorial and Global Optimization, pp. ??--??
Graph radio coloring and graph radio labelling are combinatorial models for two interesting cases... more Graph radio coloring and graph radio labelling are combinatorial models for two interesting cases of Frequency Assignment. In both problems positive integer labels (channels) must be assigned to all the vertices of a graph such that adjacent vertices get labels at distance at least two. In radio labelling all the labels must be distinct, while in radio coloring only the vertices being at distance no more than two in the input graph must be assigned distinct labels. For both problems the objective is to minimize the maximum label used.
Assignment of Reusable and Non-Reusable Frequencies
Abstract Graph radio coloring and graph radio labelling are combinatorial models for two interest... more Abstract Graph radio coloring and graph radio labelling are combinatorial models for two interesting cases of Frequency Assignment. In both problems positive integer labels (channels) must be assigned to all the vertices of a graph such that adjacent vertices get labels at distance at least two. In radio labelling all the labels must be distinct, while in radio coloring only the vertices being at distance no more than two in the input graph must be assigned distinct labels. For both problems the objective is to minimize the maximum label ...
Invexity of the Minimum Error Entropy Criterion
IEEE Signal Processing Letters, 2013
ABSTRACT In this letter, optimization properties of Minimization of Error Entropy (MEE) and Minim... more ABSTRACT In this letter, optimization properties of Minimization of Error Entropy (MEE) and Minimization of Error Entropy with Fiducial points (MEEF) are presented. It is proved that by varying the kernel parameter of the MEE and/or MEEF objective function, the resulting problem, in general leads to an invex problem. Furthermore, for certain values of the kernel parameter it is shown that the problems may transform to convex or pseudo-convex problems.
Detecting Silica-Coated Gold Nanostars within Surface-Enhanced Resonance Raman Spectroscopy Mapping via Semi-Supervised Framework Combining Feature Selection and Classification
Raman Spectroscopy provides a non-invasive approach to study cells and tissues, and its ability t... more Raman Spectroscopy provides a non-invasive approach to study cells and tissues, and its ability to provide biochemical composition information of samples shows great importance for the research, diagnosis and treatment of cancer. However, conventional Raman Spectroscopy suffers from weak signal strength observed in many biological samples. Surface-Enhanced Resonance Raman Spectroscopy (SERRS) can overcome this disadvantage with the presence of roughened nano-dimensional noble-metal surfaces. In order to study the role of integrins in breast cancer invasiveness, gold nanostars were conjugated with cyclo-RGDf/k peptide for targeting integrins on breast cancer cells and high-speed Raman mapping was employed to assess the samples. Due to the high dimensionality of the datasets collected through SERRS, we have proposed a semi-supervised framework combining feature selection and classification techniques for nanostars detection and tested our method on a breast cancer cells. The results show the advantage of our framework over other data mining technique and potentially provide a new method for evaluating the role of integrins in tumor development. Also, the features selected can possibly be used for further studies on compositional changes observed during the process of breast cancer progression and metastasis.
The Journal of the Operational Research Society, 1999
Through monographs and contributed works the objective of the series is to publish state of the a... more Through monographs and contributed works the objective of the series is to publish state of the art expository research covering all topics in the field of combinatorial optimization. In addition, the series will include books which are suitable for graduate level courses in computer science, engineering, business, applied mathematics, and operations research. Combinatorial (or discrete) optimization problems arise in various applications, including communications network design, VLSI design, machine vision, airline crew scheduling, corporate planning, computer-aided design and manufacturing, database query design, cellular telephone frequency assignment, constraint directed reasoning, and computational biology. The topics of the books will cover complexity analysis and algorithm design (parallel and serial), computational experiments and applications in science and engineering.
Finding maximum independent sets in graphs arising from coding theory
Proceedings of the 2002 ACM symposium on Applied computing, 2002
Abstract New results are presented concerning binary correcting codes, such as deletion-correctin... more Abstract New results are presented concerning binary correcting codes, such as deletion-correcting codes, transposition-correction codes, and codes for the Z-channel. These codes are important due to the possibility of packet loss and corruption on internet transmissions. It is known that the problem of finding the largest correcting codes can be reduced to a well-known combinatorial optimization problem on graphs, the maximum independent set problem. A general scheme of organizing a local search for the maximum independent set ...
Information Sciences, 2013
Harmony Search (HS), inspired by the music improvisation process, is a new meta-heuristic optimiz... more Harmony Search (HS), inspired by the music improvisation process, is a new meta-heuristic optimization method and has been successfully used to tackle the optimization problems in discrete or continuous space. Although the standard HS algorithm is able to solve binarycoded optimization problems, the pitch adjustment operator of HS is degenerated in the binary space, which spoils the performance of the algorithm. Based on the analysis of the drawback of the standard HS, an improved adaptive binary Harmony Search (ABHS) algorithm is proposed in this paper to solve the binary-coded problems more effectively. Various adaptive mechanisms are examined and investigated, and a scalable adaptive strategy is developed for ABHS to enhance its search ability and robustness. The experimental results on the benchmark functions and 0-1 knapsack problems demonstrate that the proposed ABHS is efficient and effective, which outperforms the binary Harmony Search, the novel global Harmony Search algorithm and the discrete binary Particle Swarm Optimization in terms of the search accuracy and convergence speed.
Computational Statistics & Data Analysis, 2005
Massive datasets arise in a broad spectrum of scientiÿc, engineering and commercial applications.... more Massive datasets arise in a broad spectrum of scientiÿc, engineering and commercial applications. In many practically important cases, a massive dataset can be represented as a very large graph with certain attributes associated with its vertices and edges. Studying the structure of this graph is essential for understanding the structural properties of the application it represents. Well-known examples of applying this approach are the Internet graph, the Web graph, and the Call graph. It turns out that the degree distributions of all these graphs can be described by the power-law model. Here we consider another important application-a network representation of the stock market. Stock markets generate huge amounts of data, which can be used for constructing the market graph re ecting the market behavior. We conduct the statistical analysis of this graph and show that it also follows the power-law model. Moreover, we detect cliques and independent sets in this graph. These special formations have a clear practical interpretation, and their analysis allows one to apply a new data mining technique of classifying ÿnancial instruments based on stock prices data, which provides a deeper insight into the internal structure of the stock market.
Optimal Risk Path Algorithms
Applied Optimization
An optimization approach for cooperative communication in ad hoc networks
Submitted for publication, 2005
Abstract. Mobile ad hoc networks (MANETs) are a useful organizational technique for providing com... more Abstract. Mobile ad hoc networks (MANETs) are a useful organizational technique for providing communication infrastructure to wireless devices. They consist of loosely coupled units, that communicate locally only to accessible neighbors. Routing of data among non accessible units in a MANET is made possible through multi-hop retransmission. There are many applications of MANETs, including coordination of rescue groups and other military applications such as UAVs (Unmanned Air Vehicles). We study the problem of ...
Cooperative Systems, 2004
Given a graph G = (V, E), a dominating set D is a subset of V such that any vertex not in D is ad... more Given a graph G = (V, E), a dominating set D is a subset of V such that any vertex not in D is adjacent to at least one vertex in D. Efficient algorithms for computing the minimum connected dominating set (MCDS) are essential for solving many practical problems, such as finding a minimum size backbone in ad hoc networks. Wireless ad hoc networks appear in a wide variety of applications, including mobile commerce, search and discovery, and military battlefield. In this chapter we propose a new efficient heuristic algorithm for the minimum connected dominating set problem. The algorithm starts with a feasible solution containing all vertices of the graph. Then it reduces the size of the CDS by excluding some vertices using a greedy criterion. We also discuss a distributed version of this algorithm. The results of numerical testing show that, despite its simplicity, the proposed algorithm is competitive with other existing approaches.
Journal of Optimization Theory and Applications, 2004
The Multidimensional Assignment Problem (MAP) is a NP-hard combinatorial optimization problem, oc... more The Multidimensional Assignment Problem (MAP) is a NP-hard combinatorial optimization problem, occurring in many applications, such as data association. In this paper, we prove two conjectures made in [1] and based on data from computational experiments on MAPs. We show that the mean optimal objective function cost of random instances of the MAP goes to zero as the problem size increases, when assignment costs are independent exponentially or uniformly distributed random variables. We also prove that the mean optimal solution goes to negative infinity when assignment costs are independent normally distributed random variables.
Greedy Randomized Adaptive Search for a Location Problem with Economies of Scale
Nonconvex Optimization and Its Applications, 1997
Abstract. We consider a heuristic approach for the solution of a location problem with economies ... more Abstract. We consider a heuristic approach for the solution of a location problem with economies of scale. The method chosen has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors. We define the various components comprising this GRASP approach and perform a step-by-step development of such a heuristic for the location problem with concave costs. Computational results for problems of dimensions up to 100 x 1000 are reported. Key words: Continuous ...
Economic analysis of the N−k power grid contingency selection and evaluation by graph algorithms and interdiction methods
Energy Systems, 2011
Abstract Contingency analysis is important for providing information about the vulnerability of p... more Abstract Contingency analysis is important for providing information about the vulnerability of power grids. Many methods have been purposed to use topological structures of power grids for analyzing contingency states. Considering failures of buses and lines, we present and compare several graph methods for selecting contingencies in this paper. A new method, called critical node detection, is introduced for selecting contingencies consisting of failures on buses. Besides these methods, we include an interdiction model which ...
External Memory Algorithms, 1999
We present an approach for clique and quasi-clique computations in very large multi-digraphs. We ... more We present an approach for clique and quasi-clique computations in very large multi-digraphs. We discuss graph decomposition schemes used to break up the problem into several pieces of manageable dimensions. A semiexternal greedy randomized adaptive search procedure (GRASP) for finding approximate solutions to the maximum clique problem and maximum quasiclique problem in very large sparse graphs is presented. We experiment with this heuristic on real data sets collected in the telecommunications industry. These graphs contain on the order of millions of vertices and edges.
AIP Conference Proceedings, 2007
Adverse drug reactions (ADRs) are estimated to be one of the leading causes of death. Many nation... more Adverse drug reactions (ADRs) are estimated to be one of the leading causes of death. Many national and international agencies have set up databases of ADR reports for the express purpose of determining the relationship between drugs and adverse reactions that they cause. We formulate the drug-reaction relationship problem as a continuous optimization problem and utilize C-GRASP, a new continuous global optimization heuristic, to approximately determine the relationship between drugs and adverse reactions. Our approach is compared against others in the literature and is shown to find better solutions.
Annals of Operations Research, 2015
Population growth and the massive production of automotive vehicles have lead to the increase of ... more Population growth and the massive production of automotive vehicles have lead to the increase of traffic congestion problems. Traffic congestion today is not limited to large metropolitan areas, but is observed even in medium-sized cities and highways. Traffic engineering can contribute to lessen these problems. One possibility, explored in this paper, is to assign tolls to streets and roads, with the objective of inducing drivers to take alternative routes, and thus better distribute traffic across the road network. This assignment problem is often referred to as the tollbooth problem and it is NPhard. In this paper, we propose mathematical formulations for two versions of the tollbooth problem that use piecewise-linear functions to approximate congestion cost. We also apply a biased random-key genetic algorithm on a set of real-world instances, analyzing solutions when computing shortest paths according to two different weight functions. Experimental results show that the proposed piecewise-linear functions approximate the original convex function quite well and that the biased random-key genetic algorithm produces high-quality solutions.
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Papers by Panos M Pardalos