Edit Profile (opens in new tab) Vrahatis, Michael N. Compute Distance To: Compute Author ID: vrahatis.michael-n Published as: Vrahatis, M. N.; Vrahatis, Michael N. Homepage: https://thalis.math.upatras.gr/~vrahatis/ External Links: MGP · ORCID · ResearchGate · dblp · GND Documents Indexed: 153 Publications since 1986 5 Contributions as Editor Co-Authors: 89 Co-Authors with 144 Joint Publications 1,533 Co-Co-Authors all top 5 Co-Authors 13 single-authored 21 Magoulas, George D. 18 Meletiou, Gerasimos C. 18 Ragos, Omiros 17 Androulakis, George S. 17 Grapsa, Theodoula N. 15 Parsopoulos, Konstantinos E. 15 Plagianakos, Vassilis P. 14 Laskari, E. C. 14 Tasoulis, Dimitris K. 14 Zafiropoulos, F. A. 9 Bountis, Tassos C. 8 Pavlidis, Nicos G. 7 Perdios, Efstathios A. 6 Kavvadias, Dimitris J. 5 Kalantonis, Vassilis S. 5 Perdiou, Angela E. 5 Petalas, Y. G. 4 Alexandropoulos, Stamatios-Aggelos N. 4 Hadjidimos, Apostolos 4 Kotsireas, Ilias S. 4 Makri, Frosso S. 4 Mourrain, Bernard 4 Noutsos, Dimitrios 3 Adam, Stavros P. 3 Epitropakis, Michael G. 3 Gallopoulos, Efstratios 3 Manoussakis, G. E. 3 Pardalos, Panos M. 3 Sotiropoulos, Dimitris G. 3 Stamatiou, Yannis C. 3 Triantafyllou, Dimitrios S. 3 Triantafyllou, Evangelia C. 2 Adamopoulos, A. V. 2 Akrivis, Georgios D. 2 Alevizos, Panagiotis D. 2 Antonopoulos, Chris G. 2 Bartz-Beielstein, Thomas 2 Boutsinas, Basilis 2 Dougalis, Vassilios A. 2 Groumpos, Peter P. 2 Karras, Dimitrios A. 2 Kollmann, Michael 2 Kravanja, Peter 2 Likothanassis, Spiridon D. 2 Papageorgiou, Elpiniki I. 2 Saridakis, Yiannis G. 2 Skiniotis, Takis 2 Tsirogiannis, G. A. 1 Alevizos, Philipos D. 1 Anastasiadis, Aristoklis D. 1 Andreou, Andreas S. 1 Aridas, Christos K. 1 Beligiannis, Grigorios N. 1 Bergamin, J. M. 1 Bezerianos, Anastasios 1 Daras, Nicholas J. 1 Emiris, Ioannis Z. 1 Farantos, Stavros C. 1 Georgiou, Vasileios L. 1 Hadjidoukas, Panagiotis E. 1 Iordanidis, Kosman I. 1 Isliker, Heinz 1 Kalatonis, V. S. 1 Kaliakatsos-Papakostas, Maximos A. 1 Karagiannopoulos, M. G. 1 Kontogiorgos, Panagiotis 1 Kotsiantis, Sotiris B. 1 Lagaris, Isaac E. 1 Lambrinos, J. N. 1 Markoutis, Vasileios E. 1 Mossay, Pascal 1 Nousis, N. K. 1 Papadakis, Konstantinos E. 1 Papageorgiou, D. G. 1 Papavassilopoulos, George P. 1 Pavlides, G. 1 Polymilis, C. 1 Prosmiti, R. 1 Rasskazova, Varvara 1 Servizi, Graziano 1 Stavropoulos, Elias C. 1 Turchetti, Giorgio 1 Van Barel, Marc 1 Veneti, Aphrodite N. 1 Vladutu, Liviu 1 Voglis, Constantinos A. 1 Yakoubsohn, Jean-Claude 1 Zombanakis, G. A. 1 Zottou, Dimitra-Nefeli A. all top 5 Serials 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 7 Journal of Computational and Applied Mathematics 5 Computer Physics Communications 5 Mathematical and Computer Modelling 4 Bulletin of the Greek Mathematical Society 4 Applied Numerical Mathematics 4 International Journal of Computer Mathematics 4 Nonlinear Analysis. Theory, Methods & Applications 3 ACM Transactions on Mathematical Software 3 Applied Mathematics and Computation 3 Systems Analysis, Modelling Simulation 3 SIAM Journal on Scientific Computing 2 Astrophysics and Space Science 2 Journal of Computational Physics 2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 2 SIGSAM Bulletin 2 Topology and its Applications 2 Journal of Complexity 2 Celestial Mechanics and Dynamical Astronomy 2 Neural Processing Letters 2 Natural Computing 2 ANACM. Applied Numerical Analysis and Computational Mathematics 2 Journal of Applied Mathematics and Bioinformatics 1 Artificial Intelligence 1 Computers & Mathematics with Applications 1 Journal of Mathematical Analysis and Applications 1 Nonlinearity 1 Physics Letters. A 1 Mathematics of Computation 1 Networks 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Neural Networks 1 Annals of Operations Research 1 Numerical Algorithms 1 Neural, Parallel & Scientific Computations 1 Annals of Mathematics and Artificial Intelligence 1 Reliable Computing 1 Chaos 1 Nonlinear Analysis. Real World Applications 1 Journal of Machine Learning Research (JMLR) 1 Springer Optimization and Its Applications 1 SN Operations Research Forum all top 5 Fields 71 Numerical analysis (65-XX) 41 Computer science (68-XX) 37 Operations research, mathematical programming (90-XX) 21 Dynamical systems and ergodic theory (37-XX) 14 Information and communication theory, circuits (94-XX) 12 Algebraic topology (55-XX) 8 Special functions (33-XX) 8 Mechanics of particles and systems (70-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Ordinary differential equations (34-XX) 7 Biology and other natural sciences (92-XX) 6 General and overarching topics; collections (00-XX) 4 Number theory (11-XX) 4 Field theory and polynomials (12-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Statistics (62-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 General topology (54-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 2 Relativity and gravitational theory (83-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 101 Publications have been cited 631 times in 363 Documents Cited by ▼ Year ▼ Recent approaches to global optimization problems through particle Swarm optimization. Zbl 1018.68063Parsopoulos, K. E.; Vrahatis, M. N. 71 2002 A class of gradient unconstrained minimization algorithms with adaptive stepsize. Zbl 0958.65072Vrahatis, M. N.; Androulakis, G. S.; Lambrinos, J. N.; Magoulas, G. D. 37 2000 A short proof and a generalization of Miranda’s existence theorem. Zbl 0695.55001Vrahatis, Michael N. 26 1989 Memetic particle swarm optimization. Zbl 1145.90108Petalas, Y. G.; Parsopoulos, K. E.; Vrahatis, M. N. 24 2007 Solving systems of nonlinear equations using the nonzero value of the topological degree. Zbl 0665.65052Vrahatis, Michael N. 23 1988 Algorithm 666. CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations. Zbl 0709.65518Vrahatis, Michael N. 22 1988 An efficient method for locating and computing periodic orbits of nonlinear mappings. Zbl 0826.65049Vrahatis, Michael N. 19 1995 On the complexity of isolating real roots and computing with certainty the topological degree. Zbl 1008.65022Mourrain, B.; Vrahatis, M. N.; Yakoubsohn, J. C. 19 2002 Structure and breakdown of invariant tori in a 4-D mapping model of accelerator dynamics. Zbl 0906.58013Vrahatis, M. N.; Isliker, H.; Bountis, T. C. 18 1997 A rapid generalized method of bisection for solving systems of non-linear equations. Zbl 0604.65031Vrahatis, M. N.; Iordanidis, K. I. 17 1986 Improving the particle swarm optimizer by function “stretching”. Zbl 1015.90064Parsopoulos, K. E.; Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 16 2001 Parameter selection and adaptation in Unified Particle Swarm Optimization. Zbl 1149.90432Parsopoulos, K. E.; Vrahatis, M. N. 15 2007 A new unconstrained optimization method for imprecise function and gradient values. Zbl 0887.90166Vrahatis, M. N.; Androulakis, G. S.; Manoussakis, G. E. 15 1996 Periodic orbits and invariant surfaces of 4D nonlinear mappings. Zbl 0879.58027Vrahatis, M. N.; Bountis, T. C.; Kollmann, M. 13 1996 Locating and computing all the simple roots and extrema of a function. Zbl 0862.65028Kavvadias, Dimitris J.; Vrahatis, Michael N. 10 1996 RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions. Zbl 0908.65010Vrahatis, M. N.; Ragos, O.; Skiniotis, T.; Zafiropoulos, F. A.; Grapsa, T. N. 10 1995 Modification of the particle swarm optimizer for locating all the global minima. Zbl 1011.68103Parsopoulos, K. E.; Vrahatis, M. N. 10 2001 From linear to nonlinear iterative methods. Zbl 1022.65060Vrahatis, M. N.; Magoulas, G. D.; Plagianakos, V. P. 10 2003 Minimization techniques in neural network supervised training. Zbl 0884.68106Androulakis, G. S.; Magoulas, G. D.; Vrahatis, M. N. 9 1996 Existence and computation of short-run equilibria in economic geography. Zbl 1283.91114Pavlidis, N. G.; Vrahatis, M. N.; Mossay, P. 9 2007 Objective function ”stretching” to alleviate convergence to local minima. Zbl 1042.90622Parsopoulos, K. E.; Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 8 2001 On the alleviation of the problem of local minima in back-propagation. Zbl 0891.68089Magoulas, G. D.; Vrahatis, M. N.; Androulakis, G. S. 7 1997 Computing Nash equilibria through computational intelligence methods. Zbl 1079.91004Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N. 7 2005 Parallel evolutionary training algorithms for “hardware-friendly“ neural networks. Zbl 1018.68064Plagianakos, Vassilis P.; Vrahatis, Michael N. 7 2002 Fuzzy cognitive maps learning through swarm intelligence. Zbl 1058.68593Papageorgiou, E. I.; Parsopoulos, K. E.; Groumpos, P. P.; Vrahatis, M. N. 6 2004 Locating and computing arbitrarily distributed zeros. Zbl 0967.65060Kavvadias, D. J.; Makri, F. S.; Vrahatis, M. N. 6 1999 The implicit function theorem for solving systems of nonlinear equations in \({\mathbb{R}}^ 2\). Zbl 0675.65044Grapsa, Theodoula N.; Vrahatis, Michael N. 6 1989 On the localization and computation of zeros of Bessel functions. Zbl 0915.33001Vrahatis, M. N.; Grapsa, T. N.; Ragos, O.; Zafiropoulos, F. A. 6 1997 Generalization of the Bolzano theorem for simplices. Zbl 1347.55004Vrahatis, Michael N. 6 2016 ZEAL: A mathematical software package for computing zeros of analytic functions. Zbl 0955.65033Kravanja, P.; Van Barel, M.; Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A. 6 2000 Application of the characteristic bisection method for locating and computing periodic orbits in molecular systems. Zbl 0984.65136Vrahatis, M. N.; Perdiou, A. E.; Kalantonis, V. S.; Perdios, E. A.; Papadakis, K.; Prosmiti, R.; Farantos, S. C. 6 2001 No free lunch theorem: a review. Zbl 1425.90111Adam, Stavros P.; Alexandropoulos, Stamatios-Aggelos N.; Pardalos, Panos M.; Vrahatis, Michael N. 5 2019 A dimension-reducing method for solving systems of nonlinear equations in \(\mathbb{R}{}^ n\). Zbl 0752.65040Grapsa, T. N.; Vrahatis, M. N. 5 1990 On the acceleration of the backpropagation training method. Zbl 0891.68090Vrahatis, M. N.; Androulakis, G. S.; Magoulas, G. D. 5 1997 A dimension-reducing method for unconstrained optimization. Zbl 0856.65074Grapsa, T. N.; Vrahatis, M. N. 5 1996 Locating and computing zeros of Airy functions. Zbl 0878.33001Vrahatis, M. N.; Ragos, O.; Zafiropoulos, F. A.; Grapsa, T. N. 5 1996 ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument. Zbl 0999.33003Kravanja, P.; Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A. 5 1998 Locating and computing in parallel all the simple roots of special functions using PVM. Zbl 0988.65024Plagianakos, V. P.; Nousis, N. K.; Vrahatis, M. N. 5 2001 On the equilibrium points of the relativistic restricted three-body problem. Zbl 1042.70509Ragos, O.; Perdios, E. A.; Kalantonis, V. S.; Vrahatis, M. N. 5 2001 Adaptive stepsize algorithms for on-line training of neural networks. Zbl 1042.68657Magoulas, G. D.; Plagianakos, V. P.; Vrahatis, M. N. 5 2001 Computing with certainty individual members of families of periodic orbits of a given period. Zbl 1090.70003Kalatonis, V. S.; Perdios, E. A.; Perdiou, A. E.; Vrahatis, M. N. 5 2001 Artificial nonmonotonic neural networks. Zbl 0983.68151Boutsinas, B.; Vrahatis, M. N. 5 2001 Adaptive algorithms for neural network supervised learning: a deterministic optimization approach. Zbl 1156.92004Magoulas, George D.; Vrahatis, Michael N. 4 2006 An error estimation for the method of bisection in \({\mathbb{R}}^ n\). Zbl 0649.65028Vrahatis, Michael N. 4 1986 Detecting resonances in conservative maps using evolutionary algorithms. Zbl 1227.37008Petalas, Y. G.; Antonopoulos, C. G.; Bountis, T. C.; Vrahatis, M. N. 4 2009 OPTAC: A portable software package for analyzing and comparing optimization methods by visualization. Zbl 0857.65066Androulakis, G. S.; Vrahatis, M. N. 4 1996 The topological degree theory for the localization and computation of complex zeros of Bessel functions. Zbl 0892.33002Vrahatis, M. N.; Ragos, O.; Skiniotis, T.; Zafiropoulos, F. A.; Grapsa, T. N. 4 1997 The new \(k\)-windows algorithm for improving the \(k\)-means clustering algorithm. Zbl 1004.68132Vrahatis, M. N.; Boutsinas, B.; Alevizos, P.; Pavlides, G. 4 2002 Efficient method for computing with certainty periodic orbits on a surface of section. Zbl 1027.70003Perdios, E. A.; Kalantonis, V. S.; Vrahatis, M. N. 4 2002 Learning in multilayer perceptrons using global optimization strategies. Zbl 1042.90653Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 4 2001 Dynamic search trajectory methods for neural network training. Zbl 1058.68596Petalas, Y. G.; Tasoulis, D. K.; Vrahatis, M. N. 3 2004 Aitken and Neville inverse interpolation methods over finite fields. Zbl 1068.41004Laskari, E. C.; Meletiou, G. C.; Vrahatis, M. N. 3 2005 A new hybrid genetic algorithm for global optimization. Zbl 0891.68046Sotiropoulos, D. G.; Stavropoulos, E. C.; Vrahatis, M. N. 3 1997 A variant of Jung’s theorem. Zbl 0745.53003Vrahatis, Michael N. 3 1988 Design and analysis of optimization algorithms using computational statistics. Zbl 1061.65004Bartz-Beielstein, T.; Parsopoulos, K. E.; Vrahatis, M. N. 3 2004 Homoclinic orbits of invertible maps. Zbl 1013.37019Bergamin, J. M.; Bountis, T.; Vrahatis, M. N. 3 2002 Simplex bisection and Sperner simplices. Zbl 1185.65090Vrahatis, Michael N. 3 2000 Evolutionary operators in global optimization with dynamic search trajectories. Zbl 1062.90050Laskari, E. C.; Parsopoulos, K. E.; Vrahatis, M. N. 3 2003 Multi-objective evolutionary optimization algorithms for machine learning: a recent survey. Zbl 1425.90102Alexandropoulos, Stamatios-Aggelos N.; Aridas, Christos K.; Kotsiantis, Sotiris B.; Vrahatis, Michael N. 2 2019 Solving systems of nonlinear equations in \(R^ n\) using a rotating hyperplane in \(R^{n+1}\). Zbl 0704.65038Grapsa, T. N.; Vrahatis, M. N.; Bountis, T. C. 2 1990 Analysis of particle swarm optimization using computational statistics. Zbl 1060.65603Bartz-Beielstein, T.; Parsopoulos, K. E.; Vrahatis, M. N. 2 2004 Efficiently computing many roots of a function. Zbl 1113.65049Kavvadias, D. J.; Makri, F. S.; Vrahatis, M. N. 2 2005 Novel orbit based symmetric cryptosystems. Zbl 1190.94031Vrahatis, M. N.; Tsirogiannis, G. A.; Laskari, E. C. 2 2010 Cryptography through interpolation, approximation and computational intelligence methods. Zbl 1286.94078Meletiou, G. C.; Tasoulis, D. K.; Vrahatis, M. N. 2 2003 Topological degree theory and local analysis of area preserving maps. Zbl 1080.37576Polymilis, C.; Servizi, G.; Skokos, Ch.; Turchetti, G.; Vrahatis, M. N. 2 2003 Geometry of learning: Visualizing the performance of neural network supervised training methods. Zbl 0898.68075Androulakis, G. S.; Magoulas, G. D.; Vrahatis, M. N. 2 1997 Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros. Zbl 07187683Vrahatis, Michael N. 2 2020 Global optimization for imprecise problems. Zbl 0886.90142Vrahatis, M. N.; Sotiropoulos, D. G.; Triantafyllou, E. C. 2 1997 Determining the number of real roots of polynomials through neural networks. Zbl 1100.65044Mourrain, B.; Pavlidis, N. G.; Tasoulis, D. K.; Vrahatis, M. N. 2 2006 Globally convergent modification of the quickprop method. Zbl 1060.68626Vrahatis, Michael N.; Magoulas, George D.; Plagianakos, Vassilis P. 2 2000 On the application of optimization methods to the determination of members of families of periodic solutions. Zbl 1045.83018Kalantonis, V. S.; Perdios, E. A.; Perdiou, A. E.; Ragos, O.; Vrahatis, M. N. 2 2003 Generalizations of the intermediate value theorem for approximating fixed points and zeros of continuous functions. Zbl 07250755Vrahatis, Michael N. 1 2020 Unsupervised clustering using fractal dimension. Zbl 1158.62043Tasoulis, D. K.; Vrahatis, M. N. 1 2006 Evolutionary computation based cryptanalysis: a first study. Zbl 1202.94186Laskari, E. C.; Meletiou, G. C.; Stamatiou, Y. C.; Vrahatis, M. N. 1 2005 Problems of cryptography as discrete optimization tasks. Zbl 1202.94187Laskari, E. C.; Meletiou, G. C.; Vrahatis, M. N. 1 2005 Algorithm 987: MANBIS – a C++ mathematical software package for locating and computing efficiently many roots of a function: theoretical issues. Zbl 1484.65106Zottou, Dimitra-Nefeli A.; Kavvadias, Dimitris J.; Makri, Frosso S.; Vrahatis, Michael N. 1 2018 A convergence-improving iterative method for computing periodic orbits near bifurcation points. Zbl 0704.65056Vrahatis, Michael N.; Bountis, Tassos 1 1990 Studying the performance of optimization methods by visualization. Zbl 0933.90061Androulakis, G. S.; Vrahatis, M. N.; Grapsa, T. N. 1 1996 Studying the basin of convergence of methods for computing periodic orbits. Zbl 1248.28010Epitropakis, Michael G.; Vrahatis, Michael N. 1 2011 Studying the performance of artificial neural networks on problems related to cryptography. Zbl 1109.68047Laskari, E. C.; Meletiou, G. C.; Tasoulis, D. K.; Vrahatis, M. N. 1 2006 Improved learning of neural nets through global search. Zbl 1123.92002Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 1 2006 Evolving cellular automata rules for multiple-step-ahead prediction of complex binary sequences. Zbl 1190.68039Adamopoulos, A. V.; Pavlidis, N. G.; Vrahatis, M. N. 1 2010 Bounding the search space for global optimization of neural networks learning error: an interval analysis approach. Zbl 1392.68335Adam, Stavros P.; Magoulas, George D.; Karras, Dimitrios A.; Vrahatis, Michael N. 1 2016 Aitken and Neville inverse interpolation methods for the Lucas logarithm problem. Zbl 1157.94359Laskari, E. C.; Meletiou, G. C.; Vrahatis, M. N. 1 2009 A new dimension-reducing method for solving systems of nonlinear equations. Zbl 0830.65038Grapsa, T. N.; Vrahatis, M. N. 1 1995 A generalized bisection method for large and imprecise problems. Zbl 0849.65036Vrahatis, Michael N. 1 1996 Composite dimension-reducing methods for unconstrained optimization. Zbl 0879.90169Grapsa, T. N.; Vrahatis, M. N.; Androulakis, G. S. 1 1997 New constrained optimization methods based on one-dimensional rootfinding. Zbl 0880.65038Manoussakis, G. E.; Vrahatis, M. N.; Androulakis, G. S. 1 1995 The topological degree for the computation of the total number of equilibrium points in ODEs. Zbl 0881.65068Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A. 1 1995 A new constrained optimization method for imprecise problems. Zbl 0880.65039Vrahatis, M. N.; Androulakis, G. S.; Manoussakis, G. E. 1 1995 On perturbation of roots of homogeneous algebraic systems. Zbl 1100.12001Tanabé, S.; Vrahatis, M. N. 1 2006 Solving the linear interval tolerance problem for weight initialization of neural networks. Zbl 1323.92012Adam, S. P.; Karras, D. A.; Magoulas, G. D.; Vrahatis, M. N. 1 2014 Transformations of two cryptographic problems in terms of matrices. Zbl 1341.94022Laskari, E. C.; Meletiou, G. C.; Tasoulis, D. K.; Vrahatis, M. N. 1 2005 Symmetric doubly asymptotic orbits in the photogravitational restricted three-body problem. Zbl 1042.70508Perdios, E. A.; Ragos, O.; Perdiou, A. E.; Vrahatis, M. N. 1 2001 Computing families of periodic orbits through optimization methods. Zbl 1042.70503Vrahatis, M. N.; Ragos, O.; Androulakis, G. S. 1 2001 Supervised training using global search methods. Zbl 1048.90117Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 1 2001 Learning rate adaptation in stochastic gradient descent. Zbl 1049.90139Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 1 2001 Sign methods for enumerating solutions of nonlinear algebraic systems. Zbl 1028.65052Emiris, Ioannis Z.; Mourrain, Bernard; Vrahatis, Michael N. 1 2002 Preface [Special issue: NumAn 2012]. Zbl 1335.00148 1 2016 Short-term prediction of complex binary data. Zbl 1084.68114Adamopoulos, A. V.; Likothanassis, S.; Pavlidis, N. G.; Vrahatis, M. N. 1 2005 Black box optimization, machine learning, and no-free lunch theorems. Zbl 1471.90002 1 2021 Intermediate value theorem for simplices for simplicial approximation of fixed points and zeros. Zbl 07187683Vrahatis, Michael N. 2 2020 Generalizations of the intermediate value theorem for approximating fixed points and zeros of continuous functions. Zbl 07250755Vrahatis, Michael N. 1 2020 No free lunch theorem: a review. Zbl 1425.90111Adam, Stavros P.; Alexandropoulos, Stamatios-Aggelos N.; Pardalos, Panos M.; Vrahatis, Michael N. 5 2019 Multi-objective evolutionary optimization algorithms for machine learning: a recent survey. Zbl 1425.90102Alexandropoulos, Stamatios-Aggelos N.; Aridas, Christos K.; Kotsiantis, Sotiris B.; Vrahatis, Michael N. 2 2019 Algorithm 987: MANBIS – a C++ mathematical software package for locating and computing efficiently many roots of a function: theoretical issues. Zbl 1484.65106Zottou, Dimitra-Nefeli A.; Kavvadias, Dimitris J.; Makri, Frosso S.; Vrahatis, Michael N. 1 2018 Generalization of the Bolzano theorem for simplices. Zbl 1347.55004Vrahatis, Michael N. 6 2016 Bounding the search space for global optimization of neural networks learning error: an interval analysis approach. Zbl 1392.68335Adam, Stavros P.; Magoulas, George D.; Karras, Dimitrios A.; Vrahatis, Michael N. 1 2016 Preface [Special issue: NumAn 2012]. Zbl 1335.00148 1 2016 Solving the linear interval tolerance problem for weight initialization of neural networks. Zbl 1323.92012Adam, S. P.; Karras, D. A.; Magoulas, G. D.; Vrahatis, M. N. 1 2014 Studying the basin of convergence of methods for computing periodic orbits. Zbl 1248.28010Epitropakis, Michael G.; Vrahatis, Michael N. 1 2011 Novel orbit based symmetric cryptosystems. Zbl 1190.94031Vrahatis, M. N.; Tsirogiannis, G. A.; Laskari, E. C. 2 2010 Evolving cellular automata rules for multiple-step-ahead prediction of complex binary sequences. Zbl 1190.68039Adamopoulos, A. V.; Pavlidis, N. G.; Vrahatis, M. N. 1 2010 Detecting resonances in conservative maps using evolutionary algorithms. Zbl 1227.37008Petalas, Y. G.; Antonopoulos, C. G.; Bountis, T. C.; Vrahatis, M. N. 4 2009 Aitken and Neville inverse interpolation methods for the Lucas logarithm problem. Zbl 1157.94359Laskari, E. C.; Meletiou, G. C.; Vrahatis, M. N. 1 2009 Memetic particle swarm optimization. Zbl 1145.90108Petalas, Y. G.; Parsopoulos, K. E.; Vrahatis, M. N. 24 2007 Parameter selection and adaptation in Unified Particle Swarm Optimization. Zbl 1149.90432Parsopoulos, K. E.; Vrahatis, M. N. 15 2007 Existence and computation of short-run equilibria in economic geography. Zbl 1283.91114Pavlidis, N. G.; Vrahatis, M. N.; Mossay, P. 9 2007 Adaptive algorithms for neural network supervised learning: a deterministic optimization approach. Zbl 1156.92004Magoulas, George D.; Vrahatis, Michael N. 4 2006 Determining the number of real roots of polynomials through neural networks. Zbl 1100.65044Mourrain, B.; Pavlidis, N. G.; Tasoulis, D. K.; Vrahatis, M. N. 2 2006 Unsupervised clustering using fractal dimension. Zbl 1158.62043Tasoulis, D. K.; Vrahatis, M. N. 1 2006 Studying the performance of artificial neural networks on problems related to cryptography. Zbl 1109.68047Laskari, E. C.; Meletiou, G. C.; Tasoulis, D. K.; Vrahatis, M. N. 1 2006 Improved learning of neural nets through global search. Zbl 1123.92002Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 1 2006 On perturbation of roots of homogeneous algebraic systems. Zbl 1100.12001Tanabé, S.; Vrahatis, M. N. 1 2006 Computing Nash equilibria through computational intelligence methods. Zbl 1079.91004Pavlidis, N. G.; Parsopoulos, K. E.; Vrahatis, M. N. 7 2005 Aitken and Neville inverse interpolation methods over finite fields. Zbl 1068.41004Laskari, E. C.; Meletiou, G. C.; Vrahatis, M. N. 3 2005 Efficiently computing many roots of a function. Zbl 1113.65049Kavvadias, D. J.; Makri, F. S.; Vrahatis, M. N. 2 2005 Evolutionary computation based cryptanalysis: a first study. Zbl 1202.94186Laskari, E. C.; Meletiou, G. C.; Stamatiou, Y. C.; Vrahatis, M. N. 1 2005 Problems of cryptography as discrete optimization tasks. Zbl 1202.94187Laskari, E. C.; Meletiou, G. C.; Vrahatis, M. N. 1 2005 Transformations of two cryptographic problems in terms of matrices. Zbl 1341.94022Laskari, E. C.; Meletiou, G. C.; Tasoulis, D. K.; Vrahatis, M. N. 1 2005 Short-term prediction of complex binary data. Zbl 1084.68114Adamopoulos, A. V.; Likothanassis, S.; Pavlidis, N. G.; Vrahatis, M. N. 1 2005 Fuzzy cognitive maps learning through swarm intelligence. Zbl 1058.68593Papageorgiou, E. I.; Parsopoulos, K. E.; Groumpos, P. P.; Vrahatis, M. N. 6 2004 Dynamic search trajectory methods for neural network training. Zbl 1058.68596Petalas, Y. G.; Tasoulis, D. K.; Vrahatis, M. N. 3 2004 Design and analysis of optimization algorithms using computational statistics. Zbl 1061.65004Bartz-Beielstein, T.; Parsopoulos, K. E.; Vrahatis, M. N. 3 2004 Analysis of particle swarm optimization using computational statistics. Zbl 1060.65603Bartz-Beielstein, T.; Parsopoulos, K. E.; Vrahatis, M. N. 2 2004 From linear to nonlinear iterative methods. Zbl 1022.65060Vrahatis, M. N.; Magoulas, G. D.; Plagianakos, V. P. 10 2003 Evolutionary operators in global optimization with dynamic search trajectories. Zbl 1062.90050Laskari, E. C.; Parsopoulos, K. E.; Vrahatis, M. N. 3 2003 Cryptography through interpolation, approximation and computational intelligence methods. Zbl 1286.94078Meletiou, G. C.; Tasoulis, D. K.; Vrahatis, M. N. 2 2003 Topological degree theory and local analysis of area preserving maps. Zbl 1080.37576Polymilis, C.; Servizi, G.; Skokos, Ch.; Turchetti, G.; Vrahatis, M. N. 2 2003 On the application of optimization methods to the determination of members of families of periodic solutions. Zbl 1045.83018Kalantonis, V. S.; Perdios, E. A.; Perdiou, A. E.; Ragos, O.; Vrahatis, M. N. 2 2003 Recent approaches to global optimization problems through particle Swarm optimization. Zbl 1018.68063Parsopoulos, K. E.; Vrahatis, M. N. 71 2002 On the complexity of isolating real roots and computing with certainty the topological degree. Zbl 1008.65022Mourrain, B.; Vrahatis, M. N.; Yakoubsohn, J. C. 19 2002 Parallel evolutionary training algorithms for “hardware-friendly“ neural networks. Zbl 1018.68064Plagianakos, Vassilis P.; Vrahatis, Michael N. 7 2002 The new \(k\)-windows algorithm for improving the \(k\)-means clustering algorithm. Zbl 1004.68132Vrahatis, M. N.; Boutsinas, B.; Alevizos, P.; Pavlides, G. 4 2002 Efficient method for computing with certainty periodic orbits on a surface of section. Zbl 1027.70003Perdios, E. A.; Kalantonis, V. S.; Vrahatis, M. N. 4 2002 Homoclinic orbits of invertible maps. Zbl 1013.37019Bergamin, J. M.; Bountis, T.; Vrahatis, M. N. 3 2002 Sign methods for enumerating solutions of nonlinear algebraic systems. Zbl 1028.65052Emiris, Ioannis Z.; Mourrain, Bernard; Vrahatis, Michael N. 1 2002 Improving the particle swarm optimizer by function “stretching”. Zbl 1015.90064Parsopoulos, K. E.; Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 16 2001 Modification of the particle swarm optimizer for locating all the global minima. Zbl 1011.68103Parsopoulos, K. E.; Vrahatis, M. N. 10 2001 Objective function ”stretching” to alleviate convergence to local minima. Zbl 1042.90622Parsopoulos, K. E.; Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 8 2001 Application of the characteristic bisection method for locating and computing periodic orbits in molecular systems. Zbl 0984.65136Vrahatis, M. N.; Perdiou, A. E.; Kalantonis, V. S.; Perdios, E. A.; Papadakis, K.; Prosmiti, R.; Farantos, S. C. 6 2001 Locating and computing in parallel all the simple roots of special functions using PVM. Zbl 0988.65024Plagianakos, V. P.; Nousis, N. K.; Vrahatis, M. N. 5 2001 On the equilibrium points of the relativistic restricted three-body problem. Zbl 1042.70509Ragos, O.; Perdios, E. A.; Kalantonis, V. S.; Vrahatis, M. N. 5 2001 Adaptive stepsize algorithms for on-line training of neural networks. Zbl 1042.68657Magoulas, G. D.; Plagianakos, V. P.; Vrahatis, M. N. 5 2001 Computing with certainty individual members of families of periodic orbits of a given period. Zbl 1090.70003Kalatonis, V. S.; Perdios, E. A.; Perdiou, A. E.; Vrahatis, M. N. 5 2001 Artificial nonmonotonic neural networks. Zbl 0983.68151Boutsinas, B.; Vrahatis, M. N. 5 2001 Learning in multilayer perceptrons using global optimization strategies. Zbl 1042.90653Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 4 2001 Symmetric doubly asymptotic orbits in the photogravitational restricted three-body problem. Zbl 1042.70508Perdios, E. A.; Ragos, O.; Perdiou, A. E.; Vrahatis, M. N. 1 2001 Computing families of periodic orbits through optimization methods. Zbl 1042.70503Vrahatis, M. N.; Ragos, O.; Androulakis, G. S. 1 2001 Supervised training using global search methods. Zbl 1048.90117Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 1 2001 Learning rate adaptation in stochastic gradient descent. Zbl 1049.90139Plagianakos, V. P.; Magoulas, G. D.; Vrahatis, M. N. 1 2001 A class of gradient unconstrained minimization algorithms with adaptive stepsize. Zbl 0958.65072Vrahatis, M. N.; Androulakis, G. S.; Lambrinos, J. N.; Magoulas, G. D. 37 2000 ZEAL: A mathematical software package for computing zeros of analytic functions. Zbl 0955.65033Kravanja, P.; Van Barel, M.; Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A. 6 2000 Simplex bisection and Sperner simplices. Zbl 1185.65090Vrahatis, Michael N. 3 2000 Globally convergent modification of the quickprop method. Zbl 1060.68626Vrahatis, Michael N.; Magoulas, George D.; Plagianakos, Vassilis P. 2 2000 Locating and computing arbitrarily distributed zeros. Zbl 0967.65060Kavvadias, D. J.; Makri, F. S.; Vrahatis, M. N. 6 1999 ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument. Zbl 0999.33003Kravanja, P.; Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A. 5 1998 Structure and breakdown of invariant tori in a 4-D mapping model of accelerator dynamics. Zbl 0906.58013Vrahatis, M. N.; Isliker, H.; Bountis, T. C. 18 1997 On the alleviation of the problem of local minima in back-propagation. Zbl 0891.68089Magoulas, G. D.; Vrahatis, M. N.; Androulakis, G. S. 7 1997 On the localization and computation of zeros of Bessel functions. Zbl 0915.33001Vrahatis, M. N.; Grapsa, T. N.; Ragos, O.; Zafiropoulos, F. A. 6 1997 On the acceleration of the backpropagation training method. Zbl 0891.68090Vrahatis, M. N.; Androulakis, G. S.; Magoulas, G. D. 5 1997 The topological degree theory for the localization and computation of complex zeros of Bessel functions. Zbl 0892.33002Vrahatis, M. N.; Ragos, O.; Skiniotis, T.; Zafiropoulos, F. A.; Grapsa, T. N. 4 1997 A new hybrid genetic algorithm for global optimization. Zbl 0891.68046Sotiropoulos, D. G.; Stavropoulos, E. C.; Vrahatis, M. N. 3 1997 Geometry of learning: Visualizing the performance of neural network supervised training methods. Zbl 0898.68075Androulakis, G. S.; Magoulas, G. D.; Vrahatis, M. N. 2 1997 Global optimization for imprecise problems. Zbl 0886.90142Vrahatis, M. N.; Sotiropoulos, D. G.; Triantafyllou, E. C. 2 1997 Composite dimension-reducing methods for unconstrained optimization. Zbl 0879.90169Grapsa, T. N.; Vrahatis, M. N.; Androulakis, G. S. 1 1997 A new unconstrained optimization method for imprecise function and gradient values. Zbl 0887.90166Vrahatis, M. N.; Androulakis, G. S.; Manoussakis, G. E. 15 1996 Periodic orbits and invariant surfaces of 4D nonlinear mappings. Zbl 0879.58027Vrahatis, M. N.; Bountis, T. C.; Kollmann, M. 13 1996 Locating and computing all the simple roots and extrema of a function. Zbl 0862.65028Kavvadias, Dimitris J.; Vrahatis, Michael N. 10 1996 Minimization techniques in neural network supervised training. Zbl 0884.68106Androulakis, G. S.; Magoulas, G. D.; Vrahatis, M. N. 9 1996 A dimension-reducing method for unconstrained optimization. Zbl 0856.65074Grapsa, T. N.; Vrahatis, M. N. 5 1996 Locating and computing zeros of Airy functions. Zbl 0878.33001Vrahatis, M. N.; Ragos, O.; Zafiropoulos, F. A.; Grapsa, T. N. 5 1996 OPTAC: A portable software package for analyzing and comparing optimization methods by visualization. Zbl 0857.65066Androulakis, G. S.; Vrahatis, M. N. 4 1996 Studying the performance of optimization methods by visualization. Zbl 0933.90061Androulakis, G. S.; Vrahatis, M. N.; Grapsa, T. N. 1 1996 A generalized bisection method for large and imprecise problems. Zbl 0849.65036Vrahatis, Michael N. 1 1996 An efficient method for locating and computing periodic orbits of nonlinear mappings. Zbl 0826.65049Vrahatis, Michael N. 19 1995 RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions. Zbl 0908.65010Vrahatis, M. N.; Ragos, O.; Skiniotis, T.; Zafiropoulos, F. A.; Grapsa, T. N. 10 1995 A new dimension-reducing method for solving systems of nonlinear equations. Zbl 0830.65038Grapsa, T. N.; Vrahatis, M. N. 1 1995 New constrained optimization methods based on one-dimensional rootfinding. Zbl 0880.65038Manoussakis, G. E.; Vrahatis, M. N.; Androulakis, G. S. 1 1995 The topological degree for the computation of the total number of equilibrium points in ODEs. Zbl 0881.65068Ragos, O.; Vrahatis, M. N.; Zafiropoulos, F. A. 1 1995 A new constrained optimization method for imprecise problems. Zbl 0880.65039Vrahatis, M. N.; Androulakis, G. S.; Manoussakis, G. E. 1 1995 A dimension-reducing method for solving systems of nonlinear equations in \(\mathbb{R}{}^ n\). Zbl 0752.65040Grapsa, T. N.; Vrahatis, M. N. 5 1990 Solving systems of nonlinear equations in \(R^ n\) using a rotating hyperplane in \(R^{n+1}\). Zbl 0704.65038Grapsa, T. N.; Vrahatis, M. N.; Bountis, T. C. 2 1990 A convergence-improving iterative method for computing periodic orbits near bifurcation points. Zbl 0704.65056Vrahatis, Michael N.; Bountis, Tassos 1 1990 A short proof and a generalization of Miranda’s existence theorem. Zbl 0695.55001Vrahatis, Michael N. 26 1989 The implicit function theorem for solving systems of nonlinear equations in \({\mathbb{R}}^ 2\). Zbl 0675.65044Grapsa, Theodoula N.; Vrahatis, Michael N. 6 1989 Solving systems of nonlinear equations using the nonzero value of the topological degree. Zbl 0665.65052Vrahatis, Michael N. 23 1988 Algorithm 666. CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations. Zbl 0709.65518Vrahatis, Michael N. 22 1988 A variant of Jung’s theorem. Zbl 0745.53003Vrahatis, Michael N. 3 1988 A rapid generalized method of bisection for solving systems of non-linear equations. Zbl 0604.65031Vrahatis, M. N.; Iordanidis, K. I. 17 1986 ...and 1 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 694 Authors 50 Vrahatis, Michael N. 11 Shi, Zhenjun 10 Fernandes, Edite M. G. P. 10 Grapsa, Theodoula N. 9 Eshima, Nobuoki 9 Tabata, Minoru 8 Magoulas, George D. 8 Rocha, Ana Maria A. C. 8 Shen, Jie 6 Costa, M. Fernanda P. 6 Laskari, E. C. 6 Meletiou, Gerasimos C. 6 Mourrain, Bernard 6 Parsopoulos, Konstantinos E. 6 Singh, Jagadish 5 Pavlidis, Nicos G. 5 Tasoulis, Dimitris K. 5 Yuan, Gonglin 4 Androulakis, George S. 4 Bäcker, Arnd 4 Bountis, Tassos C. 4 Boutsinas, Basilis 4 Katsanikas, Matthaios 4 Meiss, James D. 4 Perdios, Efstathios A. 4 Tawhid, Mohamed Aly 4 Wang, Yongjun 3 Barrio, Roberto 3 Bello, Nakone 3 Engelbrecht, Andries Petrus 3 Gasull, Armengol 3 Ip, Wai-Hung 3 Kalantonis, Vassilis S. 3 Kravanja, Peter 3 Mañosa, Víctor 3 Patsis, P. A. 3 Plagianakos, Vassilis P. 3 Sakai, Yuusuke 3 Segura, Javier 3 Stamatiou, Yannis C. 3 Stanimirović, Predrag S. 3 Tsigaridas, Elias P. 3 Wei, Zengxin 2 Abraham, Ajith 2 Alexandropoulos, Stamatios-Aggelos N. 2 Anastasiadis, Aristoklis D. 2 Antonopoulos, Chris G. 2 Arakawa, Masao 2 Archetti, Francesco 2 Barcelos, Manuel N. D. jun. 2 Bartz-Beielstein, Thomas 2 Blesa, Fernando 2 Borzabadi, Akbar Hashemi 2 Candelieri, Antonio 2 Chen, Hanning 2 Costa, Lino A. 2 Dai, Yu-Hong 2 Emiris, Ioannis Z. 2 Fan, Yingying 2 Fard, Omid Solaymani 2 Gao, Fei 2 Gil, Amparo 2 Groumpos, Peter P. 2 Gyegwe, Jessica Mrumun 2 Huang, Chongchao 2 Ivanov, Branislav 2 Jiang, Yan 2 Ketzmerick, Roland 2 Kitayama, Satoshi 2 Kotsireas, Ilias S. 2 Lange, Steffen 2 Li, Bin 2 Li, Pengyuan 2 Locatelli, Marco 2 Maute, Kurt 2 Nosratipour, Hadi 2 Onken, Franziska 2 Papageorgiou, Elpiniki I. 2 Pedroso, Dorival M. 2 Perego, Riccardo 2 Pereira, Ana Isabel P. N. 2 Petalas, Y. G. 2 Polymilis, C. 2 Ragos, Omiros 2 Schoen, Fabio 2 Servizi, Graziano 2 Sheng, Daichao 2 Skiniotis, Takis 2 Thota, Srinivasarao 2 Tong, Hengqing 2 Turchetti, Giorgio 2 van den Bergh, Frans 2 Vicente, Luis Nunes 2 Wang, Dingwei 2 Wang, Hongfeng 2 Wu, Xianing 2 Yakoubsohn, Jean-Claude 2 Yamazaki, Koetsu 2 Yang, Shengxiang 2 Yang, Xiaoqi ...and 594 more Authors all top 5 Cited in 146 Serials 31 Applied Mathematics and Computation 24 Journal of Computational and Applied Mathematics 15 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11 Journal of Global Optimization 9 Information Sciences 7 Journal of Symbolic Computation 7 Mathematical and Computer Modelling 6 Computers & Mathematics with Applications 6 Optimization 6 Numerical Algorithms 6 International Journal of Computer Mathematics 6 Mathematical Problems in Engineering 4 Astrophysics and Space Science 4 Chaos, Solitons and Fractals 4 Theoretical Computer Science 4 Physica D 4 Annals of Operations Research 4 European Journal of Operational Research 4 Pattern Recognition 4 Computational Optimization and Applications 4 Optimization Methods & Software 4 Chaos 4 Communications in Nonlinear Science and Numerical Simulation 4 Optimization and Engineering 3 Computer Methods in Applied Mechanics and Engineering 3 Journal of Mathematical Analysis and Applications 3 Mathematics of Computation 3 Applied Numerical Mathematics 3 Journal of Complexity 3 Abstract and Applied Analysis 3 Discrete Dynamics in Nature and Society 3 Nonlinear Analysis. 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Series B 1 Journal of Mathematical Imaging and Vision 1 Annals of Mathematics and Artificial Intelligence 1 Reliable Computing 1 Bernoulli ...and 46 more Serials all top 5 Cited in 41 Fields 167 Operations research, mathematical programming (90-XX) 114 Numerical analysis (65-XX) 64 Computer science (68-XX) 38 Dynamical systems and ergodic theory (37-XX) 22 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Mechanics of particles and systems (70-XX) 19 Statistics (62-XX) 17 Ordinary differential equations (34-XX) 16 Information and communication theory, circuits (94-XX) 13 Mechanics of deformable solids (74-XX) 13 Systems theory; control (93-XX) 12 Special functions (33-XX) 12 Partial differential equations (35-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 11 Biology and other natural sciences (92-XX) 8 Operator theory (47-XX) 7 Algebraic topology (55-XX) 5 Functions of a complex variable (30-XX) 5 Difference and functional equations (39-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Field theory and polynomials (12-XX) 4 Real functions (26-XX) 4 General topology (54-XX) 4 Fluid mechanics (76-XX) 4 Astronomy and astrophysics (85-XX) 3 Commutative algebra (13-XX) 3 Algebraic geometry (14-XX) 3 Probability theory and stochastic processes (60-XX) 2 Combinatorics (05-XX) 2 Approximations and expansions (41-XX) 2 Optics, electromagnetic theory (78-XX) 2 Relativity and gravitational theory (83-XX) 2 Geophysics (86-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year