@article {30,
	title = {Chaos and Music: From time series analysis to evolutionary composition},
	journal = {International Journal of Bifurcation and Chaos (IJBC)},
	volume = {23},
	year = {2013},
	pages = {1350181},
	abstract = {Music is an amalgam of logic and emotion, order and dissonance, along with many combinations of contradicting notions which allude to deterministic chaos. Therefore, it comes as no surprise that several research works have examined the utilization of dynamical systems for symbolic music composition. The main motivation of the paper at hand is the analysis of the tonal composition potentialities of several discrete dynamical systems, in comparison to genuine human compositions. Therefore, a set of human musical compositions is utilized to provide {\textquoteleft}{\textquoteleft}compositional guidelines{\textquoteright}{\textquoteright} to several dynamical systems, the parameters of which are properly adjusted through evolutionary computation. This procedure exposes the extent to which a system is capable of composing tonal sequences that resemble human composition. In parallel, a time series analysis on the genuine compositions is performed, which firstly provides an overview of their dynamical characteristics and secondly, allows a comparative analysis with the dynamics of the artificial compositions. The results expose the tonal composition capabilities of the examined iterative maps, providing specific references to the tonal characteristics that they can capture.},
	doi = {10.1142/S0218127413501812},
	url = {http://www.worldscientific.com/doi/abs/10.1142/S0218127413501812},
	author = {M. A. Kaliakatsos-Papakostas and M. G. Epitropakis and A. Floros and M. N. Vrahatis}
}
@article {4,
	title = {Controlling interactive evolution of 8-bit melodies with genetic programming},
	journal = {Soft Computing - A Fusion of Foundations, Methodologies and Applications},
	volume = {16},
	year = {2012},
	pages = {1997-2008},
	abstract = {Automatic music composition and sound synthesis is a field of study that gains continuously increasing attention. The introduction of evolutionary computation has further boosted the research towards exploring ways to incorporate human supervision and guidance in the automatic evolution of melodies and sounds. This kind of human{\textendash}machine interaction belongs to a larger methodological context called interactive evolution (IE). For the automatic creation of art and especially for music synthesis, user fatigue requires that the evolutionary process produces interesting content that evolves fast. This paper addresses this issue by presenting an IE system that evolves melodies using genetic programming (GP). A modification of the GP operators is proposed that allows the user to have control on the randomness of the evolutionary process. The results obtained by subjective tests indicate that the utilization of the proposed genetic operators drives the evolution to more user-preferable sounds.
},
	issn = {1432-7643},
	doi = {10.1007/s00500-012-0872-y},
	author = {M. A. Kaliakatsos{\textendash}Papakostas and M. G. Epitropakis and A. Floros and M. N. Vrahatis}
}
@article {3,
	title = {Evolving cognitive and social experience in Particle Swarm Optimization through Differential Evolution: A hybrid approach},
	journal = {Information Sciences},
	volume = {216},
	year = {2012},
	pages = {50-92},
	abstract = {In recent years, the Particle Swarm Optimization has rapidly gained increasing popularity and many variants and hybrid approaches have been proposed to improve it. In this paper, motivated by the behavior and the spatial characteristics of the social and cognitive experience of each particle in the swarm, we develop a hybrid framework that combines the Particle Swarm Optimization and the Differential Evolution algorithm. Particle Swarm Optimization has the tendency to distribute the best personal positions of the swarm particles near to the vicinity of problem{\textquoteright}s optima. In an attempt to efficiently guide the evolution and enhance the convergence, we evolve the personal experience or memory of the particles with the Differential Evolution algorithm, without destroying the search capabilities of the algorithm. The proposed framework can be applied to any Particle Swarm Optimization algorithm with minimal effort. To evaluate the performance and highlight the different aspects of the proposed framework, we initially incorporate six classic Differential Evolution mutation strategies in the canonical Particle Swarm Optimization, while afterwards we employ five state-of-the-art Particle Swarm Optimization variants and four popular Differential Evolution algorithms. Extensive experimental results on 25 high dimensional multimodal benchmark functions along with the corresponding statistical analysis, suggest that the hybrid variants are very promising and significantly improve the original algorithms in the majority of the studied cases.},
	issn = {0020-0255},
	doi = {10.1016/j.ins.2012.05.017},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@inbook {11,
	title = {Interactive Evolution of 8{\textendash}Bit Melodies with Genetic Programming towards Finding Aesthetic Measures for Sound},
	booktitle = {Evolutionary and Biologically Inspired Music, Sound, Art and Design},
	series = {Lecture Notes in Computer Science},
	volume = {7247},
	year = {2012},
	pages = {141-152},
	publisher = {Springer Berlin / Heidelberg},
	organization = {Springer Berlin / Heidelberg},
	abstract = {The efficient specification of aesthetic measures for music as a part of modelling human conception of sound is a challenging task and has motivated several research works. It is not only targeted to the creation of automatic music composers and raters, but also reinforces the research for a deeper understanding of human noesis. The aim of this work is twofold: first, it proposes an Interactive Evolution system that uses Genetic Programming to evolve simple 8{\textendash}bit melodies. The results obtained by subjective tests indicate that evolution is driven towards more user{\textendash}preferable sounds. In turn, by monitoring features of the melodies in different evolution stages, indications are provided that some sound features may subsume information about aesthetic criteria. The results are promising and signify that further study of aesthetic preference through Interactive Evolution may accelerate the progress towards defining aesthetic measures for sound and music.},
	isbn = {978-3-642-29141-8},
	doi = {10.1007/978-3-642-29142-5_13},
	author = {M. A. Kaliakatsos{\textendash}Papakostas and M. G. Epitropakis and A. Floros and M. N. Vrahatis},
	editor = {Penousal Machado and Juan Romero and Adrian Carballal}
}
@conference {7,
	title = {Multimodal Optimization Using Niching Differential Evolution with Index-based Neighborhoods},
	booktitle = {IEEE Congress on Evolutionary Computation, 2012. CEC 2012. (IEEE World Congress on Computational Intelligence)},
	year = {2012},
	month = {June},
	address = {Brisbane, Australia},
	abstract = {A new family of Differential Evolution mutation strategies (DE/nrand) that are able to handle multimodal functions, have been recently proposed. The DE/nrand family incorporates information regarding the real nearest neighborhood of each potential solution, which aids them to accurately locate and maintain many global optimizers simultaneously, without the need of additional parameters. However, these strategies have increased computational cost. To alleviate this problem, instead of computing the real nearest neighbor, we incorporate an index-based neighborhood into the mutation strategies. The new mutation strategies are evaluated on eight well-known and widely used multimodal problems and their performance is compared against five state-of-the-art algorithms. Simulation results suggest that the proposed strategies are promising and exhibit competitive behavior, since with a substantial lower computational cost they are able to locate and maintain many global optima throughout the evolution process.},
	doi = {10.1109/CEC.2012.6256480},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@inbook {10,
	title = {Tracking Differential Evolution Algorithms: An Adaptive Approach through Multinomial Distribution Tracking with Exponential Forgetting},
	booktitle = {Artificial Intelligence: Theories and Applications},
	series = {Lecture Notes in Computer Science},
	volume = {7297},
	year = {2012},
	pages = {214-222},
	publisher = {Springer Berlin / Heidelberg},
	organization = {Springer Berlin / Heidelberg},
	abstract = {Several Differential Evolution variants with modified search dynamics have been recently proposed, to improve the performance of the method. This work borrows ideas from adaptive filter theory to develop an {\textquotedblleft}online{\textquotedblright} algorithmic adaptation framework. The proposed framework is based on tracking the parameters of a multinomial distribution to reflect changes in the evolutionary process. As such, we design a multinomial distribution tracker to capture the successful evolution movements of three Differential Evolution algorithms, in an attempt to aggregate their characteristics and their search dynamics. Experimental results on ten benchmark functions and comparisons with five state-of-the-art algorithms indicate that the proposed framework is competitive and very promising.},
	isbn = {978-3-642-30447-7},
	doi = {10.1007/978-3-642-30448-4_27},
	author = {M. G. Epitropakis and D. K. Tasoulis and N. G. Pavlidis and V. P. Plagianakos and M. N. Vrahatis},
	editor = {Ilias Maglogiannis and Vassilis P. Plagianakos and Ioannis Vlahavas}
}
@conference {8,
	title = {Tracking Particle Swarm Optimizers: An adaptive approach through multinomial distribution tracking with exponential forgetting},
	booktitle = {IEEE Congress on Evolutionary Computation, 2012. CEC 2012. (IEEE World Congress on Computational Intelligence)},
	year = {2012},
	month = {June},
	address = {Brisbane, Australia},
	abstract = {An active research direction in Particle Swarm Optimization (PSO) is the integration of PSO variants in adaptive, or self-adaptive schemes, in an attempt to aggregate their characteristics and their search dynamics. In this work we borrow ideas from adaptive filter theory to develop an {\textquotedblleft}online{\textquotedblright} algorithm adaptation framework. The proposed framework is based on tracking the parameters of a multinomial distribution to capture changes in the evolutionary process. As such, we design a multinomial distribution tracker to capture the successful evolution movements of three PSO variants. Extensive experimental results on ten benchmark functions and comparisons with five state-of-the-art algorithms indicate that the proposed framework is competitive and very promising. On the majority of tested cases, the proposed framework achieves substantial performance gain, while it seems to identify accurately the most appropriate algorithm for the problem at hand.},
	doi = {10.1109/CEC.2012.6256425},
	author = {M. G. Epitropakis and D. K. Tasoulis and N. G. Pavlidis and V. P. Plagianakos and M. N. Vrahatis}
}
@article {5,
	title = {Enhancing Differential Evolution Utilizing Proximity-based Mutation Operators},
	journal = {IEEE Transactions on Evolutionary Computation},
	volume = {15},
	year = {2011},
	pages = {99-119},
	abstract = {Differential evolution is a very popular optimization algorithm and considerable research has been devoted to the development of efficient search operators. Motivated by the different manner in which various search operators behave, we propose a novel framework based on the proximity characteristics among the individual solutions as they evolve. Our framework incorporates information of neighboring individuals, in an attempt to efficiently guide the evolution of the population toward the global optimum, without sacrificing the search capabilities of the algorithm. More specifically, the random selection of parents during mutation is modified, by assigning to each individual a probability of selection that is inversely proportional to its distance from the mutated individual. The proposed framework can be applied to any mutation strategy with minimal changes. In this paper, we incorporate this framework in the original differential evolution algorithm, as well as other recently proposed differential evolution variants. Through an extensive experimental study, we show that the proposed framework results in enhanced performance for the majority of the benchmark problems studied.},
	issn = {1089-778X},
	doi = {10.1109/TEVC.2010.2083670},
	author = {M. G. Epitropakis and D. K. Tasoulis and N. G. Pavlidis and V. P. Plagianakos and M. N. Vrahatis}
}
@inbook {25,
	title = {Feature Extraction Using Pitch Class Profile Information Entropy},
	booktitle = {Mathematics and Computation in Music},
	series = {Lecture Notes in Computer Science},
	volume = {6726},
	year = {2011},
	pages = {354-357},
	publisher = {Springer Berlin / Heidelberg},
	organization = {Springer Berlin / Heidelberg},
	abstract = {Computer aided musical analysis has led a research stream to explore the description of an entire musical piece by a single value. Combinations of such values, often called global features, have been used for several identification tasks on pieces with symbolic music representation. In this work we extend some ideas that estimate information entropy of sections of musical pieces, to utilize the Pitch Class Profile information entropy for global feature extraction. Two approaches are proposed and tested, the first approach considers musical sections as overlapping sliding onset windows, while the second one as non-overlapping fixed-length time windows.},
	doi = {10.1007/978-3-642-21590-2_32},
	url = {http://dx.doi.org/10.1007/978-3-642-21590-2_32},
	author = {M. A. Kaliakatsos-Papakostas and M. G. Epitropakis and M. N. Vrahatis},
	editor = {Agon, Carlos and Andreatta, Moreno and Assayag, G{\'e}rard and Amiot, Emmanuel and Bresson, Jean and Mandereau, John}
}
@conference {12,
	title = {Finding Multiple Global Optima Exploiting Differential Evolution{\textquoteright}s Niching Capability},
	booktitle = {IEEE Symposium on Differential Evolution, 2011. SDE 2011. (IEEE Symposium Series on Computational Intelligence)},
	year = {2011},
	month = {April},
	address = {Paris, France},
	abstract = {Handling multimodal functions is a very important and challenging task in evolutionary computation community, since most of the real-world applications exhibit highly multi-modal landscapes. Motivated by the dynamics and the proximity characteristics of Differential Evolution{\textquoteright}s mutation strategies tending to distribute the individuals of the population to the vicinity of the problem{\textquoteright}s minima, we introduce two new Differential Evolution mutation strategies. The new mutation strategies incorporate spatial information about the neighborhood of each potential solution and exhibit a niching formation, without incorporating any additional parameter. Experimental results on eight well known multimodal functions and comparisons with some state-of-the-art algorithms indicate that the proposed mutation strategies are competitive and very promising, since they are able to reliably locate and maintain many global optima throughout the evolution process.},
	doi = {10.1109/SDE.2011.5952058},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@article {6,
	title = {Studying the basin of convergence of methods for computing periodic orbits},
	journal = {International Journal of Bifurcation and Chaos (IJBC)},
	volume = {21},
	year = {2011},
	pages = {1-28},
	abstract = {Starting from the well-known Newton{\textquoteright}s fractal which is formed by the basin of convergence of Newton{\textquoteright}s method applied to a cubic equation in one variable in the field ℂ, we were able to find methods for which the corresponding basins of convergence do not exhibit a fractal-like structure. Using this approach we are able to distinguish reliable and robust methods for tackling a specific problem. Also, our approach is illustrated here for methods for computing periodic orbits of nonlinear mappings as well as for fixed points of the Poincar{\'e} map on a surface of section.},
	doi = {10.1142/S0218127411029653},
	author = {M. G. Epitropakis and M. N. Vrahatis}
}
@conference {13,
	title = {Weighted Markov Chain Model for Musical Composer Identification},
	booktitle = {Applications of Evolutionary Computation},
	year = {2011},
	publisher = {Springer Berlin / Heidelberg},
	organization = {Springer Berlin / Heidelberg},
	abstract = {Several approaches based on the {\textquoteleft}Markov chain model{\textquoteright} have been proposed to tackle the composer identification task. In the paper at hand, we propose to capture phrasing structural information from inter onset and pitch intervals of pairs of consecutive notes in a musical piece, by incorporating this information into a weighted variation of a first order Markov chain model. Additionally, we propose an evolutionary procedure that automatically tunes the introduced weights and exploits the full potential of the proposed model for tackling the composer identification task between two composers. Initial experimental results on string quartets of Haydn, Mozart and Beethoven suggest that the proposed model performs well and can provide insights on the inter onset and pitch intervals on the considered musical collection.},
	doi = {10.1007/978-3-642-20520-0_34},
	author = {M. A. Kaliakatsos-Papakostas and M. G. Epitropakis and M. N. Vrahatis},
	editor = {Di Chio, Cecilia and Brabazon, Anthony and Di Caro, Gianni and Drechsler, Rolf and Farooq, Muddassar and Grahl, J{\"o}rn and Greenfield, Gary and Prins, Christian and Romero, Juan and Squillero, Giovanni and Tarantino, Ernesto and Tettamanzi, Andrea and Urquhart, Neil and Uyar, A.}
}
@conference {16,
	title = {Evolving cognitive and social experience in Particle Swarm Optimization through Differential Evolution},
	booktitle = {IEEE Congress on Evolutionary Computation, 2010. CEC 2010. (IEEE World Congress on Computational Intelligence)},
	year = {2010},
	month = {July},
	address = {Barcelona, Spain},
	abstract = {In recent years, the Particle Swarm Optimization has rapidly gained increasing popularity and many variants and hybrid approaches have been proposed to improve it. Motivated by the behavior and the proximity characteristics of the social and cognitive experience of each particle in the swarm, we develop a hybrid approach that combines the Particle Swarm Optimization and the Differential Evolution algorithm. Particle Swarm Optimization has the tendency to distribute the best personal positions of the swarm near to the vicinity of problem{\textquoteright}s optima. In an attempt to efficiently guide the evolution and enhance the convergence, we evolve the personal experience of the swarm with the Differential Evolution algorithm. Extensive experimental results on twelve high dimensional multimodal benchmark functions indicate that the hybrid variants are very promising and improve the original algorithm.},
	keywords = {cognitive experience, convergence, differential evolution, evolutionary computation, particle swarm optimisation, particle swarm optimization, social experience},
	doi = {10.1109/CEC.2010.5585967},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@article {14,
	title = {Hardware-Friendly Higher-Order Neural Network Training Using Distributed Evolutionary Algorithms},
	journal = {Applied Soft Computing},
	volume = {10},
	year = {2010},
	pages = {398-408},
	abstract = {In this paper, we study the class of Higher-Order Neural Networks and especially the Pi-Sigma Networks. The performance of Pi-Sigma Networks is evaluated through several well known Neural Network Training benchmarks. In the experiments reported here, Distributed Evolutionary Algorithms are implemented for Pi-Sigma neural networks training. More specifically the distributed versions of the Differential Evolution and the Particle Swarm Optimization algorithms have been employed. To this end, each processor is assigned a subpopulation of potential solutions. The subpopulations are independently evolved in parallel and occasional migration is employed to allow cooperation between them. The proposed approach is applied to train Pi-Sigma Networks using threshold activation functions. Moreover, the weights and biases were confined to a narrow band of integers, constrained in the range [-32,32]. Thus, the trained Pi-Sigma neural networks can be represented by using 6~bits. Such networks are better suited than the real weight ones for hardware implementation and to some extend are immune to low amplitude noise that possibly contaminates the training data. Experimental results suggest that the proposed training process is fast, stable and reliable and the distributed trained Pi-Sigma Networks exhibited good generalization capabilities.},
	keywords = {Higher-Order Neural Networks},
	issn = {1568-4946},
	doi = {10.1016/j.asoc.2009.08.010},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@conference {17,
	title = {Musical Composer Identification through Probabilistic and Feedforward Neural Networks},
	booktitle = {Applications of Evolutionary Computation},
	year = {2010},
	publisher = {Springer Berlin / Heidelberg},
	organization = {Springer Berlin / Heidelberg},
	abstract = {During the last decade many efforts for music information retrieval have been made utilizing Computational Intelligence methods. Here, we examine the information capacity of the Dodecaphonic Trace Vector for composer classification and identification. To this end, we utilize Probabilistic Neural Networks for the construction of a similarity matrix of different composers and analyze the Dodecaphonic Trace Vector{\textquoteright}s ability to identify a composer through trained Feedforward Neural Networks. The training procedure is based on classical gradient-based methods as well as on the Differential Evolution algorithm. An experimental analysis on the pieces of seven classical composers is presented to gain insight about the most important strengths and weaknesses of the aforementioned approach.},
	doi = {10.1007/978-3-642-12242-2\_42},
	author = {M. A. Kaliakatsos-Papakostas and M. G. Epitropakis and M. N. Vrahatis},
	editor = {Di Chio, Cecilia and Brabazon, Anthony and Di Caro, Gianni and Ebner, Marc and Farooq, Muddassar and Fink, Andreas and Grahl, J{\"o}rn and Greenfield, Gary and Machado, Penousal and O{\textquoteright}Neill, Michael and Tarantino, Ernesto and Urquhart, Neil}
}
@conference {18,
	title = {Evolutionary Adaptation of the Differential Evolution Control Parameters},
	booktitle = {IEEE Congress on Evolutionary Computation, 2009. CEC 2009},
	year = {2009},
	month = {May},
	address = {Trondheim, Norway},
	abstract = {This paper proposes a novel self-adaptive scheme for the evolution of crucial control parameters in evolutionary algorithms. More specifically, we suggest to utilize the differential evolution algorithm to endemically evolve its own control parameters. To achieve this, two simultaneous instances of Differential Evolution are used, one of which is responsible for the evolution of the crucial user-defined mutation and recombination constants. This self-adaptive differential evolution algorithm alleviates the need of tuning these user-defined parameters while maintains the convergence properties of the original algorithm. The evolutionary self-adaptive scheme is evaluated through several well-known optimization benchmark functions and the experimental results indicate that the proposed approach is promising.},
	keywords = {adaptive control, differential evolution control parameter, evolutionary adaptation, evolutionary computation, optimisation, optimization, self-adaptive differential evolution algorithm, self-adjusting systems, user-defined parameter tuning},
	doi = {10.1109/CEC.2009.4983102},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@inbook {24,
	title = {Evolutionary Algorithm Training of Higher-Order Neural Networks},
	booktitle = {Artificial Higher Order Neural Networks for Computer Science and Engineering: Tends for Emerging Applications},
	year = {2009},
	publisher = {IGI Global},
	organization = {IGI Global},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis},
	editor = {Ming Zhang}
}
@conference {19,
	title = {Balancing the exploration and exploitation capabilities of the Differential Evolution Algorithm},
	booktitle = {IEEE Congress on Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence)},
	year = {2008},
	month = {June},
	address = {Hong Kong},
	abstract = {The hybridization and composition of different Evolutionary Algorithms to improve the quality of the solutions and to accelerate execution is a common research practice. In this paper we propose a hybrid approach that combines differential evolution mutation operators in an attempt to balance their exploration and exploitation capabilities. Additionally, a self-balancing hybrid mutation operator is presented, which favors the exploration of the search space during the first phase of the optimization, while later opts for the exploitation to aid convergence to the optimum. Extensive experimental results indicate that the proposed approaches effectively enhance DEpsilas ability to accurately locate solutions in the search space.},
	keywords = {differential evolution algorithm, evolutionary computation, optimization, search problems, self-balancing hybrid mutation operator},
	doi = {10.1109/CEC.2008.4631159},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@conference {20,
	title = {Non-Monotone Differential Evolution},
	booktitle = {Proceedings of the 10th annual inproceedings on Genetic evolutionary computation, GECCO 2008},
	year = {2008},
	publisher = {ACM},
	organization = {ACM},
	address = {New York, NY, USA},
	abstract = {The Differential Evolution algorithm uses an elitist selection, constantly pushing the population in a strict downhill search, in an attempt to guarantee the conservation of the best individuals. However, when this operator is combined with an exploitive mutation operator can lead to premature convergence to an undesired region of attraction. To alleviate this problem, we propose the Non-Monotone Differential Evolution algorithm. To this end, we allow the best individual to perform some uphill movements, greatly enhancing the exploration of the search space. This approach further aids algorithm{\textquoteright}s ability to escape undesired regions of the search space and improves its performance. The proposed approach utilizes already computed pieces of information and does not require extra function evaluations. Experimental results indicate that the proposed approach provides stable and reliable convergence." keywords = "differential evolution, evolutionary algorithms, global optimization, non-monotone differential evolution},
	isbn = {978-1-60558-130-9},
	doi = {http://doi.acm.org/10.1145/1389095.1389195},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@conference {21,
	title = {Computational Intelligence Algorithms For Risk-Adjusted Trading Strategies},
	booktitle = {IEEE Congress on Evolutionary Computation, 2007. CEC 2007},
	year = {2007},
	month = {September},
	address = {Singapore},
	abstract = {This paper investigates the performance of trading strategies identified through computational intelligence techniques. We focus on trading rules derived by genetic programming, as well as, generalized moving average rules optimized through differential evolution. The performance of these rules is investigated using recently proposed risk-adjusted evaluation measures and statistical testing is carried out through simulation. Overall, the moving average rules proved to be more robust, but genetic programming seems more promising in terms of generating higher profits and detecting novel patterns in the data.},
	keywords = {computational intelligence algorithm, differential evolution, financial market, foreign exchange market, foreign exchange trading, generalized moving average rule, genetic algorithms, genetic programming, optimization, pattern detection, risk analysis, risk-adjusted trading strategy, statistical testing},
	doi = {10.1109/CEC.2007.4424517},
	author = {N. G. Pavlidis and E. G. Pavlidis and M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@conference {22,
	title = {Higher-Order Neural Networks Training Using Differential Evolution},
	booktitle = {International Conference of Numerical Analysis and Applied Mathematics},
	year = {2006},
	publisher = {Wiley-VCH},
	organization = {Wiley-VCH},
	address = {Hersonissos, Crete, Greece},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@conference {23,
	title = {Integer Weight Higher-Order Neural Network Training Using Distributed Differential Evolution},
	booktitle = {International Conference of Computational Methods in Sciences and Engineering},
	year = {2006},
	publisher = {LSCCS},
	organization = {LSCCS},
	address = {Crete, Greece},
	author = {M. G. Epitropakis and V. P. Plagianakos and M. N. Vrahatis}
}
@article {15,
	title = {Root finding and approximation approaches through neural networks},
	journal = {ACM SIGSAM Bulleting},
	volume = {39},
	year = {2005},
	pages = {118-121},
	abstract = {In this paper, we propose two approaches to approximate high order multivariate polynomials and to estimate the number of roots of high order univariate polynomials. We employ high order neural networks such as Ridge Polynomial Networks and Pi -- Sigma Networks, respectively. To train the networks efficiently and effectively, we recommend the application of stochastic global optimization techniques. Finally, we propose a two step neural network based technique, to estimate the number of roots of a high order univariate polynomial.
},
	issn = {0163-5824},
	doi = {http://doi.acm.org/10.1145/1140378.1140382},
	author = {M. G. Epitropakis and M. N. Vrahatis}
}
