Alberto Cano is an Assistant Professor with the Department of Computer Science, Virginia Commonwealth University, Richmond, Virginia, United States, where he heads the High-Performance Data Mining laboratory. His research is focused on machine learning, data mining, big data, evolutionary computation, general-purpose computing on graphics processing units, and distributed computing.

Department of Computer Science, College of Engineering, Virginia Commonwealth University

401 W. Main St, East Hall, E4251, Richmond, Virginia, United States

+1 (804) 827-4002

acano@vcu.edu

Education

  • Ph.D. in Computer Science, University of Granada, Spain, 2014.
  • M.Sc. in Intelligent Systems, University of Córdoba, Spain, 2013.
  • M.Sc. in Soft Computing and Intelligent Systems, University of Granada, Spain, 2011.
  • B.Sc. in Computer Science, University of Córdoba, Spain, 2010.
  • B.Sc. in Computer Engineering, University of Córdoba, Spain, 2008.

Research

Director of the High-Performance Data Mining laboratory at the Virginia Commonwalth University

Graduate, summer, and visiting research positions are available in the areas of machine learning, data mining, and high performance computing. Please reach me by email at acano@vcu.edu.

Research projects (Principal Investigator)

  • Industry Sponsored Research, Hamilton Beach Brands Inc., 2019-2020.
  • Hate Speech Detection on Amazon Reviews using Data Stream Mining on Spark and AWS, Amazon Machine Learning Awards, 2018-2019.
  • Interpretable Data Mining Models for Early Prediction of Student Performance and Dropout, VCU Presidential Research Quest Fund, 2018-2019.

Research projects (Participant)

  • Emerging Trends in Data Analysis, Spanish Ministry of Economy and Enterprise, 2018-2020.
  • HEETF: High-throughput Power Edge System for Big Data & Modeling, State council of higher education for Virginia, 2017-2020.
  • Diagnosis and post-surgical prognosis employing a new interactomic personalized approach for human glioma, Junta de Andalucía, Spain, 2017-2019.
  • Data Mining with Flexible Representations, Spanish Ministry of Economy and Enterprise, 2015-2017.
  • New Challenges in Knowledge Discovery: A Genetic Programming Approach, Spanish Ministry of Science and Innovation, 2012-2014.
  • Knowledge extraction in Educational Data, Junta de Andalucía, Spain, 2009-2012.

Ph.D. adviser (Graduated)

  • J. Gonzalez-Lopez, Distributed multi-label learning on Apache Spark, 2016-2019.
  • G. Melki, Novel Support Vector Machines for Diverse Learning Paradigms, 2016-2018.

Ph.D. adviser (Current)

  • M. Roseberry, Adaptive multi-label classification for drifting data streams, 2018-2022.

Publications

Journal articles

  1. A. Cano and B. Krawczyk. Evolving Rule-Based Classifiers with Genetic Programming on GPUs for Drifting Data Streams. Pattern Recognition, vol. 87, 248-268, 2019.
  2. H.T. Nguyen, A. Cano, V. Tam, and T.N. Dinh. Blocking Self-avoiding Walks Stops Cyber-epidemics: A Scalable GPU-based Approach. IEEE Transactions on Knowledge and Data Engineering, In press, 2019.
  3. A. Cano and J.D. Leonard. Interpretable Multi-view Early Warning System adapted to Underrepresented Student Populations. IEEE Transactions on Learning Technologies, 12(2), 198-211, 2019.
  4. Y. Djenouri, A. Belhadi, J. Lin, D. Djenouri, and A. Cano. A Survey on Urban Traffic Anomalies Detection Algorithms. IEEE Access, vol. 7, 12192-12205, 2019.
  5. Y. Djenouri, A. Belhadi, J. Lin, and A. Cano. Adapted k Nearest Neighbors for Detecting Anomalies on Spatio-Temporal Traffic Flow. IEEE Access, vol. 7, 10015-10027, 2019.
  6. P. Skryjomski, B. Krawczyk, and A. Cano. Speeding up k-Nearest Neighbors Classifier for Large-Scale Multi-Label Learning on GPUs. Neurocomputing, vol. 354, 10-19, 2019.
  7. Y. Djenouri, D. Djenouri, A. Belhadi, and A. Cano. Exploiting GPU and Cluster Parallelism in Single Scan Frequent Itemset Mining. Information Sciences, vol. 496, 363-377, 2019.
  8. A. Cano. A survey on graphic processing unit computing for large-scale data mining. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 8(1), e1232, 2018.
  9. J. Gonzalez-Lopez, S. Ventura, and A. Cano. Distributed Nearest Neighbor Classification for Large-Scale Multi-label Data on Spark. Future Generation Computer Systems, vol. 87, 66-82, 2018.
  10. G. Melki, V. Kecman, S. Ventura, and A. Cano. OLLAWV: OnLine Learning Algorithm using Worst-Violators. Applied Soft Computing, vol. 66, 384-393, 2018.
  11. G. Melki, A. Cano, and S. Ventura. MIRSVM: Multi-Instance Support Vector Machine with Bag Representatives. Pattern Recognition, vol. 79, 228-241, 2018.
  12. B. Krawczyk and A. Cano. Online Ensemble Learning with Abstaining Classifiers for Drifting and Noisy Data Streams. Applied Soft Computing, vol. 68, 677-692, 2018.
  13. A. Cano, E. Yeguas-Bolivar, R. Muñoz-Salinas, R. Medina-Carnicer, and S. Ventura. Parallelization Strategies for Markerless Human Motion Capture. Journal of Real-Time Image Processing, 14(2), 453-467, 2018.
  14. O. Reyes, A. Cano, H. Fardoun, and S. Ventura. A locally weighted learning method based on a data gravitation model for multi-target regression. International Journal of Computational Intelligence Systems, 11(1), 282-295, 2018.
  15. A. Cano. An ensemble approach to multi-view multi-instance learning. Knowledge-Based Systems, vol. 136, 46-57, 2017.
  16. A. Cano, C. Garcia, and S. Ventura. Extremely High-dimensional Optimization with MapReduce: Scaling Functions and Algorithm. Information Sciences, vol. 415-416, 110-127, 2017.
  17. G. Melki, A. Cano, V. Kecman, and S. Ventura. Multi-Target Support Vector Regression Via Correlation Regressor Chains. Information Sciences, vol. 415-416, 53-69, 2017.
  18. A. Cano, S. Ventura, and K.J. Cios. Multi-Objective Genetic Programming for Feature Extraction and Data Visualization. Soft Computing, 21(8), 2069-2089, 2017.
  19. J.M. Luna, A. Cano, V. Sakalauskas, and S. Ventura. Discovering Useful Patterns from Multiple Instance Data. Information Sciences, vol. 357, 23-38, 2016.
  20. A. Cano, J.M. Luna, E.L. Gibaja, and S. Ventura. LAIM discretization for multi-label data. Information Sciences, vol. 330, 370-384, 2016.
  21. A. Cano, D.T. Nguyen, S. Ventura and K.J. Cios. ur-CAIM: improved CAIM discretization for unbalanced and balanced data. Soft Computing, 20(1), 173-188, 2016.
  22. J.M. Luna, A. Cano, M. Pecheniskiy, and S. Ventura. Speeding-up Association Rule Mining with Inverted Index Compression. IEEE Transactions on Cybernetics, 46(12), 3059-3072, 2016.
  23. C. Márquez-Vera, A. Cano, C. Romero, A. Yousef Mohammad, H. Mousa Fardoun, and S. Ventura. Early Dropout Prediction using Data Mining: A Case Study with High School Students. Expert Systems, 33(1), 107-124, 2016.
  24. A. Cano, J.M. Luna, A. Zafra, and S. Ventura. A Classification Module for Genetic Programming Algorithms in JCLEC. Journal of Machine Learning Research, vol. 16, 491-494, 2015.
  25. A. Cano, A. Zafra, and S. Ventura. Speeding up multiple instance learning classification rules on GPUs. Knowledge and Information Systems, 44(1), 127-145, 2015.
  26. A. Cano, S. Ventura, and K.J. Cios. Scalable CAIM discretization on multiple GPUs using concurrent kernels. Journal of Supercomputing, 69(1), 273-292, 2014.
  27. A. Cano, A. Zafra, and S. Ventura. Parallel evaluation of Pittsburgh rule-based classifiers on GPUs. Neurocomputing, vol. 126, 45-57, 2014.
  28. C. Márquez-Vera, A. Cano, C. Romero, and S. Ventura. Predicting student failure at school using genetic programming and different data mining approaches with high dimensional and imbalanced data. Applied Intelligence, 38 (3), 315-330, 2013.
  29. A. Cano, J.M. Luna, and S. Ventura. High Performance Evaluation of Evolutionary-Mined Association Rules on GPUs. Journal of Supercomputing, 66(3), 1438-1461, 2013.
  30. A. Cano, A. Zafra, and S. Ventura. An Interpretable Classification Rule Mining Algorithm. Information Sciences, vol. 240, 1-20, 2013.
  31. A. Cano, J.L. Olmo, and S. Ventura. Parallel Multi-Objective Ant Programming for Classification Using GPUs. Journal of Parallel and Distributed Computing, 73 (6), 713-728, 2013.
  32. A. Cano, A. Zafra, and S. Ventura. Weighted Data Gravitation Classification for Standard and Imbalanced Data. IEEE Transactions on Cybernetics, 43 (6) pages 1672-1687, 2013.
  33. A. Cano, A. Zafra, and S. Ventura. Speeding up the evaluation phase of GP classification algorithms on GPUs. Soft Computing, 16 (2), 187-202, 2012.

Edited books

  1. A. Cano, Social Media and Machine Learning, InTech, ISBN 978-1-78984-028-5, 2018.
  2. S. Ventura, J. M. Luna, and A. Cano, Big Data on Real-World Applications, InTech, ISBN 978-953-51-2490-0, 2016.

Book chapters

  1. J.M. Luna, A. Cano and S. Ventura. Genetic Programming for Mining Association Rules in Relational Database Environments. In Handbook of Genetic Programming Applications, Springer, 2015. ISBN 978-3-319-20882-4.
  2. J.M. Luna, A. Cano and S. Ventura. An Evolutionary Self-Adaptive Algorithm for Mining Association Rules. In Data Mining: Principles, Applications and Emerging Challenges, Nova Publishers, 2015. ISBN 978-1-63463-770-1.

International conference contributions

  1. B. Krawczyk and A. Cano. Adaptive ensemble active learning for drifting data stream mining. In International Joint Conference on Artificial Intelligence, 2763-2771, 2019.
  2. J. Gonzalez-Lopez, S. Ventura, and A. Cano. ARFF data source library for distributed single/multiple instance, single/multiple output learning on Apache Spark. In International Conference on Computational Science, 173-179, 2019.
  3. J.M. Moyano, E. Gibaja, S. Ventura, and A. Cano. Speeding up Classifier Chains in Multi-Label Classification. In International Conference on Internet of Things, Big Data and Security, 29-37, 2019.
  4. M. Roseberry and A. Cano. Multi-label kNN Classifier with Self Adjusting Memory for Drifting Data Streams. In Second International Workshop on Learning with Imbalanced Domains: Theory and Applications, LIDTA@PKDD/ECML, PMLR 94:23-37, 2018.
  5. A. Cano and B. Krawczyk. Learning classification rules with differential evolution for high-speed data stream mining on GPUs. In IEEE Congress on Evolutionary Computation, 197-204, 2018.
  6. B. Krawczyk, A. Cano, and M. Wozniak. Selecting local ensembles for multi-class imbalanced data classification. In International Joint Conference on Neural Networks, 1848-1855, 2018.
  7. J. Gonzalez-Lopez, A. Cano, and S. Ventura. Large-scale multi-label ensemble learning on Spark. In IEEE Trustcom/BigDataSE/ICESS, 893-900, 2017.
  8. A. Olex, B. McInnes, and A. Cano. Parsing MetaMap Files in Hadoop. In American Medical Informatics Association Symposium, 2017.
  9. B. Krawczyk, B. McInnes, and A. Cano. Sentiment Classification from Multi-Class Imbalanced Twitter Data using Binarization. In 12th International Conference on Hybrid Artificial Intelligent Systems, Lecture Notes in Computer Science, vol 10334, 26-37, 2017.
  10. A. Cano and C. Garcia-Martinez. 100 Million Dimensions Large-Scale Global Optimization Using Distributed GPU Computing. In IEEE Congress on Evolutionary Computation, 3566-3573, 2016.
  11. F. Padillo, J.M. Luna, A. Cano, and S. Ventura. A Data Structure to Speed-Up Machine Learning Algorithms on Massive Datasets. In 11th International Conference on Hybrid Artificial Intelligent Systems. Lecture Notes in Computer Science, vol 9648, 365-376, 2016.
  12. D. Pinheiro, A. Cano and S. Ventura. Synthesis of In-Place Iterative Sorting Algorithms Using GP: A Comparison Between STGP, SFGP, G3P and GE. In 17th Portuguese Conference on Artificial Intelligence. Lecture Notes in Computer Science, vol 9273, 305-310, 2015.
  13. A. Cano and S. Ventura. GPU-parallel subtree interpreter for genetic programming. In Conference on Genetic and Evolutionary Computation, 887-894, 2014.
  14. J.A. Pedraza, C. Garcia-Martinez, A. Cano, and S. Ventura. Classification Rule Mining with Iterated Greedy. In 9th International Conference on Hybrid Artificial Intelligent Systems (HAIS). Lecture Notes in Computer Science, 8480 LNCS:585-596, 2014.
  15. A. Cano, A. Zafra, E.L. Gibaja, and S. Ventura. A Grammar-Guided Genetic Programming Algorithm for Multi-Label Classification. In 16th European Conference on Genetic Programming, EuroGP'13. Lecture Notes in Computer Science, vol 7831, 217-228, 2013.
  16. J.L. Olmo, A. Cano, J.R. Romero, and S. Ventura. Binary and Multiclass Imbalanced Classification Using Multi-Objective Ant Programming. In 12th International Conference on Intelligent Systems Design and Applications, ISDA'12, 70-76, 2012.
  17. A. Cano, A. Zafra, and S. Ventura. An EP algorithm for learning highly interpretable classifiers. In 11th International Conference on Intelligent Systems Design and Applications, ISDA'11, 325-330, 2011.
  18. A. Cano, A. Zafra, and S. Ventura. A parallel genetic programming algorithm for classification. In 6th International Conference on Hybrid Artificial Intelligent Systems (HAIS). Lecture Notes in Computer Science, 6678 LNAI(PART 1):172-181, 2011.
  19. A. Cano, J.M. Luna, J.L. Olmo, and S. Ventura. JCLEC meets WEKA! In 6th International Conference on Hybrid Artificial Intelligent Systems (HAIS). Lecture Notes in Computer Science, 6678 LNAI(PART 1):388-395, 2011.
  20. A. Cano, A. Zafra, and S. Ventura. Solving classification problems using genetic programming algorithms on GPUs. In 5th International Conference on Hybrid Artificial Intelligent Systems (HAIS). Lecture Notes in Computer Science, 6077 LNAI(PART 2):17-26, 2010.
  21. J. Fernández-Berni, R. Carmona-Galán, L. Carranza-González, A. Cano-Rojas, J. F. Martínez-Carmona, Á. Rodríguez-Vázquez, and S. Morillas-Castillo. On-site forest fire smoke detection by low-power autonomous vision sensor. In VI International Conference on Forest Fire Research, page 94, 2010.

National conference contributions

  1. A. Cano and C. Garcia-Martinez. Optimización con 100 millones de variables reales sobre múltiples unidades de procesamiento gráfico. XI Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB), 377-386, 2016.
  2. F. Ibáñez A. Cano, and S. Ventura. Evaluación distribuida transparente para algoritmos evolutivos en JCLEC. II Jornadas de Algoritmos Evolutivos y Metaheurísticas (XVI CAEPIA), 231-240, 2015.
  3. J.M. Moyano, E.L. Gibaja, A. Cano, J.M. Luna, and S. Ventura. Diseño Automático de Multi-Clasificadores Basados en Proyecciones de Etiquetas. II Jornadas de Fusión de la Información y ensembles (XVI CAEPIA), 355-366, 2015.
  4. J.M. Moyano, E.L. Gibaja, A. Cano, J.M. Luna, and S. Ventura. Algoritmo evolutivo para optimizar ensembles de clasificadores multi-etiqueta. X Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB), 219-225, 2015.
  5. A. Cano, J.L. Olmo, and S. Ventura. Programación Automática con Colonias de Hormigas Multi-Objetivo en GPUs. IX Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB), 288-297, 2013.
  6. A. Cano, A. Zafra, and S. Ventura. Parallel Data Mining Algorithms on GPUs. Doctoral Consortium de la Conferencia de la Asociación Española para la Inteligencia Artificial (CAEPIA), 1603-1606, 2013.
  7. A. Cano, J.M. Luna, A. Zafra, and S. Ventura. Modelo gravitacional para clasificación. VIII Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB), 63-70, 2012.
  8. J.L. Olmo, A. Cano, J.R. Romero, and S. Ventura. Programación con Hormigas Multi-Objetivo para la Extracción de Reglas de Clasificación. VIII Congreso Español sobre Metaheurísticas, Algoritmos Evolutivos y Bioinspirados (MAEB), 219-226, 2012.
  9. A. Cano, A. Zafra, and S. Ventura. Speeding up evolutionary learning algorithms using GPUs. In ESTYLF 2010 XV Congreso Español sobre Tecnologías y Lógica Fuzzy, 229-234, 2010.
  10. R. Molina, J. Jiménez, C. Sánchez, and A. Cano. Adecuación de la red WiFi para cumplimiento de la normativa y permitir acceso a internet a los pacientes. In XI Congreso Nacional de Informática de la Salud, 2008.

Teaching

  • 2016 - to date: Spr. CMSC 508 - Database Theory.
  • 2016 - to date: Fall. CMSC 603 - High Performance Distributed Systems.

Teaching publications

  1. A. Cano and A. Rojas. Autómatas celulares y aplicaciones. UNIÓN. Revista Iberoamericana de Educación Matemática, (46):33-48, 2016.
  2. A. Cano, J.M. Luna, and A. Rojas. Cómo compartir un secreto usando sistemas de ecuaciones lineales. Suma, (79):33-39, 2015.
  3. A. Rojas and A. Cano. Cifrado de imágenes y matemáticas. TE&ET. Revista Iberoamericana de Tecnología en Educación y Educación en Tecnología, (6):30-37, 2011.
  4. A. Rojas and A. Cano. Una clase de aritmética modular, matrices y cifrado para ingeniería. UNIÓN. Revista Iberoamericana de Educación Matemática, 1(25):89-108, 2011.
  5. A. Rojas and A. Cano. Trabajando con imágenes digitales en clase de matemáticas. La Gaceta de la Real Sociedad Matemática Española, 2(13):317-336, 2010.
  6. A. Rojas and A. Cano. Interpolación polinómica y la división de secretos. In XIV Congreso de Enseñanza y Aprendizaje de las Matemáticas, 2012.
  7. A. Rojas and A. Cano. Motivando el aprendizaje del Álgebra lineal a través de sus aplicaciones: la división de secretos. In XX Congreso universitario de innovación educativa en las enseñanzas técnicas, 2012.
  8. E. Gibaja, A. Zafra, M. Luque, and A. Cano. Recursos didácticos en el grado en ingeniería informática para el aprendizaje de matemáticas a través de la programación de ordenadores. In II Jornadas Andaluzas de Informática, 90-95, 2011.
  9. A. Rojas and A. Cano. Cifrado de imágenes y reparto de secretos en clase de matemáticas. In XV Jornadas para el Aprendizaje y Enseñanza de las Matemáticas, 2011.
  10. A. Rojas and A. Cano. Motivando el aprendizaje del álgebra lineal a través de sus aplicaciones. In II Jornadas sobre Innovación Docente y Adaptación al EEES en las Titulaciones Técnicas, 2011.
  11. A. Rojas and A. Cano. Álgebra lineal y cifrado de imágenes. In CEAM 2010 XIII Congreso de enseñanza y aprendizaje de las matemáticas, 2010.
  12. A. Cano. Reparto de secretos usando un sudoku. In CEAM 2010 XIII Congreso de enseñanza y aprendizaje de las matemáticas, 2010.
  13. A. Cano and A. Rojas. Coloreado de imágenes y sistemas de ecuaciones lineales. In CEAM 2010 XIII Congreso de enseñanza y aprendizaje de las matemáticas, 2010.
  14. A. Cano and A. Rojas. Fotomontajes de imágenes digitales y sistemas de ecuaciones lineales. In CEAM 2010 XIII Congreso de enseñanza y aprendizaje de las matemáticas, 2010.
  15. A. Rojas and A. Cano. Descomposición en valores singulares e imágenes. In CEAM 2010 XIII Congreso de enseñanza y aprendizaje de las matemáticas, 2010.
  16. A. Rojas and A. Cano. Álgebra lineal, secretos e imágenes. In CUIEET 2010 XVIII Congreso universitario de innovación educativa en las enseñanzas técnicas, 2010.
  17. A. Rojas and A. Cano. Innovación en clase de matemáticas. In CUIEET 2010 XVIII Congreso universitario de innovación educativa en las enseñanzas técnicas, 2010.
  18. A. Cano and A. Rojas. Descomposición en valores singulares e imágenes. In I Jornadas Andaluzas de Informática, 2009.
  19. A. Rojas and A. Cano. Aplicaciones del álgebra lineal en la vida cotidiana. In XIV Jornadas para el Aprendizaje y Enseñanza de las Matemáticas, 2009.

Professional service

Associate Editor

  • IEEE Access. ISSN 2169-3536.
  • Applied Intelligence. ISSN 0924-669X.

Reviewer for research projects

  • National Science Foundation (GRFP and CISE). United States.
  • Israeli Science Foundation. Israel.
  • Chilean National Science and Technology, Chile.
  • Fonds Wetenschappelijk Onderzoek, Belgium.
  • National Centre of Science and Technology Evaluation, Kazakhstan.

Reviewer for journals and conferences (Reviewer profile in publons)

  • Technical Program Committee in +150 International Conferences, including IEEE CEC, IEEE BIG DATA, GECCO, ECML.
  • ACM Transactions on Knowledge Discovery from Data. ISSN 1556-4681.
  • Applied Intelligence (Associate Editor). ISSN 0924-669X.
  • Applied Soft Computing. ISSN 1568-4946.
  • Artificial Intelligence in Medicine. ISSN 0933-3657.
  • Artificial Intelligence Review. ISSN 1573-7462.
  • Cognitive Computation. ISSN 1866-9964.
  • Computer Networks. ISSN 1389-1286.
  • Computers & Electrical Engineering. ISSN 0045-7906.
  • Computers and Education. ISSN 0360-1315.
  • Distributed and Parallel Databases. ISSN 1573-7578.
  • Expert Systems. ISSN 1468-0394.
  • Expert Systems with Applications. ISSN 0957-4174.
  • Future Generation Computer Systems. ISSN 0167-739X.
  • IEEE Access. ISSN 2169-3536. (Associate Editor)
  • IEEE Transactions on Cybernetics. ISSN 2168-2267.
  • IEEE Transactions on Evolutionary Computation. ISSN 1089-778X.
  • IEEE Transactions on Industrial Informatics. ISSN 1551-3203.
  • IEEE Transactions on Knowledge and Data Engineering. ISSN 1041-4347.
  • IEEE Transactions on Learning Technologies. ISSN 1939-1382.
  • Information Fusion. ISSN 1566-2535.
  • Information Processing in Agriculture. ISSN 2214-3173.
  • Information Sciences. ISSN 0020-0255.
  • Journal of Parallel and Distributed Computing. ISSN 0743-7315.
  • Knowledge-Based Systems. ISSN 0950-7051.
  • Knowledge and Information Systems. ISSN 0219-3116.
  • Neural Computing and Applications. ISSN 1433-3058.
  • Neural Networks. ISSN 0893-6080.
  • Neurocomputing. ISSN 0925-2312.
  • Pattern Recognition. ISSN 0031-3203.
  • PeerJ Computer Science. ISSN 2376-5992.
  • PLOS ONE. ISSN 1932-6203.
  • Progress in Artificial Intelligence. ISSN 2192-6360.
  • Soft Computing. ISSN 1432-7643.
  • Swarm and Evolutionary Computation. ISSN 2210-6502.
New Classification Models through Evolutionary Algorithms A. Cano, XPS: EXPL: Scalable distributed GPU computing for extremely high-dimensional optimization