Semi-multifractal optimization algorithm

Observations on living organism systems are the inspiration for the creation of modern computational techniques. The article presents an algorithm implementing the division of a solution space in the optimization process. A method for the algorithm operation controlling shows the wide range of its use possibilities. The article presents properties of fractal dimensions of subareas created in the process of optimization. The paper also presents the possibilities of using this method to determine function extremes. The approach proposed in the paper gives more opportunities for its use.Alrawi A, Sagheer A, Ibrahim D (2012) Texture segmentation based on multifractal dimension. Int J Soft Comput ( IJSC ) 3(1):1–10Belussi A, Catania B, Clementini E, Ferrari EE (eds) (2007) Spatial data on the web modeling and management. Springer, Berlin. doi: 10.1007/978-3-540-69878-4Corso G, Freitas J, Lucena L (2004) A multifractal scale-free lattice. Phys A Stat Mech Appl 342(1–2):214–220. doi: 10.1016/j.physa.2004.04.081Corso G, Lucena L (2005) Multifractal lattice and group theory. Phys A Stat Mech Appl 357(1):64–70. doi: 10.1016/j.physa.2005.05.049Gosciniak I (2017) Discussion on semi-immune algorithm behaviour based on fractal analysis. Soft Comput 21(14):3945–3956. doi: 10.1007/s00500-016-2044-yHwang WJ, Derin H (1995) Multiresolution multiresource progressive image transmission. IEEE Trans Image Process 4:1128–1140. doi: 10.1109/83.403418Iwanicki K, van Steen M (2009) Using area hierarchy for multi-resolution storage and search in large wireless sensor networks. In: Communications, 2009. ICC ’09. IEEE international conference on, pp 1–6. doi: 10.1109/ICC.2009.5199556Juliany J, Vose M (1994) The genetic algorithm fractal. Evol Comput 2(2):165–180. doi: 10.1162/evco.1994.2.2.165Kies P (2001) Information dimension of a population’s attractor a binary genetic algorithm. In: Artificial neural nets and genetic algorithms: proceedings of the international conference in Prague, Czech Republic. Springer, pp 232–235. doi: 10.1007/978-3-7091-6230-9_57Kotowski S, Kosinski W, Michalewicz Z, Nowicki J, Przepiorkiewicz B (2008) Fractal dimension of trajectory as invariant of genetic algorithms. In: Artificial intelligence and soft computing (ICAISC 2008). Springer, pp 414–425. doi: 10.1007/978-3-540-69731-2_41Lu Y, Huo X, Tsiotras P (2012) A beamlet-based graph structure for path planning using multiscale information. IEEE Trans Autom Control 57(5):1166–1178. doi: 10.1109/TAC.2012.2191836Marinov M, Kobbelt L (2005) Automatic generation of structure preserving multiresolution models. In: Eurographics, pp 1–8Masayoshi K, Masaru N, Yoshio S (1996) Identification of complicated shape objects by fractal characteristic variables categorizing dust particles on LSI wafer surface. Syst Comput Jpn 27(6):82–91. doi: 10.1002/scj.4690270608Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, Berlin. doi: 10.1007/978-3-662-03315-9Mo H (2008) Handbook of research on artificial immune systems and natural computing: applying complex adaptive technologies. Information Science Reference - Imprint of: IGI Publishing. doi: 10.4018/978-1-60566-310-4Pereira M, Corso G, Lucena L, Freitas J (2005) A random multifractal tilling. Chaos Solitons Fractals 23:1105–1110. doi: 10.1016/j.chaos.2004.06.045Rejaur Rahman M, Saha SK (2009) Multi-resolution segmentation for object-based classification and accuracy assessment of land use/land cover classification using remotely sensed data. J Indian Soc Remote Sens 36:189–201. doi: 10.1007/s12524-008-0020-4Song J, Qian F (2006) Fractal algorithm for finding global optimal solution. In: International conference on computational intelligence for modelling control and automation, and international conference on intelligent agents, web technologies and internet commerce (CIMCA–IAWTIC’06). IEEE Computer Society, pp 149–153Urrutia J, Sack JR (eds) (2000) Handbook of computational geometry. North-Holland, Amsterdam. doi: 10.1016/B978-0-444-82537-7.50027-9Weise T (2009) Global Optimization Algorithms—Theory and Applications, 2nd edn. University of Kassel, Distributed Systems Group. http://www.it-weise.deWeller R (2013) New geometric data structures for collision detection and haptics. Springer, Cham. doi: 10.1007/978-3-319-01020-5Vujovic I (2014) Multiresolution approach to processing images for different applications: interaction of lower processing with higher vision. Springer, Cham. doi: 10.1007/978-3-319-14457-3 Google Scholar Virtual library of simulation experiments: test functions and datasets, optimization test problems. https://www.sfu.ca/ssurjano/optimization.html. Accessed 28 July 201

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures

Discussion of the Semi-Immune Algorithm Behaviour Based on Fractal Analysis

A group of immune systems is similar to a multi-population system. Immune systems can be influenced by vaccines and serums, similarly to that which occurs in nature. The discussed algorithm has more parameters of work control than other immune algorithms. Fractal and multi-fractal analyses of the proposed algorithm, supported by quantitative analysis, are discussed. Fractal and multifractal analyses illustrate the algorithm behaviour. These analyses allow comparing algorithm settings considering their impact on the exploration and exploitation of the solution space. Fractal and multifractal analyses will be a valuable completion of knowledge of their work mechanisms

A new approach to particle swarm optimization algorithm

Particularly interesting group consists of algorithms that implement co-evolution or co-operation in natural environments, giving much more powerful implementations. The main aim is to obtain the algorithm which operation is not influenced by the environment. An unusual look at optimization algorithms made it possible to develop a new algorithm and its metaphors define for two groups of algorithms. These studies concern the particle swarm optimization algorithm as a model of predator and prey. New properties of the algorithm resulting from the co-operation mechanism that determines the operation of algorithm and significantly reduces environmental influence have been shown. Definitions of functions of behavior scenarios give new feature of the algorithm. This feature allows self controlling the optimization process. This approach can be successfully used in computer games. Properties of the new algorithm make it worth of interest, practical application and further research on its development. This study can be also an inspiration to search other solutions that implementing co-operation or co-evolution.Angeline, P. (1998). Using selection to improve particle swarm optimization. In Proceedings of the IEEE congress on evolutionary computation, Anchorage (pp. 84–89).Arquilla, J., & Ronfeldt, D. (2000). Swarming and the future of conflict, RAND National Defense Research Institute, Santa Monica, CA, US.Bessaou, M., & Siarry, P. (2001). A genetic algorithm with real-value coding to optimize multimodal continuous functions. Structural and Multidiscipline Optimization, 23, 63–74.Bird, S., & Li, X. (2006). Adaptively choosing niching parameters in a PSO. In Proceedings of the 2006 genetic and evolutionary computation conference (pp. 3–10).Bird, S., & Li, X. (2007). Using regression to improve local convergence. In Proceedings of the 2007 IEEE congress on evolutionary computation (pp. 592–599).Blackwell, T., & Bentley, P. (2002). Dont push me! Collision-avoiding swarms. In Proceedings of the IEEE congress on evolutionary computation, Honolulu (pp. 1691–1696).Brits, R., Engelbrecht, F., & van den Bergh, A. P. (2002). Solving systems of unconstrained equations using particle swarm optimization. In Proceedings of the 2002 IEEE conference on systems, man, and cybernetics (pp. 102–107).Brits, R., Engelbrecht, A., & van den Bergh, F. (2002). A niching particle swarm optimizer. In Proceedings of the fourth asia-pacific conference on simulated evolution and learning (pp. 692–696).Chelouah, R., & Siarry, P. (2000). A continuous genetic algorithm designed for the global optimization of multimodal functions. Journal of Heuristics, 6(2), 191–213.Chelouah, R., & Siarry, P. (2000). Tabu search applied to global optimization. European Journal of Operational Research, 123, 256–270.Chelouah, R., & Siarry, P. (2003). Genetic and Nelder–Mead algorithms hybridized for a more accurate global optimization of continuous multiminima function. European Journal of Operational Research, 148(2), 335–348.Chelouah, R., & Siarry, P. (2005). A hybrid method combining continuous taboo search and Nelder–Mead simplex algorithms for the global optimization of multiminima functions. European Journal of Operational Research, 161, 636–654.Chen, T., & Chi, T. (2010). On the improvements of the particle swarm optimization algorithm. Advances in Engineering Software, 41(2), 229–239.Clerc, M., & Kennedy, J. (2002). The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), 58–73.Fan, H., & Shi, Y. (2001). Study on Vmax of particle swarm optimization. In Proceedings of the workshop particle swarm optimization, Indianapolis.Gao, H., & Xu, W. (2011). Particle swarm algorithm with hybrid mutation strategy. Applied Soft Computing, 11(8), 5129–5142.Gosciniak, I. (2008). Immune algorithm in non-stationary optimization task. In Proceedings of the 2008 international conference on computational intelligence for modelling control & automation, CIMCA ’08 (pp. 750–755). Washington, DC, USA: IEEE Computer Society.He, Q., & Wang, L. (2007). An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engineering Applications of Artificial Intelligence, 20(1), 89–99.Higashitani, M., Ishigame, A., & Yasuda, K., (2006). Particle swarm optimization considering the concept of predator–prey behavior. In 2006 IEEE congress on evolutionary computation (pp. 434–437).Higashitani, M., Ishigame, A., & Yasuda, K. (2008). Pursuit-escape particle swarm optimization. IEEJ Transactions on Electrical and Electronic Engineering, 3(1), 136–142.Hu, X., & Eberhart, R. (2002). Multiobjective optimization using dynamic neighborhood particle swarm optimization. In Proceedings of the evolutionary computation on 2002. CEC ’02. Proceedings of the 2002 congress (Vol. 02, pp. 1677–1681). Washington, DC, USA: IEEE Computer Society.Hu, X., Eberhart, R., & Shi, Y. (2003). Engineering optimization with particle swarm. In IEEE swarm intelligence symposium, SIS 2003 (pp. 53–57). Indianapolis: IEEE Neural Networks Society.Jang, W., Kang, H., Lee, B., Kim, K., Shin, D., & Kim, S. (2007). Optimized fuzzy clustering by predator prey particle swarm optimization. In IEEE congress on evolutionary computation, CEC2007 (pp. 3232–3238).Kennedy, J. (2000). Stereotyping: Improving particle swarm performance with cluster analysis. In Proceedings of the 2000 congress on evolutionary computation (pp. 1507–1512).Kennedy, J., & Mendes, R. (2002). Population structure and particle swarm performance. In IEEE congress on evolutionary computation (pp. 1671–1676).Kuo, H., Chang, J., & Shyu, K. (2004). A hybrid algorithm of evolution and simplex methods applied to global optimization. Journal of Marine Science and Technology, 12(4), 280–289.Leontitsis, A., Kontogiorgos, D., & Pange, J. (2006). Repel the swarm to the optimum. Applied Mathematics and Computation, 173(1), 265–272.Li, X. (2004). Adaptively choosing neighborhood bests using species in a particle swarm optimizer for multimodal function optimization. In Proceedings of the 2004 genetic and evolutionary computation conference (pp. 105–116).Li, C., & Yang, S. (2009). A clustering particle swarm optimizer for dynamic optimization. In Proceedings of the 2009 congress on evolutionary computation (pp. 439–446).Liang, J., Suganthan, P., & Deb, K. (2005). Novel composition test functions for numerical global optimization. In Proceedings of the swarm intelligence symposium [Online]. Available: .Liang, J., Qin, A., Suganthan, P., & Baskar, S. (2006). Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Transactions on Evolutionary Computation, 10(3), 281–295.Lovbjerg, M., & Krink, T. (2002). Extending particle swarm optimizers with self-organized criticality. In Proceedings of the congress on evolutionary computation, Honolulu (pp. 1588–1593).Lung, R., & Dumitrescu, D. (2007). A collaborative model for tracking optima in dynamic environments. In Proceedings of the 2007 congress on evolutionary computation (pp. 564–567).Mendes, R., Kennedy, J., & Neves, J. (2004). The fully informed particle swarm: simpler, maybe better. IEEE Transaction on Evolutionary Computation, 8(3), 204–210.Miranda, V., & Fonseca, N. (2002). New evolutionary particle swarm algorithm (EPSO) applied to voltage/VAR control. In Proceedings of the 14th power systems computation conference, Seville, Spain [Online] Available: .Parrott, D., & Li, X. (2004). A particle swarm model for tracking multiple peaks in a dynamic environment using speciation. In Proceedings of the 2004 congress on evolutionary computation (pp. 98–103).Parrott, D., & Li, X. (2006). Locating and tracking multiple dynamic optima by a particle swarm model using speciation. In IEEE transaction on evolutionary computation (Vol. 10, pp. 440–458).Parsopoulos, K., & Vrahatis, M. (2004). UPSOA unified particle swarm optimization scheme. Lecture Series on Computational Sciences, 868–873.Passaroand, A., & Starita, A. (2008). Particle swarm optimization for multimodal functions: A clustering approach. Journal of Artificial Evolution and Applications, 2008, 15 (Article ID 482032).Peram, T., Veeramachaneni, K., & Mohan, C. (2003). Fitness-distance-ratio based particle swarm optimization. In Swarm intelligence symp. (pp. 174–181).Sedighizadeh, D., & Masehian, E. (2009). Particle swarm optimization methods, taxonomy and applications. International Journal of Computer Theory and Engineering, 1(5), 1793–8201.Shi, Y., & Eberhart, R. (2001). Particle swarm optimization with fuzzy adaptive inertia weight. In Proceedings of the workshop particle swarm optimization, Indianapolis (pp. 101–106).Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. In Proceedings of IEEE International Conference on Evolutionary Computation (pp. 69–73). Washington, DC, USA: IEEE Computer Society.Thomsen, R. (2004). Multimodal optimization using crowding-based differential evolution. In Proceedings of the 2004 congress on evolutionary computation (pp. 1382–1389).Trojanowski, K., & Wierzchoń, S. (2009). Immune-based algorithms for dynamic optimization. Information Sciences, 179(10), 1495–1515.Tsoulos, I., & Stavrakoudis, A. (2010). Enhancing PSO methods for global optimization. Applied Mathematics and Computation, 216(10), 2988–3001.van den Bergh, F., & Engelbrecht, A. (2004). A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8, 225–239.Wolpert, D., & Macready, W. (1997). No free lunch theorems for optimization. IEEE Transaction on Evolutionary Computation, 1(1), 67–82.Xie, X., Zhang, W., & Yang, Z. (2002). Dissipative particle swarm optimization. In Proceedings of the congress on evolutionary computation (pp. 1456–1461).Yang, S., & Li, C. (2010). A clustering particle swarm optimizer for locating and tracking multiple optima in dynamic environments. In IEEE Trans. on evolutionary computation (Vol. 14, pp. 959–974).Kuo, H., Chang, J., & Liu, C. (2006). Particle swarm optimization for global optimization problems. Journal of Marine Science and Technology, 14(3), 170–181

Wavelet Image Restoration Using Multifractal Priors

Bayesian image restoration has had a long history of successful application but one of the limitations that has prevented more widespread use is that the methods are generally computationally intensive. The authors recently addressed this issue by developing a method that performs the image enhancement in an orthogonal space (Fourier space in that case) which effectively transforms the problem from a large multivariate optimization problem to a set of smaller independent univariate optimization problems. The current paper extends these methods to analysis in another orthogonal basis, wavelets. While still providing the computational efficiency obtained with the original method in Fourier space, this extension allows more flexibility in adapting to local properties of the images, as well as capitalizing on the long history of developments for wavelet shrinkage methods. In addition, wavelet methods, including empirical Bayes specific methods, have recently been developed to effectively capture multifractal properties of images. An extension of these methods is utilized to enhance the recovery of textural characteristics of the underlying image. These enhancements should be beneficial in characterizing textural differences such as those occurring in medical images of diseased and healthy tissues. The Bayesian framework defined in the space of wavelets provides a flexible model that is easily extended to a variety of imaging contexts.Comment: 19 pages, 4 figure