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. 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B16: Genetic programming in feedback registers designing

In BIST structures feedback registers play the role of test generators and test response compactors. Linear feedback shift registers (LFSR) are here of predominating importance. These registers are relatively simple in designing. Non-linear feedback shift registers designing to diagnostic aims is considerably more complicated. The possibility to use the genetic programming to design the non-linear feedback shift registers is presented in the article. Usefulness of this approach to design the registers helpful in the BIST structures is testified by numerous examples.Badura D. (1992). Techniki projektowania samotestowalnych układów i pakietów cyfrowych wykorzystujące rejestry szeregowe z nieliniowym sprzężeniem zwrotnym, Uniwersytet Śląski.Elmrych M. (2004). Metody genetyczne w projektowaniu rejestrów z nieliniowym sprzężeniem zwrotnym, Uniwersytet Śląski, Sosnowiec.Gościniak I. (1996). Liniowa metoda zwiększania efektywności diagnostycznej ścieżki samotestującej i pierścienia samotestującego. Pomiary Automatyka Kontrola, nr 4, Warszawa.Gościniak I., Chodacki M. (2003). Genetic algorithms for the designing feedback shift registers, 6 th IEEE International Workshop on Design and Diagnostics of Electronic Circuits and Systems, Poznań, Poland, pp 301-302.Hławiczka A. (1997). Rejestry liniowe – analiza, synteza i zastosowania w testowaniu układów cyfrowych, Wydawnictwo Politechniki Śląskiej, Gliwice.Hürner H. (1996). A C++ Class Library for Genetic Programming, The Vienna University of Economics.Koza J. R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press.Słota T. (2004). Metody genetyczne w projektowaniu rejestrów liczących, Uniwersytet Śląski, Sosnowiec.Wagner F. (1977). Projektowanie krótkich rejestrów liczących, Politechnika Śląska, ZN Nr. 526

Extended class of linear feedback shift registers

Shift registers with linear feedback are frequently used. They owe their popularity to very well developed theoretical base. Registers with feedback of prime polynomials are of particular practical importance. They are willingly applied as test sequence generators and test response compactors. The article presents an attempt to extend the class of registers with linear feedback. Basing on the formal description of the register, the algorithms of register transformation are proposed. It allows to obtain the registers with equivalent graphs.[1] I. Gosciniak, “Linear Registers with Mixed Feedback, in Polish; Rejestry liniowe z mieszanym sprzȩżeniem zwrotnym,” Pomiary Automatyka Kontrola, no. 1, pp. 4–6, 1996.[2] K. Iwasaki, “Analysis and proposal of signature circuits for LSI testing,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 7, no. 1, pp. 84–90, 1988.[3] L.-T. Wang, N. Touba, R. Brent, H. Xu, and H. Wang, “On Designing Transformed Linear Feedback Shift Registers with Minimum Hardware Cost – Technical Report,” Computer Engineering Research Center Department of Electrical & Computer Engineering The University of Texas at Austin, 2011.[4] J. Rajski, J. Tyszer, M. Kassab, and N. Mukherjee, “Method for Synthesizing Linear Finite State Machines,” U.S. Patent, No. 6,353,842, 2002.[5] I. Gosciniak, “Equivalent Form of Linear Feedback Shift Registers,” in XIXth National Conference Circuit Theory and Eletronic Networks, 1996, pp. 115–120.[6] L. Alaus, D. Noguet, and J. Palicot, “A Reconfigurable LFSR for Tristandard SDR Transceiver, Architecture and Complexity Analysis,” in Digital System Design Architectures, Methods and Tools, 2008. DSD ’08. 11th EUROMICRO Conference on. IEEE Computer Society, 2008, pp. 61–67.[7] R. Ash, Information Theory. John Wiley & Sons, 1967.[8] M. Kopec, “Can Nonlinear Compactors Be Better than Linear Ones?” IEEE Trans. Comput., no. 11, pp. 1275–1282, 1995.[9] A. Gucha and L. Kinney, “Relating the Cyclic Behaviour of Linear Intrainverted Feedback shift Registers,” IEEE Transactions on Computers, vol. 41, no. 9, pp. 1088–1100, 1992

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

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

One more look on visualization of operation of a root-finding algorithm

Many algorithms that iteratively find solution of an equation require tuning. Due to the complex dependence of many algorithm’s elements, it is difficult to know their impact on the work of the algorithm. The article presents a simple root-finding algorithm with self-adaptation that requires tuning, similarly to evolutionary algorithms. Moreover, the use of various iteration processes instead of the standard Picard iteration is presented. In the algorithm’s analysis, visualizations of the dynamics were used. The conducted experiments and the discussion regarding their results allow to understand the influence of tuning on the proposed algorithm. The understanding of the tuning mechanisms can be helpful in using other evolutionary algorithms. Moreover, the presented visualizations show intriguing patterns of potential artistic applications

Visual Analysis of Dynamics Behaviour of an Iterative Method Depending on Selected Parameters and Modifications

There is a huge group of algorithms described in the literature that iteratively find solutions of a given equation. Most of them require tuning. The article presents root-finding algorithms that are based on the Newton-Raphson method which iteratively finds the solutions, and require tuning. The modification of the algorithm implements the best position of particle similarly to the particle swarm optimisation algorithms. The proposed approach allows visualising the impact of the algorithm's elements on the complex behaviour of the algorithm. Moreover, instead of the standard Picard iteration, various feedback iteration processes are used in this research. Presented examples and the conducted discussion on the algorithm's operation allow to understand the influence of the proposed modifications on the algorithm's behaviour. Understanding the impact of the proposed modification on the algorithm's operation can be helpful in using it in other algorithms. The obtained images also have potential artistic applications

Nowe ujęcie wybranych zagadnień optymalizacji

In solving complex optimization tasks evolutionary algorithms have a leading position. Unusual look at the optimization algorithms presented in the thesis, led to the creation of the new algorithm and work on its development to put its metaphors in a group of artificial life. The resulting algorithms are still the effective optimization algorithms and the proposed approach introduces new properties in their operation. The study presents a new algorithm of observation - as the base algorithm and its metaphors placed in a group of immune algorithm and particle swarm optimization algorithms. Research on the mechanics of these algorithms demonstrated new properties, i.e.: behavior resembling observation, and co-evolution mechanism determines the behavior of independence on influences of the environment. Implementation of the assumptions imposed the need to develop effective mechanism of mutation for immune algorithm. The functions of behavior scenarios were defined for the particle swarm optimization algorithm. A group of immune systems is proposed which is an equivalent to the multi-population system and methods of information exchange between systems in the group are defined. The thesis presents a theoretical background of algorithms’ operation and a simulation study. To check the efficiency of the algorithms the typical test environment for stationary and non-stationary problems were applied. In the study, fractal and multifractal analysis was used and its usefulness was demonstrated in research on behavior of algorithms. Optimization of diagnostic structure of digital circuit is an issue of multimodal optimization and is a particular kind of challenge. A comprehensive approach to test multi-module circuit may lead to new solutions, also in terms of a single module testing. Such concepts are included in this study, basing on an untypical approach to testing multi-module circuit, the conclusion has a strong theoretical base. The original achievements in this dissertation are as follows: a proposal of BIST architecture based on the so-called linear modification, the introduction of the diagnostic structure description, and determination of the theoretical basis of this concept, confirmation of the formulated theoretical basement and simultaneously the verification of the diagnostic efficiency of the proposed solutions by means of simulation methods basing on modeling with using ISCAS’89 benchmark, the demonstration of permanent features of modules during testing, the presentation of a formal description of any diagnostic structure with a description of the optimization framework and the concept of simulation tools used in the current research. Simultaneously, the study shows the original use of a genetic algorithm to give a high efficiency optimization. This part of the study presents a complete system of description of any diagnostic structure with the optimization method. The solutions presented in the dissertation open the way for the further research. This dissertation is composed of two parts, despite of the common basis in a form of evolutionary algorithms, they are present different and closed thematically issues. Keywords: optimization, multi-criteria optimization, multimodal optimization, evolutionary algorithms, genetic algorithms, immune algorithms, particle swarm optimization algorithms, a group of immune system, the algorithm of observation, exchange of genetic material, fractal analysis, multifractal analysis, beset game algorithm, immune algorithm with auto-aggression, stationary problems, non-stationary problems, BIST structure, BIST structure optimization, BIST structure description, multi-modular circuit BIST

An Approach to Determine the Features of Dental X-ray Images Based on the Fractal Dimension

Applications of the fractal dimension include the analysis and interpretation of medical images. The article presents a method for determining image features that are based on fractal dimension. In the proposed method, an optimization process (modified semi-multifractal optimization algorithm) creates a division into sub-areas similarly to a multi-resolution method. Using this division, a characteristic spectrum based on the fractal dimensions is calculated. This spectrum is applied to the recognition method of X-ray images of teeth. The obtained experimental results showed that the proposed method can effectively recognize such images

Control of Dynamics of the Modified Newton-Raphson Algorithm

Many algorithms that iteratively find solution of an equation are described in the literature. In this article we propose an algorithm that is based on the Newton-Raphson root finding method and which uses an adaptation mechanics. The adaptation mechanics is based on a linear combination of some membership functions and allows a better control of algorithm's dynamics. The proposed approach allows to visualize the adaptation mechanics impact on the operation of the algorithm. Moreover, various iteration processes and their operation mechanics are discussed in this research. The understanding of the impact of the proposed modifications on the algorithm's operation can be helpful at using other algorithms. The obtained visualizations have also an artistic potential and can be used for instance in creating mosaics, wallpapers etc