Development of an enhanced scatter search algorithm using discrete chaotic Arnold’s cat map
Keywords:scatter search, Arnold's cat map, chaotic, TSP, metaheuristic, optimization problems
Solving optimization problems is an ever-growing subject with an enormous number of algorithms. Examples of such algorithms are Scatter Search (SS) and genetic algorithms. Modifying and improving of algorithms can be done by adding diversity and guidance to them. Chaotic maps are quite sensitive to the initial point, which means even a very slight change in the value of the initial point would result in a dramatic change of the sequence produced by the chaotic map Arnold's Cat Map. Arnold's Cat Map is a chaotic map technique that provides long non-repetitive random-like sequences.
Chaotic maps play an important role in improving evolutionary optimization algorithms and meta-heuristics by avoiding local optima and speeding up the convergence. This paper proposes an implementation of the scatter search algorithm with travelling salesman as a case study, then implements and compares the developed hyper Scatter Arnold's Cat Map Search (SACMS) method against the traditional Scatter Search Algorithm. SACMS is a hyper Scatter Search Algorithm with Arnold's Cat Map Chaotic Algorithm. Scatter Arnold's Cat Map Search shows promising results by decreasing the number of iterations required by the Scatter Search Algorithm to get an optimal solution(s). Travelling Salesman Problem, which is a popular and well-known optimization example, is implemented in this paper to demonstrate the results of the modified algorithm Scatter Arnold's Cat Map Search (SACMS). Implementation of both algorithms is done with the same parameters: population size, number of cities, maximum number of iterations, reference set size, etc. The results show improvement by the modified algorithm in terms of the number of iterations required by SS with an iteration reduction of 10–46 % and improvements in time to obtain solutions with 65 % time reduction
AlObaidi, A. T. S., Hamad, A. G. (2010). BSA: A Hybrid Bees’ Simulated Annealing Algorithm To Solve Optimization & NP-Complete Problems. Engineering And Technology Journal, 28 (2), 271–281.
Saeed, E. M. H., Hammood, B. A. (2021). Estimation and evaluation of Students’ behaviors in E-learning Environment using adaptive computing. Materials Today: Proceedings. Elsevier. doi: http://doi.org/10.1016/j.matpr.2021.04.519
Woźniak, M., Połap, D. (2017). Hybrid neuro-heuristic methodology for simulation and control of dynamic systems over time interval. Neural Networks, 93, 45–56. doi: http://doi.org/10.1016/j.neunet.2017.04.013
Brociek, R., Słota, D. (2016). Application and comparison of intelligent algorithms to solve the fractional heat conduction inverse problem. Information Technology And Control, 45 (2), 184–194. doi: http://doi.org/10.5755/j01.itc.45.2.13716
AlSudani, H. A., Hussain, E. M., Khalil, E. A. (2020). Classification the Mammograms Based on Hybrid Features Extraction Techniques Using Multilayer Perceptron Classifier. Al-Mustansiriyah Journal of Science, 31 (4), 72–79. doi: http://doi.org/10.23851/mjs.v31i4.902
Stallings, W. (2013). Cryptography and Network Security: Principles and Practice. Pearson, 752.
Bassham, L. E., Rukhin, A. L., Soto, J., Nechvatal, J. R., Smid, M. E., Barker, E. B. et. al. (2010). A statistical test suite for random and pseudorandom number generators for cryptographic applications. Gaithersburg, 131. doi: http://doi.org/10.6028/nist.sp.800-22r1a
Brown, R. G. (2020). Dieharder: A Random Number Test Suite. Available at: http://webhome.phy.duke.edu/~rgb/General/dieharder.php
Saeed, E. M. H., Hammood, B. A. (2021). Article Review: Survey Fuzzy Logic and Aprior Algorithms Employed for E-learning Environment. Turkish Journal of Computer and Mathematics Education, 12 (9), 1393–1402.
Brownlee, J. (2012). Clever Algorithms: Nature-Inspired Programming Recipes. Lulu, 436.
Borisenko, A., Gorlatch, S. (2018). Comparing GPU-parallelized metaheuristics to branch-and-bound for batch plants optimization. The Journal of Supercomputing, 75 (12), 7921–7933. doi: http://doi.org/10.1007/s11227-018-2472-9
Abdulelah, A. J., Shaker, K., Sagheer, A. M., Jalab, H. A. (2017). A Dynamic Scatter Search Algorithm for Solving Traveling Salesman Problem. 9th International Conference on Robotic, Vision, Signal Processing and Power Applications. Lecture Notes in Electrical Engineering LNEE. Singapore: Springer, 398, 117–124. doi: http://doi.org/10.1007/978-981-10-1721-6_13
Sagheer, A. M., Sadiq, A. T., Ibrahim, M. S. (2012). Improvement of scatter search using Bees Algorithm. 2012 6th International Conference on Signal Processing and Communication Systems. Gold Coast. doi: http://doi.org/10.1109/icspcs.2012.6507943
Souza, D. S., Santos, H. G., Coelho, I. M. (2017). A Hybrid Heuristic in GPU-CPU Based on Scatter Search for the Generalized Assignment Problem. Procedia Computer Science, 108, 1404–1413. doi: http://doi.org/10.1016/j.procs.2017.05.188
Prerna, D., Bhawna, K. (2015). Image Encryption Using Arnold’s Cat Map and Logistic Map for Secure Transmission. International Journal of Computer Science and Mobile Computing, 4 (6), 194–199.
Shrivastava, S. (2011). A Novel 2D Cat Map based Fast Data Encryption Scheme. International Journal of Electronics and Communication Engineering, 4 (2), 217–223.
Meymand, M. Z., Rashidinejad, M., Khorasani, H., Rahmani, M., Mahmoudabadi, A. (2012). An Implementation of Modified Scatter Search Algorithm to Transmission Expansion Planning. Turkish Journal of Electrical Engineering Computer Sciences, 20 (1), 1206–1219.
Laguna, M., Martí, R. (2003). Scatter Search Methodology and Implementations in C. Research/Computer Science Interfaces Series ORCS Vol. 24. Erratum E1. Springer. doi: http://doi.org/10.1007/978-1-4615-0337-8
Yas, R. M. (2017). Permuting Convergence Overcoming of Genetic Algorithm Using Arnold Cat Map. International Journal of Science and Research, 6 (5), 2588–2590.
AlObaidi, A. T. S., Hamad, A. G. (2012). Exploration-Balanced Bees Algorithms to Solve Optimization and NP-Complete Problems. International Journal of Research and Reviews in Soft and Intelligent Computing, 2 (1), 108–113.
Mohammed, R. S., Hussien, E. M., Mutter, J. R. (2016). A novel technique of privacy preserving association rule mining. 2016 Al-Sadeq International Conference on Multidisciplinary in IT and Communication Science and Applications (AIC-MITCSA), 1–6. doi: http://doi.org/10.1109/aic-mitcsa.2016.7759930
Gilbert, N. (1993). Analyzing Tabular Data: Loglinear and Logistic Models for Social Researchers. London: UCL Press, 196.
Dorian, G. (2004). Natural Algorithms for Optimisation Problems. Imperial College, 143.
Yas, R. M., Hashem, S. H. (2020). Unequal clustering and scheduling in Wireless Sensor Network using Advance Genetic Algorithm. Journal of Physics: Conference Series, 1530, 012076. doi: http://doi.org/10.1088/1742-6596/1530/1/012076
Yas, R. M., Hashem, S. H. (2020). A Survey on Enhancing Wire/Wireless Routing Protocol Using Machine Learning Algorithms. IOP Conference Series: Materials Science and Engineering, 870, 012037. doi: http://doi.org/10.1088/1757-899x/870/1/012037
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