Cosine Harmony Search (CHS) for Static Optimization

Harmony Search (HS) is a behaviour imitation of a musician looking for the balance harmony. HS suffers to find the best parameter tuning especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. However, PAR in HS requires to be initialized with a constant value at the beginning step. On top of that, it also causes delay in convergence speed due to disproportion of global and local search capabilities. Even though, some HS variants claimed to overcome that shortcoming by introducing the self-modification of pitch adjustment rate, some of their justification were imprecise and required deeper and extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step either as global or worst. If the value of η is large, the opportunity to select the global adaptive step is high, so the algorithm will further exploit for better harmony value. Otherwise, if η is small, the worst adaptive step is prone to be selected, therefore the algorithm will close to the global best solution. In this paper, regarding to the HS problem, we introduce a Cosine Harmony Search (CHS) by incorporating embedment of cosine and additional strategy rule with self-modification of pitch tuning to enlarge the exploitation capability of solution space. The additional strategy employs the η inspired by LHS and contains the cosine parameter. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed with other state-of-the-art in accuracy and convergence speed evaluations

Cellular Harmony Search for Optimization Problems

Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors.Thememory consideration and population update aremodified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS

Grand Tour Algorithm: Novel Swarm-Based Optimization for High-Dimensional Problems

[EN] Agent-based algorithms, based on the collective behavior of natural social groups, exploit innate swarm intelligence to produce metaheuristic methodologies to explore optimal solutions for diverse processes in systems engineering and other sciences. Especially for complex problems, the processing time, and the chance to achieve a local optimal solution, are drawbacks of these algorithms, and to date, none has proved its superiority. In this paper, an improved swarm optimization technique, named Grand Tour Algorithm (GTA), based on the behavior of a peloton of cyclists, which embodies relevant physical concepts, is introduced and applied to fourteen benchmarking optimization problems to evaluate its performance in comparison to four other popular classical optimization metaheuristic algorithms. These problems are tackled initially, for comparison purposes, with 1000 variables. Then, they are confronted with up to 20,000 variables, a really large number, inspired in the human genome. The obtained results show that GTA clearly outperforms the other algorithms. To strengthen GTA's value, various sensitivity analyses are performed to verify the minimal influence of the initial parameters on efficiency. It is demonstrated that the GTA fulfils the fundamental requirements of an optimization algorithm such as ease of implementation, speed of convergence, and reliability. Since optimization permeates modeling and simulation, we finally propose that GTA will be appealing for the agent-based community, and of great help for a wide variety of agent-based applications.Meirelles, G.; Brentan, B.; Izquierdo Sebastián, J.; Luvizotto, EJ. (2020). Grand Tour Algorithm: Novel Swarm-Based Optimization for High-Dimensional Problems. Processes. 8(8):1-19. https://doi.org/10.3390/pr8080980S11988Mohamed, A. W., Hadi, A. A., & Mohamed, A. K. (2019). Gaining-sharing knowledge based algorithm for solving optimization problems: a novel nature-inspired algorithm. International Journal of Machine Learning and Cybernetics, 11(7), 1501-1529. doi:10.1007/s13042-019-01053-xMirjalili, S., & Lewis, A. (2016). The Whale Optimization Algorithm. Advances in Engineering Software, 95, 51-67. doi:10.1016/j.advengsoft.2016.01.008Chatterjee, A., & Siarry, P. (2006). Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Computers & Operations Research, 33(3), 859-871. doi:10.1016/j.cor.2004.08.012Dorigo, M., & Blum, C. (2005). Ant colony optimization theory: A survey. Theoretical Computer Science, 344(2-3), 243-278. doi:10.1016/j.tcs.2005.05.020Karaboga, D., & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39(3), 459-471. doi:10.1007/s10898-007-9149-xGandomi, A. H., Yang, X.-S., & Alavi, A. H. (2011). Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Engineering with Computers, 29(1), 17-35. doi:10.1007/s00366-011-0241-yKirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by Simulated Annealing. Science, 220(4598), 671-680. doi:10.1126/science.220.4598.671Wu, Z. Y., & Simpson, A. R. (2002). A self-adaptive boundary search genetic algorithm and its application to water distribution systems. Journal of Hydraulic Research, 40(2), 191-203. doi:10.1080/00221680209499862Trelea, I. C. (2003). The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters, 85(6), 317-325. doi:10.1016/s0020-0190(02)00447-7Brentan, B., Meirelles, G., Luvizotto, E., & Izquierdo, J. (2018). Joint Operation of Pressure-Reducing Valves and Pumps for Improving the Efficiency of Water Distribution Systems. Journal of Water Resources Planning and Management, 144(9), 04018055. doi:10.1061/(asce)wr.1943-5452.0000974Freire, R. Z., Oliveira, G. H. C., & Mendes, N. (2008). Predictive controllers for thermal comfort optimization and energy savings. Energy and Buildings, 40(7), 1353-1365. doi:10.1016/j.enbuild.2007.12.007Bollinger, L. A., & Evins, R. (2015). Facilitating Model Reuse and Integration in an Urban Energy Simulation Platform. Procedia Computer Science, 51, 2127-2136. doi:10.1016/j.procs.2015.05.484Yang, Y., & Chui, T. F. M. (2019). Developing a Flexible Simulation-Optimization Framework to Facilitate Sustainable Urban Drainage Systems Designs Through Software Reuse. Reuse in the Big Data Era, 94-99. doi:10.1007/978-3-030-22888-0_7Mavrovouniotis, M., Li, C., & Yang, S. (2017). A survey of swarm intelligence for dynamic optimization: Algorithms and applications. Swarm and Evolutionary Computation, 33, 1-17. doi:10.1016/j.swevo.2016.12.005Hybinette, M., & Fujimoto, R. M. (2001). Cloning parallel simulations. ACM Transactions on Modeling and Computer Simulation, 11(4), 378-407. doi:10.1145/508366.508370Proceedings of the 2004 Winter Simulation Conference (IEEE Cat. No.04CH37614C). (2004). Proceedings of the 2004 Winter Simulation Conference, 2004. doi:10.1109/wsc.2004.1371294Li, Z., Wang, W., Yan, Y., & Li, Z. (2015). PS–ABC: A hybrid algorithm based on particle swarm and artificial bee colony for high-dimensional optimization problems. Expert Systems with Applications, 42(22), 8881-8895. doi:10.1016/j.eswa.2015.07.043Montalvo, I., Izquierdo, J., Pérez-García, R., & Herrera, M. (2014). Water Distribution System Computer-Aided Design by Agent Swarm Optimization. Computer-Aided Civil and Infrastructure Engineering, 29(6), 433-448. doi:10.1111/mice.12062Heuristic Optimization. (s. f.). Advances in Computational Management Science, 38-76. doi:10.1007/0-387-25853-1_2Zong Woo Geem, Joong Hoon Kim, & Loganathan, G. V. (2001). A New Heuristic Optimization Algorithm: Harmony Search. SIMULATION, 76(2), 60-68. doi:10.1177/003754970107600201Blocken, B., van Druenen, T., Toparlar, Y., Malizia, F., Mannion, P., Andrianne, T., … Diepens, J. (2018). Aerodynamic drag in cycling pelotons: New insights by CFD simulation and wind tunnel testing. Journal of Wind Engineering and Industrial Aerodynamics, 179, 319-337. doi:10.1016/j.jweia.2018.06.011Clerc, 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. doi:10.1109/4235.985692GAMS World, GLOBAL Libraryhttp://www.gamsworld.org/global/globallib.htmlCUTEr, A Constrained and Un-Constrained Testing Environment, Revisitedhttp://cuter.rl.ac.uk/cuter-www/problems.htmlGO Test Problemshttp://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htmJamil, M., & Yang, X. S. (2013). A literature survey of benchmark functions for global optimisation problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2), 150. doi:10.1504/ijmmno.2013.055204Sharma, G. (2012). The Human Genome Project and its promise. Journal of Indian College of Cardiology, 2(1), 1-3. doi:10.1016/s1561-8811(12)80002-2Li, W. (2011). On parameters of the human genome. Journal of Theoretical Biology, 288, 92-104. doi:10.1016/j.jtbi.2011.07.021Hughes, M., Goerigk, M., & Wright, M. (2019). A largest empty hypersphere metaheuristic for robust optimisation with implementation uncertainty. Computers & Operations Research, 103, 64-80. doi:10.1016/j.cor.2018.10.013Zaeimi, M., & Ghoddosian, A. (2020). Color harmony algorithm: an art-inspired metaheuristic for mathematical function optimization. Soft Computing, 24(16), 12027-12066. doi:10.1007/s00500-019-04646-4Singh, G. P., & Singh, A. (2014). Comparative Study of Krill Herd, Firefly and Cuckoo Search Algorithms for Unimodal and Multimodal Optimization. International Journal of Intelligent Systems and Applications in Engineering, 2(3), 26. doi:10.18201/ijisae.31981Taheri, S. M., & Hesamian, G. (2012). A generalization of the Wilcoxon signed-rank test and its applications. Statistical Papers, 54(2), 457-470. doi:10.1007/s00362-012-0443-