A Spring Search Algorithm Applied to Engineering Optimization Problems

At present, optimization algorithms are used extensively. One particular type of such algorithms includes random-based heuristic population optimization algorithms, which may be created by modeling scientific phenomena, like, for example, physical processes. The present article proposes a novel optimization algorithm based on Hooke’s law, called the spring search algorithm (SSA), which aims to solve single-objective constrained optimization problems. In the SSA, search agents are weights joined through springs, which, as Hooke’s law states, possess a force that corresponds to its length. The mathematics behind the algorithm are presented in the text. In order to test its functionality, it is executed on 38 established benchmark test functions and weighed against eight other optimization algorithms: a genetic algorithm (GA), a gravitational search algorithm (GSA), a grasshopper optimization algorithm (GOA), particle swarm optimization (PSO), teaching–learning-based optimization (TLBO), a grey wolf optimizer (GWO), a spotted hyena optimizer (SHO), as well as an emperor penguin optimizer (EPO). To test the SSA’s usability, it is employed on five engineering optimization problems. The SSA delivered better fitting results than the other algorithms in unimodal objective function, multimodal objective functions, CEC 2015, in addition to the optimization problems in engineering.

[1]  Jiang Jianjun,et al.  A Dolphin Partner Optimization , 2009, 2009 WRI Global Congress on Intelligent Systems.

[2]  Hossein Nezamabadi-pour,et al.  GSA: A Gravitational Search Algorithm , 2009, Inf. Sci..

[3]  Mohammad Mardaneh,et al.  DTO: Donkey Theorem Optimization , 2019, 2019 27th Iranian Conference on Electrical Engineering (ICEE).

[4]  S. N. Kramer,et al.  An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and Its Applications to Mechanical Design , 1994 .

[5]  Om P. Malik,et al.  OSA: Orientation Search Algorithm , 2019 .

[6]  Monique Snoeck,et al.  Profit maximizing logistic model for customer churn prediction using genetic algorithms , 2017, Swarm Evol. Comput..

[7]  Enrique Cortés-Toro,et al.  A New Metaheuristic Inspired by the Vapour-Liquid Equilibrium for Continuous Optimization , 2018, Applied Sciences.

[8]  Ali Ehsanifar,et al.  Calculating the leakage inductance for transformer inter-turn fault detection using finite element method , 2017, 2017 Iranian Conference on Electrical Engineering (ICEE).

[9]  J. S. Dowker,et al.  Fundamentals of Physics , 1970, Nature.

[10]  Josep M. Guerrero,et al.  MLO: Multi Leader Optimizer , 2020, International Journal of Intelligent Engineering and Systems.

[11]  A. E. Eiben,et al.  On Evolutionary Exploration and Exploitation , 1998, Fundam. Informaticae.

[12]  Mohamed Cheriet,et al.  Curved Space Optimization: A Random Search based on General Relativity Theory , 2012, ArXiv.

[13]  Adel Nadjaran Toosi,et al.  Artificial fish swarm algorithm: a survey of the state-of-the-art, hybridization, combinatorial and indicative applications , 2012, Artificial Intelligence Review.

[14]  Carlos A. Coello Coello,et al.  Useful Infeasible Solutions in Engineering Optimization with Evolutionary Algorithms , 2005, MICAI.

[15]  A. Kaveh,et al.  A new meta-heuristic method: Ray Optimization , 2012 .

[16]  Josep M. Guerrero,et al.  Football Game Based Optimization: an Application to Solve Energy Commitment Problem , 2020 .

[17]  Ali Reza Seifi,et al.  Planning of energy carriers based on final energy consumption using dynamic programming and particle swarm optimization , 2018 .

[18]  Siew Mooi Lim,et al.  A Brief Survey on Intelligent Swarm-Based Algorithms for Solving Optimization Problems , 2018 .

[19]  Taher Niknam,et al.  OPTIMAL UTILIZATION OF ELECTRICAL ENERGY FROM POWER PLANTS BASED ON FINAL ENERGY CONSUMPTION USING GRAVITATIONAL SEARCH ALGORITHM , 2018 .

[20]  Seyed Mohammad Mirjalili,et al.  Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm , 2015, Knowl. Based Syst..

[21]  Zeinab Montazeri,et al.  Line loss reduction and voltage profile improvement in radial distribution networks using battery energy storage system , 2017, 2017 IEEE 4th International Conference on Knowledge-Based Engineering and Innovation (KBEI).

[22]  Om P. Malik,et al.  GO: Group Optimization , 2020, GAZI UNIVERSITY JOURNAL OF SCIENCE.

[23]  Gerbrand Ceder,et al.  Constructing first-principles phase diagrams of amorphous LixSi using machine-learning-assisted sampling with an evolutionary algorithm. , 2018, The Journal of chemical physics.

[24]  Mark Borodovsky,et al.  Prediction of lncRNAs and their interactions with nucleic acids: benchmarking bioinformatics tools , 2019, Briefings Bioinform..

[25]  Bilal Alatas,et al.  ACROA: Artificial Chemical Reaction Optimization Algorithm for global optimization , 2011, Expert Syst. Appl..

[26]  Sam Kwong,et al.  Genetic algorithms and their applications , 1996, IEEE Signal Process. Mag..

[27]  Kamal Al-Haddad,et al.  HOGO: Hide Objects Game Optimization , 2020 .

[28]  Gerd Gigerenzer,et al.  Heuristic decision making. , 2011, Annual review of psychology.

[29]  John Daniel. Bagley,et al.  The behavior of adaptive systems which employ genetic and correlation algorithms : technical report , 1967 .

[30]  Seyedali Mirjalili,et al.  Introduction to Evolutionary Single-Objective Optimisation , 2018, Studies in Computational Intelligence.

[31]  M. J. Mahjoob,et al.  A novel meta-heuristic optimization algorithm inspired by group hunting of animals: Hunting search , 2010, Comput. Math. Appl..

[32]  Tom V. Mathew Genetic Algorithm , 2022 .

[33]  Taher Niknam,et al.  Energy carriers management based on energy consumption , 2017, 2017 IEEE 4th International Conference on Knowledge-Based Engineering and Innovation (KBEI).

[34]  Hossein Nezamabadi-pour,et al.  A comprehensive survey on gravitational search algorithm , 2018, Swarm Evol. Comput..

[35]  O. P. Malik,et al.  Optimal Sizing and Placement of Capacitor Banks and Distributed Generation in Distribution Systems Using Spring Search Algorithm , 2020 .

[36]  Andrew Lewis,et al.  The Whale Optimization Algorithm , 2016, Adv. Eng. Softw..

[37]  Luca G. Tallini,et al.  A Fuzzy Gravitational Search Algorithm to Design Optimal IIR Filters , 2018 .

[38]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[39]  Richard Formato,et al.  Central Force Optimization: A New Nature Inspired Computational Framework for Multidimensional Search and Optimization , 2007, NICSO.

[40]  Alan S. Perelson,et al.  The immune system, adaptation, and machine learning , 1986 .

[41]  Modestus O. Okwu,et al.  Moths–Flame Optimization Algorithm , 2020 .

[42]  Haopeng Zhang,et al.  A Coupled Spring Forced Bat Searching Algorithm: Design, Analysis and Evaluation , 2020, 2020 American Control Conference (ACC).

[43]  Huimin Zhao,et al.  An Improved Quantum-Inspired Differential Evolution Algorithm for Deep Belief Network , 2020, IEEE Transactions on Instrumentation and Measurement.

[44]  Sam Kwong,et al.  Adaptive Granularity Learning Distributed Particle Swarm Optimization for Large-Scale Optimization , 2020, IEEE Transactions on Cybernetics.

[45]  Richard Alan Peters,et al.  Particle Swarm Optimization: A survey of historical and recent developments with hybridization perspectives , 2018, Mach. Learn. Knowl. Extr..

[46]  J. Paulo Davim,et al.  Evolutionary-Based Methods , 2019 .

[47]  Colin Fyfe,et al.  Ant Colony Optimisation , 2008 .

[48]  John R. Koza,et al.  Genetic programming as a means for programming computers by natural selection , 1994 .

[49]  Om P. Malik,et al.  Shell Game Optimization: A Novel Game-Based Algorithm , 2020 .

[50]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[51]  Om P. Malik,et al.  ENERGY COMMITMENT: A PLANNING OF ENERGY CARRIER BASED ON ENERGY CONSUMPTION , 2019, Electrical Engineering & Electromechanics.

[52]  Josep M. Guerrero,et al.  A NEW METHODOLOGY CALLED DICE GAME OPTIMIZER FOR CAPACITOR PLACEMENT IN DISTRIBUTION SYSTEMS , 2020, Electrical Engineering & Electromechanics.

[53]  Amir Hossein Gandomi,et al.  Benchmark Problems in Structural Optimization , 2011, Computational Optimization, Methods and Algorithms.

[54]  Xin-She Yang,et al.  A New Metaheuristic Bat-Inspired Algorithm , 2010, NICSO.

[55]  Zeinab Montazeri,et al.  Spring search algorithm: A new meta-heuristic optimization algorithm inspired by Hooke's law , 2017, 2017 IEEE 4th International Conference on Knowledge-Based Engineering and Innovation (KBEI).

[56]  Hamed Shah-Hosseini,et al.  Principal components analysis by the galaxy-based search algorithm: a novel metaheuristic for continuous optimisation , 2011, Int. J. Comput. Sci. Eng..

[57]  Andrew Lewis,et al.  Grasshopper Optimisation Algorithm: Theory and application , 2017, Adv. Eng. Softw..

[58]  Youcef Djenouri,et al.  Bees swarm optimization guided by data mining techniques for document information retrieval , 2018, Expert Syst. Appl..

[59]  Amir Hossein Gandomi,et al.  Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems , 2011, Engineering with Computers.

[60]  Xin-She Yang,et al.  Firefly algorithm, stochastic test functions and design optimisation , 2010, Int. J. Bio Inspired Comput..

[61]  Bo Xing,et al.  Gravitational Search Algorithm , 2014 .

[62]  Uday K. Chakraborty,et al.  Advances in Differential Evolution , 2010 .

[63]  Lawrence J. Fogel,et al.  Artificial Intelligence through Simulated Evolution , 1966 .

[64]  Mohammad Mardaneh,et al.  SPRING SEARCH ALGORITHM FOR SIMULTANEOUS PLACEMENT OF DISTRIBUTED GENERATION AND CAPACITORS , 2018 .

[65]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[66]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[67]  Seyedali Mirjalili,et al.  Biogeography-Based Optimisation , 2018, Studies in Computational Intelligence.

[68]  Atulya K. Nagar,et al.  A novel algorithm for global optimization: Rat Swarm Optimizer , 2020, Journal of Ambient Intelligence and Humanized Computing.

[69]  Abdolreza Hatamlou,et al.  Black hole: A new heuristic optimization approach for data clustering , 2013, Inf. Sci..

[70]  Erik Cuevas,et al.  An Improved Crow Search Algorithm Applied to Energy Problems , 2018 .

[71]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[72]  Vijay Kumar,et al.  Emperor penguin optimizer: A bio-inspired algorithm for engineering problems , 2018, Knowl. Based Syst..

[73]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[74]  Tarun Biswas,et al.  A Novel Genetic Algorithm Based Scheduling for Multi-core Systems , 2018, Smart Innovations in Communication and Computational Sciences.

[75]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[76]  Elwood S. Buffa,et al.  A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities , 1963 .

[77]  Josep M. Guerrero,et al.  A New “Doctor and Patient” Optimization Algorithm: An Application to Energy Commitment Problem , 2020 .

[78]  Gaurav Dhiman,et al.  Spotted hyena optimizer: A novel bio-inspired based metaheuristic technique for engineering applications , 2017, Adv. Eng. Softw..

[79]  A. Kaveh,et al.  A novel heuristic optimization method: charged system search , 2010 .

[80]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[81]  BOSA: Binary Orientation Search Algorithm , 2019, International Journal of Innovative Technology and Exploring Engineering.

[82]  Dan Simon,et al.  Biogeography-Based Optimization , 2022 .

[83]  Hadi Givi,et al.  Darts Game Optimizer: A New Optimization Technique Based on Darts Game , 2020 .

[84]  Rajiv Tiwari,et al.  Optimum design of rolling element bearings using genetic algorithms , 2007 .

[85]  Om P. Malik,et al.  DGO: Dice Game Optimizer , 2019, GAZI UNIVERSITY JOURNAL OF SCIENCE.

[86]  Xiaodong Wu,et al.  Small-World Optimization Algorithm for Function Optimization , 2006, ICNC.

[87]  Chui-Yu Chiu,et al.  A Dynamic Adjusting Novel Global Harmony Search for Continuous Optimization Problems , 2018, Symmetry.

[88]  Om P. Malik,et al.  FOA: ‘Following’ Optimization Algorithm for solving Power engineering optimization problems , 2020 .

[89]  A. Mucherino,et al.  Monkey search: a novel metaheuristic search for global optimization , 2007 .

[90]  Tom Fearn,et al.  Particle Swarm Optimisation , 2014 .

[91]  Omid Bozorg-Haddad,et al.  Teaching-Learning-Based Optimization (TLBO) Algorithm , 2018 .