Billiards-inspired optimization algorithm; a new meta-heuristic method

Abstract This paper introduces a new physics-based meta-heuristic algorithm called Billiards-inspired Optimization Algorithm (BOA). The optimization process of this algorithm resembles the billiards game. Each solution candidate is considered as a multi-dimensional billiards ball and the best obtained solutions as pockets. When the balls encounter other balls, vector algebra and conservation laws determine final positions of the balls in optimization search space. In order to evaluate the validity of the proposed approach, twenty-three mathematical functions and seven constrained engineering benchmark problems are studied. The results indicated that the BOA can play an effective role in the field of optimization.

[1]  Ling Wang,et al.  An effective co-evolutionary differential evolution for constrained optimization , 2007, Appl. Math. Comput..

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

[3]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[4]  Ali Kaveh,et al.  Truss optimization with natural frequency constraints using a hybridized CSS-BBBC algorithm with trap recognition capability , 2012 .

[5]  Robert M. Parkin,et al.  A theoretical analysis of billiard ball dynamics under cushion impacts , 2010 .

[6]  Seyed Mohammad Mirjalili,et al.  Multi-Verse Optimizer: a nature-inspired algorithm for global optimization , 2015, Neural Computing and Applications.

[7]  Thomas Stützle,et al.  Ant Colony Optimization , 2009, EMO.

[8]  Ali Kaveh,et al.  Water strider algorithm: A new metaheuristic and applications , 2020, Structures.

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

[10]  A. Kaveh,et al.  A new optimization method: Dolphin echolocation , 2013, Adv. Eng. Softw..

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

[12]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[13]  A. Kaveh,et al.  A novel meta-heuristic optimization algorithm: Thermal exchange optimization , 2017, Adv. Eng. Softw..

[14]  Jean-Pierre Dussault,et al.  AI Optimization of a Billiard Player , 2007, J. Intell. Robotic Syst..

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

[16]  MirjaliliSeyedali.  Moth-flame optimization algorithm , 2015 .

[17]  K. M. Ragsdell,et al.  Optimal Design of a Class of Welded Structures Using Geometric Programming , 1976 .

[18]  Charles V. Camp,et al.  Optimal design of truss structures for size and shape with frequency constraints using a collaborative optimization strategy , 2016, Expert Syst. Appl..

[19]  A. Kaveh,et al.  Democratic PSO for truss layout and size optimization with frequency constraints , 2014 .

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

[21]  M. Fesanghary,et al.  An improved harmony search algorithm for solving optimization problems , 2007, Appl. Math. Comput..

[22]  Ling Wang,et al.  An effective co-evolutionary particle swarm optimization for constrained engineering design problems , 2007, Eng. Appl. Artif. Intell..

[23]  A. Kaveh,et al.  Improved GWO algorithm for optimal design of truss structures , 2017, Engineering with Computers.

[24]  Hyun Myung,et al.  Evolutionary programming techniques for constrained optimization problems , 1997, IEEE Trans. Evol. Comput..

[25]  Amir Hossein Gandomi,et al.  Bat algorithm for constrained optimization tasks , 2012, Neural Computing and Applications.

[26]  A. Kaveh,et al.  Enhanced colliding bodies optimization for design problems with continuous and discrete variables , 2014, Adv. Eng. Softw..

[27]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[28]  Mitat Uysal,et al.  Migrating Birds Optimization: A new metaheuristic approach and its performance on quadratic assignment problem , 2012, Inf. Sci..

[29]  Min-Yuan Cheng,et al.  Symbiotic Organisms Search: A new metaheuristic optimization algorithm , 2014 .

[30]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[31]  E. Sandgren,et al.  Nonlinear Integer and Discrete Programming in Mechanical Design Optimization , 1990 .

[32]  Kalyanmoy Deb,et al.  Optimal design of a welded beam via genetic algorithms , 1991 .

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

[34]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[35]  Ali Kaveh,et al.  Colliding bodies optimization: A novel meta-heuristic method , 2014 .

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

[37]  MirjaliliSeyedali,et al.  Grasshopper Optimisation Algorithm , 2017 .

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

[39]  Ashok Dhondu Belegundu,et al.  A Study of Mathematical Programming Methods for Structural Optimization , 1985 .

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

[41]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010 .

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

[43]  Ali Kaveh,et al.  Vibrating particles system algorithm for truss optimization with multiple natural frequency constraints , 2017 .

[44]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..