Chaos driven discrete artificial bee algorithm for location and assignment optimisation problems

Abstract The chaos driven discrete artificial bee colony (CDABC) algorithm is introduced in this paper. Four unique chaos maps of Burgers, Lozi, Delayed Logistic and Tinkerbell are embedded as chaos pseudo-random number generators and compared with the Mersenne Twister pseudo-random number generator. Two unique problems of quadratic assignment and capacitated vehicle routing problem are solved using five different variants of the algorithm and analytical comparison is conducted. Furthermore, paired t-test is done pairwise on all variants, and from these results it is ascertained that the Tinkerbell variant of CDABC is the best performing for both problem classes.

[1]  Michal Pluhacek,et al.  Chaos PSO algorithm driven alternately by two different chaotic maps - An initial study , 2013, 2013 IEEE Congress on Evolutionary Computation.

[2]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[3]  Michal Pluhacek,et al.  Chaos Driven Evolutionary Algorithm: a New Approach for Evolutionary Optimization , 2013 .

[4]  Magdalena Metlicka,et al.  Scheduling the Flowshop with Zero Intermediate Storage Using Chaotic Discrete Artificial Bee Algorithm , 2014 .

[5]  J. Rogers.  Chaos , 1876 .

[6]  Paolo Toth,et al.  Exact algorithms for routing problems under vehicle capacity constraints , 2010, Ann. Oper. Res..

[7]  Wei-Chiang Hong,et al.  SVR with hybrid chaotic genetic algorithms for tourism demand forecasting , 2011, Appl. Soft Comput..

[8]  Charles Fleurent,et al.  Genetic Hybrids for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[9]  Qi Wu.  A self-adaptive embedded chaotic particle swarm optimization for parameters selection of Wv-SVM , 2011, Expert Syst. Appl..

[10]  Li-Yeh Chuang,et al.  Chaotic catfish particle swarm optimization for solving global numerical optimization problems , 2011, Appl. Math. Comput..

[11]  Azah Mohamed,et al.  Power system stabilizer design using hybrid multi-objective particle swarm optimization with chaos , 2011 .

[12]  Jing J. Liang,et al.  Effective hybrid discrete artificial bee colony algorithms for the total flowtime minimization in the blocking flowshop problem , 2013 .

[13]  Quan-Ke Pan,et al.  Discrete artificial bee colony algorithm for lot-streaming flowshop with total flowtime minimization , 2012, Chinese Journal of Mechanical Engineering.

[14]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem , 2011, Inf. Sci..

[15]  Éric D. Taillard,et al.  Robust taboo search for the quadratic assignment problem , 1991, Parallel Comput..

[16]  Yaonan Wang,et al.  Hybrid chaos optimization algorithm with artificial emotion , 2012, Appl. Math. Comput..

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

[18]  B. Alatas,et al.  Chaos embedded particle swarm optimization algorithms , 2009 .

[19]  Li Ke.  Multi-objective genetic algorithm based on improved chaotic optimization , 2011 .

[20]  Donald Davendra,et al.  Differential Evolution for Permutation—Based Combinatorial Problems , 2009 .

[21]  Yang Yi-xian.  New chaos-particle swarm optimization algorithm , 2012 .

[22]  T. C. Bora,et al.  A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem , 2012, IEEE Transactions on Magnetics.

[23]  Mostafa Zandieh,et al.  An artificial immune algorithm for the flexible job-shop scheduling problem , 2010, Future Gener. Comput. Syst..

[24]  George B. Dantzig,et al.  The Truck Dispatching Problem , 1959 .

[25]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[26]  Ivan Zelinka,et al.  SOMA—Self-organizing Migrating Algorithm , 2016 .

[27]  Ge Li,et al.  Network intrusion detection based on least squares support vector machine and chaos particle swarm optimization algorithm , 2012 .

[28]  Nicos Christofides,et al.  An exact algorithm for the vehicle routing problem based on the set partitioning formulation with additional cuts , 2008, Math. Program..

[29]  Fang Liu,et al.  chaotic quantum-behaved particle swarm optimization based on lateral nhibition for image matching , 2012 .

[30]  Roman Senkerik,et al.  Discrete Self-Organising Migrating Algorithm for flow-shop scheduling with no-wait makespan , 2013, Math. Comput. Model..

[31]  Michal Pluhacek,et al.  Optimization of the Batch Reactor by Means of Chaos Driven Differential Evolution , 2012, SOCO.

[32]  Roman Senkerik,et al.  Chaos driven evolutionary algorithms for the task of PID control , 2010, Comput. Math. Appl..

[33]  Gilbert Laporte,et al.  The vehicle routing problem: An overview of exact and approximate algorithms , 1992 .

[34]  I. Maksimov,et al.  The thermofrictional oscillations under sliding , 1987 .

[35]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[36]  Michal Pluhacek,et al.  Designing PID controller for 4th order system by means of enhanced PSO algorithm with discrete chaotic Dissipative standard map , 2012 .

[37]  Mariam Faied,et al.  Vehicle Routing Problem Instances: Application to Multi-UAV Mission Planning , 2010 .

[38]  Shih-Wei Lin,et al.  Applying hybrid meta-heuristics for capacitated vehicle routing problem , 2009, Expert Syst. Appl..

[39]  R. Lozi.  Chaotic Pseudo Random Number Generators via Ultra Weak Coupling of Chaotic Maps and Double Threshold Sampling Sequences , 2009 .

[40]  Thomas Stützle,et al.  Ant colony optimization: artificial ants as a computational intelligence technique , 2006 .

[41]  Ahmet Bedri Özer,et al.  CIDE: Chaotically Initialized Differential Evolution , 2010, Expert Syst. Appl..

[42]  Dervis Karaboga,et al.  Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems , 2007, IFSA.

[43]  J. M. Burgers,et al.  Mathematical Examples Illustrating Relations Occurring in the Theory of Turbulent Fluid Motion , 1995 .

[44]  Michal Pluhacek,et al.  On the behavior and performance of chaos driven PSO algorithm with inertia weight , 2013, Comput. Math. Appl..

[45]  Nicolas Jozefowiez,et al.  The vehicle routing problem: Latest advances and new challenges , 2007 .

[46]  J. Sprott.  Chaos and time-series analysis , 2001 .

[47]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[48]  R. R. Whitehead,et al.  A chaotic mapping that displays its own homoclinic structure , 1984 .

[49]  Xiaohui Yuan,et al.  Hydrothermal scheduling using chaotic hybrid differential evolution , 2008 .

[50]  Dong Liu,et al.  APPLICATION OF CHAOTIC PARTICLE SWARM OPTIMIZATION ALGORITHM TO PATTERN SYNTHESIS OF ANTENNA ARRAYS , 2011, Progress In Electromagnetics Research.

[51]  Xin-She Yang,et al.  Chaos-enhanced accelerated particle swarm optimization , 2013, Commun. Nonlinear Sci. Numer. Simul..

[52]  Mehmet Fatih Tasgetiren,et al.  A discrete artificial bee colony algorithm for the total flowtime minimization in permutation flow shops , 2011, Inf. Sci..

[53]  R. Lozi.  New Enhanced Chaotic Number Generators , 2007 .

[54]  KarabogaDervis,et al.  A powerful and efficient algorithm for numerical function optimization , 2007 .

[55]  Charles Herring,et al.  Random number generators are chaotic , 1989, CACM.

[56]  Michal Pluhacek,et al.  Do Evolutionary Algorithms Indeed Require Random Numbers? Extended Study , 2013, NOSTRADAMUS.

[57]  Wei Liang,et al.  The chaos differential evolution optimization algorithm and its application to support vector regression machine , 2011, J. Softw..

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

[59]  Leandro dos Santos Coelho,et al.  A chaotic quantum-behaved particle swarm approach applied to optimization of heat exchangers , 2012 .

[60]  Zengqiang Chen,et al.  Chaos particle swarm optimization and T-S fuzzy modeling approaches to constrained predictive control , 2012, Expert Syst. Appl..

[61]  Gang Liu,et al.  Dynamic economic dispatch for wind-thermal power system using a novel bi-population chaotic differential evolution algorithm , 2012 .

[62]  Zhang Chen.  Multi-objective reactive power optimization based on adaptive chaos particle swarm optimization algorithm , 2011 .

[63]  J. Palmore,et al.  Shadowing by computable chaotic orbits , 1987 .

[64]  L. Kocarev,et al.  Chaos-based random number generators-part I: analysis [cryptography] , 2001 .

[65]  Quan-Ke Pan,et al.  Pareto-based discrete artificial bee colony algorithm for multi-objective flexible job shop scheduling problems , 2011 .

[66]  Farookh Khadeer Hussain,et al.  Support vector regression with chaos-based firefly algorithm for stock market price forecasting , 2013, Appl. Soft Comput..

[67]  Michal Pluhacek,et al.  Utilising the chaos-induced discrete self organising migrating algorithm to solve the lot-streaming flowshop scheduling problem with setup time , 2014, Soft Comput..

[68]  Michal Pluhacek,et al.  Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems , 2014, TheScientificWorldJournal.

[69]  Jing Liu,et al.  A chaotic non-dominated sorting genetic algorithm for the multi-objective automatic test task scheduling problem , 2013, Appl. Soft Comput..

[70]  Michal Pluhacek,et al.  Hidden Periodicity - Chaos Dependance on Numerical Precision , 2013, NOSTRADAMUS.

[71]  David Connolly.  An improved annealing scheme for the QAP , 1990 .