Continuous ant colony system and tabu search algorithms hybridized for global minimization of continuous multi-minima functions

A new hybrid optimization method, combining Continuous Ant Colony System (CACS) and Tabu Search (TS) is proposed for minimization of continuous multi-minima functions. The new algorithm incorporates the concepts of promising list, tabu list and tabu balls from TS into the framework of CACS. This enables the resultant algorithm to avoid bad regions and to be guided toward the areas more likely to contain the global minimum. New strategies are proposed to dynamically tune the radius of the tabu balls during the execution and also to handle the variable correlations. The promising list is also used to update the pheromone distribution over the search space. The parameters of the new method are tuned based on the results obtained for a set of standard test functions. The results of the proposed scheme are also compared with those of some recent ant based and non-ant based meta-heuristics, showing improvements in terms of accuracy and efficiency.

[1]  Patrick Siarry,et al.  Genetic and Nelder-Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions , 2003, Eur. J. Oper. Res..

[2]  Marco Dorigo,et al.  Ant colony optimization for continuous domains , 2008, Eur. J. Oper. Res..

[3]  J. Dréo,et al.  Continuous interacting ant colony algorithm based on dense heterarchy , 2004, Future Gener. Comput. Syst..

[4]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[5]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[6]  Ian C. Parmee,et al.  The Ant Colony Metaphor for Searching Continuous Design Spaces , 1995, Evolutionary Computing, AISB Workshop.

[7]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[8]  Nicolas Monmarché,et al.  On how Pachycondyla apicalis ants suggest a new search algorithm , 2000, Future Gener. Comput. Syst..

[9]  Johann Dréo,et al.  A New Ant Colony Algorithm Using the Heterarchical Concept Aimed at Optimization of Multiminima Continuous Functions , 2002, Ant Algorithms.

[10]  Krzysztof Socha,et al.  ACO for Continuous and Mixed-Variable Optimization , 2004, ANTS Workshop.

[11]  T. Stützle,et al.  MAX-MIN Ant System and local search for the traveling salesman problem , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[12]  Patrick Siarry,et al.  Enhanced simulated annealing for globally minimizing functions of many-continuous variables , 1997, TOMS.

[13]  Roberto Battiti,et al.  The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization , 1996, Ann. Oper. Res..

[14]  Jie Sheng,et al.  A Method for Solving Optimization Problems in Continuous Space Using Ant Colony Algorithm , 2002, Ant Algorithms.

[15]  Fred W. Glover,et al.  Tabu Search - Part I , 1989, INFORMS J. Comput..

[16]  Tie-jun Wu,et al.  An adaptive ant colony system algorithm for continuous-space optimization problems. , 2003, Journal of Zhejiang University. Science.

[17]  Fred Glover,et al.  Tabu Search - Part II , 1989, INFORMS J. Comput..

[18]  Patrick Siarry,et al.  Tabu Search applied to global optimization , 2000, Eur. J. Oper. Res..

[19]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[20]  Patrick Siarry,et al.  A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions , 2000, J. Heuristics.

[21]  P. Siarry,et al.  Enhanced Continuous Tabu Search: An Algorithm for Optimizing Multiminima Functions , 1999 .

[22]  Seid H. Pourtakdoust,et al.  OPTIMIZATION OF FUZZY RULE BASES USING CONTINUOUS ANT COLONY SYSTEM , 2005 .

[23]  D Cvijovicacute,et al.  Taboo search: an approach to the multiple minima problem. , 1995, Science.

[24]  Seid H. Pourtakdoust,et al.  An Extension of Ant Colony System to Continuous Optimization Problems , 2004, ANTS Workshop.

[25]  Marco Dorigo,et al.  Ant algorithms and stigmergy , 2000, Future Gener. Comput. Syst..

[26]  Seid H. Pourtakdoust,et al.  Optimal Fuzzy CLOS Guidance Law Design Using Ant Colony Optimization , 2005, SAGA.

[27]  Li Yan-jun,et al.  An adaptive ant colony system algorithm for continuous-space optimization problems , 2003 .

[28]  R. Steele Optimization , 2005 .

[29]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[30]  Alain Hertz,et al.  Ants can colour graphs , 1997 .

[31]  Luca Maria Gambardella,et al.  Ant-Q: A Reinforcement Learning Approach to the Traveling Salesman Problem , 1995, ICML.

[32]  Silvano Martello,et al.  Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization , 2012 .

[33]  P. Siarry,et al.  FITTING OF TABU SEARCH TO OPTIMIZE FUNCTIONS OF CONTINUOUS VARIABLES , 1997 .

[34]  N. Hu Tabu search method with random moves for globally optimal design , 1992 .