An Incremental ACO R with Local Search for Continuous Optimization Problems

One of the most popular Ant Colony Optimization (ACO) algorithms for continuous optimization problems is ACOR. In this paper, we propose an incremental ACOR with local search (IACOR-LS) that obtains better results than the original ACOR on a number of continuous optimization problems. We first present a mechanism that improves the search diversification of ACOR. This mechanism consists of a growing solution archive with a special initialization rule applied to entrant solutions. The resulting algorithm, called IACOR, is then hybridized with a local search procedure in order to enhance its search intensification. We experiment with Powell’s conjugate directions set, Powell’s BOBYQA, and Lin-Yu Tseng’s Mtsls1 methods as local search procedures. Automatic parameter tuning results show that IACOR-LS with Mtsls1 (IACOR-Mtsls1) is not only a significant improvement over ACOR, but that it is also competitive with the state-of-the-art algorithms described in a recent special issue of the journal Soft Computing. Further experimentation with IACOR-Mtsls1 on the combined benchmark functions suite from both the special issue of Soft Computing and the IEEE 2005 Congress on Evolutionary Computation (CEC 2005) demonstrates its good performance in continuous optimization.

[1]  L. J. Eshelman,et al.  chapter Real-Coded Genetic Algorithms and Interval-Schemata , 1993 .

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

[3]  Thomas Stützle,et al.  F-Race and Iterated F-Race: An Overview , 2010, Experimental Methods for the Analysis of Optimization Algorithms.

[4]  Min Kong,et al.  A Direct Application of Ant Colony Optimization to Function Optimization Problem in Continuous Domain , 2006, ANTS Workshop.

[5]  Chun Chen,et al.  Multiple trajectory search for Large Scale Global Optimization , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[6]  Ponnuthurai Nagaratnam Suganthan,et al.  Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization , 2008 .

[7]  Thomas Bartz-Beielstein,et al.  Experimental Methods for the Analysis of Optimization Algorithms , 2010 .

[8]  张军,et al.  Orthogonal Methods Based Ant Colony Search for Solving Continuous Optimization Problems , 2008 .

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

[10]  Thomas Stützle,et al.  Incremental Social Learning in Particle Swarms , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Carlos A. Coello Coello,et al.  An Alternative ACO \BbbR_{\Bbb{R}} Algorithm for Continuous Optimization Problems , 2010, ANTS Conference.

[12]  Thomas Stützle,et al.  Improvement Strategies for the F-Race Algorithm: Sampling Design and Iterative Refinement , 2007, Hybrid Metaheuristics.

[13]  C. Coello,et al.  An Alternative ACOR Algorithm for Continuous Optimization Problems , .

[14]  Thomas Stützle,et al.  An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms , 2011, Soft Comput..

[15]  Thomas Stützle,et al.  Towards incremental social learning in optimization and multiagent systems , 2008, GECCO '08.

[16]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[17]  M. Powell.  The BOBYQA algorithm for bound constrained optimization without derivatives , 2009 .

[18]  Francisco Herrera,et al.  Editorial scalability of evolutionary algorithms and other metaheuristics for large-scale continuous optimization problems , 2011, Soft Comput..

[19]  Qin Ling.  A Method for Solving Optimization Problem in Continuous Space by Using Ant Colony Algorithm , 2002 .

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

[21]  Thomas Stützle,et al.  Ant Colony Optimization Theory , 2004 .

[22]  Christian Blum,et al.  An ant colony optimization algorithm for continuous optimization: application to feed-forward neural network training , 2007, Neural Computing and Applications.

[23]  Nikolaus Hansen,et al.  On the Adaptation of Arbitrary Normal Mutation Distributions in Evolution Strategies: The Generating Set Adaptation , 1995, ICGA.

[24]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

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

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

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

[29]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[30]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..