Ant colony optimization for continuous domains

In this paper we present an extension of ant colony optimization (ACO) to continuous domains. We show how ACO, which was initially developed to be a metaheuristic for combinatorial optimization, can be adapted to continuous optimization without any major conceptual change to its structure. We present the general idea, implementation, and results obtained. We compare the results with those reported in the literature for other continuous optimization methods: other ant-related approaches and other metaheuristics initially developed for combinatorial optimization and later adapted to handle the continuous case. We discuss how our extended ACO compares to those algorithms, and we present some analysis of its efficiency and robustness.

[1]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[2]  MaronOden,et al.  The Racing Algorithm , 1997 .

[3]  Luca Maria Gambardella,et al.  A Multiple Ant Colony System for Vehicle Routing Problems with Time Windows , 1999 .

[4]  Nikolaus Hansen,et al.  Step-Size Adaption Based on Non-Local Use of Selection Information , 1994, PPSN.

[5]  Michael Sampels,et al.  Ant Algorithms for the University Course Timetabling Problem with Regard to the State-of-the-Art , 2003, EvoWorkshops.

[6]  Josef Schwarz,et al.  Estimation Distribution Algorithm for mixed continuous-discrete optimization problems , 2002 .

[7]  Mauro Birattari,et al.  Tuning Metaheuristics - A Machine Learning Perspective , 2009, Studies in Computational Intelligence.

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

[9]  David E. Goldberg,et al.  Bayesian optimization algorithm, decision graphs, and Occam's razor , 2001 .

[10]  J. Deneubourg,et al.  Self-organized shortcuts in the Argentine ant , 1989, Naturwissenschaften.

[11]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[12]  Hartmut Schmeck,et al.  Ant colony optimization for resource-constrained project scheduling , 2000, IEEE Trans. Evol. Comput..

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

[14]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

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

[16]  M. A. Wolfe.  A first course in numerical analysis , 1972 .

[17]  Rich Caruana,et al.  Removing the Genetics from the Standard Genetic Algorithm , 1995, ICML.

[18]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

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

[20]  D. Fogel,et al.  Fitness distributions in evolutionary computation: analysis of local extrema in the continuous domain , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[22]  A. Ralston.  A first course in numerical analysis , 1965 .

[23]  Luca Maria Gambardella,et al.  MACS-VRPTW: a multiple ant colony system for vehicle routing problems with time windows , 1999 .

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

[25]  Christian Blum,et al.  Theoretical and practical aspects of ant colony optimization , 2004 .

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

[27]  Thomas Stützle,et al.  A Racing Algorithm for Configuring Metaheuristics , 2002, GECCO.

[28]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[29]  Martin Middendorf,et al.  A Population Based Approach for ACO , 2002, EvoWorkshops.

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

[31]  Christian Blum,et al.  An Ant Colony Optimization Algorithm for Shop Scheduling Problems , 2004, J. Math. Model. Algorithms.

[32]  Thomas Bäck,et al.  Empirical Investigation of Multiparent Recombination Operators in Evolution Strategies , 1997, Evolutionary Computation.

[33]  Petros Koumoutsakos,et al.  Learning Probability Distributions in Continuous Evolutionary Algorithms - a Comparative Review , 2004, Nat. Comput..

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

[35]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

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

[37]  M. Dorigo,et al.  Aco Algorithms for the Traveling Salesman Problem , 1999 .

[38]  Marcus Gallagher,et al.  Playing in continuous spaces: some analysis and extension of population-based incremental learning , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[39]  Richard F. Hartl,et al.  D-Ants: Savings Based Ants divide and conquer the vehicle routing problem , 2004, Comput. Oper. Res..

[40]  Marc Gravel,et al.  Comparing an ACO algorithm with other heuristics for the single machine scheduling problem with sequence-dependent setup times , 2002, J. Oper. Res. Soc..

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

[42]  Reinhard Männer,et al.  Parallel Problem Solving from Nature — PPSN III , 1994, Lecture Notes in Computer Science.

[43]  Gene H. Golub,et al.  Matrix computations , 1983 .

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

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

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

[47]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[48]  V. K. Jayaraman,et al.  Ant Colony Approach to Continuous Function Optimization , 2000 .

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

[50]  P. Bosman,et al.  Continuous iterated density estimation evolutionary algorithms within the IDEA framework , 2000 .

[51]  Kenneth Holmström,et al.  Global Optimization Using the DIRECT Algorithm in Matlab , 1999 .

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

[53]  David B. Fogel,et al.  A Note on the Empirical Evaluation of Intermediate Recombination , 1995, Evolutionary Computation.

[54]  Kalyanmoy Deb,et al.  A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization , 2002, Evolutionary Computation.

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