Tuning the Performance of the MMAS Heuristic

This paper presents an in-depth Design of Experiments (DOE) methodology for the performance analysis of a stochastic heuristic. The heuristic under investigation is Max-Min Ant System (MMAS). for the Travelling Salesperson Problem (TSP). Specifically, the Response Surface Methodology is used to model and tune MMAS performance with regard to 10 tuning parameters, 2 problem characteristics and 2 performance metrics--solution quality and solution time. The accuracy of these predictions is methodically verified in a separate series of confirmation experiments. The two conflicting responses are simultaneously optimised using desirability functions. Recommendations on optimal parameter settings are made. The optimal parameters are methodically verified. The large number of degrees-of-freedom in the MMAS design are overcome with a Minimum Run Resolution V design. Publicly available algorithm and problem generator implementations are used throughout. The paper should therefore serve as an illustrative case study of the principled engineering of a stochastic heuristic.

[1]  J. Wishart,et al.  Statistics in Research. , 1956 .

[2]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[3]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[4]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[5]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[6]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[7]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[8]  R. H. Myers,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[9]  Mark E. Johnson,et al.  A case study in experimental design applied to genetic algorithms with applications to DNA sequence assembly , 1997 .

[10]  Yeong-Dae Kim,et al.  A systematic procedure for setting parameters in simulated annealing algorithms , 1998, Comput. Oper. Res..

[11]  David S. Johnson,et al.  A theoretician's guide to the experimental analysis of algorithms , 1999, Data Structures, Near Neighbor Searches, and Methodology.

[12]  Veronica Czitrom,et al.  One-Factor-at-a-Time versus Designed Experiments , 1999 .

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

[14]  George C. Runger,et al.  Using Experimental Design to Find Effective Parameter Settings for Heuristics , 2001, J. Heuristics.

[15]  Juan Julián Merelo Guervós,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[16]  Marco Dorigo,et al.  Model-Based Search for Combinatorial Optimization: A Comparative Study , 2002, PPSN.

[17]  William J. Cook,et al.  Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems , 2003, Math. Program..

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

[19]  Mauro Birattari.  The Problem of Tuning Metaheuristics , 2005 .

[20]  Keith L. Clark,et al.  On Optimal Parameters for Ant Colony Optimization Algorithms , 2005, IC-AI.

[21]  D. Kudenko,et al.  Sequential Experiment Designs for Screening and Tuning Parameters of Stochastic Heuristics , 2006 .

[22]  Manuel Laguna,et al.  Fine-Tuning of Algorithms Using Fractional Experimental Designs and Local Search , 2006, Oper. Res..

[23]  Abraham P. Punnen,et al.  The traveling salesman problem and its variations , 2007 .

[24]  Daniel Kudenko,et al.  Analyzing heuristic performance with response surface models: prediction, optimization and robustness , 2007, GECCO '07.

[25]  Daniel Kudenko,et al.  An Analysis of Problem Difficulty for a Class of Optimisation Heuristics , 2007, EvoCOP.

[26]  David S. Johnson,et al.  Experimental Analysis of Heuristics for the STSP , 2007 .