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Metaheuristic algorithms and probabilistic behaviour: a comprehensive analysis of Ant Colony Optimization and its variants


The application of metaheuristic algorithms to combinatorial optimization problems is on the rise and is growing rapidly now than ever before. In this paper the historical context and the conducive environment that accelerated this particular trend of inspiring analogies or metaphors from various natural phenomena are analysed. We have implemented the Ant System Model and the other variants of ACO including the 3-Opt, Max–Min, Elitist and the Rank Based Systems as mentioned in their original works and we converse the missing pieces of Dorigo’s Ant System Model. Extensive analysis of the variants on Travelling Salesman Problem and Job Shop Scheduling Problem shows how much they really contribute towards obtaining better solutions. The stochastic nature of these algorithms has been preserved to the maximum extent to keep the implementations as generic as possible. We observe that stochastic implementations show greater resistance to changes in parameter values, still obtaining near optimal solutions. We report how Polynomial Turing Reduction helps us to solve Job Shop Scheduling Problem without making considerable changes in the implementation of Travelling Salesman Problem, which could be extended to solve other NP-Hard problems. We elaborate on the various parallelization options based on the constraints enforced by strong scaling (fixed size problem) and weak scaling (fixed time problem). Also we elaborate on how probabilistic behaviour helps us to strike a balance between intensification and diversification of the search space.

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The authors would like to acknowledge the infrastructure support provided by the Massively Parallel Programming Laboratory (CUDA Teaching Centre), Department of Computer Applications, National Institute of Technology, Trichy. The authors would like to thank Dr. Hemalatha Thiagarajan, Professor, Department of Mathematics, National Institute of Technology, Trichy for providing valuable insights on the simulation of various probability distribution functions. The authors would also like to thank their fellow researchers Mr.S.Thiruselvan, Mr.P.Arish and Ms.R.Eswari for their valuable suggestions and support.

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Correspondence to Anandkumar Prakasam.

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The code is licensed and made available under the open source Creative Commons License to enable constructive criticism, reproducible research and to ensure maximum dissemination of the research work. The code, results and graphs are provided as supplementary materials which will also be made available as a project in Google code and Git-Hub.

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Prakasam, A., Savarimuthu, N. Metaheuristic algorithms and probabilistic behaviour: a comprehensive analysis of Ant Colony Optimization and its variants. Artif Intell Rev 45, 97–130 (2016).

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  • Ant Colony Optimization
  • Metaheuristics
  • Ant System
  • ACO variants
  • Travelling Salesman Problem
  • Job Shop Scheduling Problem