A Transgenetic Algorithm for the bi-objective traveling purchaser problem

This work proposes an algorithm based on Computational Transgenetic (CT) metaphor to deal with the bi-objective traveling purchaser problem (2TPP). The 2TPP consists in determining a route through a subset of markets to collect a set of products, minimizing the travel distance and the purchasing cost simultaneously. This problem contains a finite set of solutions and belongs to the field of the bi-objective combinatorial optimization. CT is an evolutionary algorithm based on the endosymbiotic evolution and others interactions of the intracellular flow. In the proposed approach, named bi-objective Transgenetic Algorithm (2TA), a pair of transponson agents (one for each objective) and a plasmid agent associated with the cost are applied. The method is validated in 175 uncapacitated instances of the TPPLib benchmark. In these instances the multi-objective version (2TA) is compared to a scalarized version (1TA). The results demonstrate the superiority of 2TA and encourage further research.

[1]  Carolina P. de Almeida,et al.  TA-PFP: A Transgenetic Algorithm to Solve the Protein Folding Problem , 2007, Seventh International Conference on Intelligent Systems Design and Applications (ISDA 2007).

[2]  Juan José Salazar González,et al.  A heuristic approach for the Travelling Purchaser Problem , 2005, Eur. J. Oper. Res..

[3]  Juan José Salazar González,et al.  The biobjective travelling purchaser problem , 2005, Eur. J. Oper. Res..

[4]  David W. Corne,et al.  Properties of an adaptive archiving algorithm for storing nondominated vectors , 2003, IEEE Trans. Evol. Comput..

[5]  William J. Cook,et al.  Finding Tours in the TSP , 1999 .

[6]  D. Oudheusden,et al.  A branch and bound algorithm for the traveling purchaser problem , 1997 .

[7]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[8]  Lothar Thiele,et al.  Quality Assessment of Pareto Set Approximations , 2008, Multiobjective Optimization.

[9]  Marco César Goldbarg,et al.  A Hybrid Transgenetic Algorithm for the Prize Collecting Steiner Tree Problem , 2008, J. Univers. Comput. Sci..

[10]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[11]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[12]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[13]  M. F. Fuller,et al.  Practical Nonparametric Statistics; Nonparametric Statistical Inference , 1973 .

[14]  Marco Laumanns,et al.  PISA: A Platform and Programming Language Independent Interface for Search Algorithms , 2003, EMO.

[15]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[16]  Juan José Salazar González,et al.  A Branch-and-Cut Algorithm for the Undirected Traveling Purchaser Problem , 2003, Oper. Res..

[17]  Lynn Margulis,et al.  Symbiosis in Cell Evolution: Microbial Communities in the Archean and Proterozoic Eons , 1992 .

[18]  Marco César Goldbarg,et al.  Transgenetic algorithm for the Traveling Purchaser Problem , 2009, Eur. J. Oper. Res..

[19]  Marco Laumanns,et al.  A Tutorial on Evolutionary Multiobjective Optimization , 2004, Metaheuristics for Multiobjective Optimisation.