Particle Swarm Optimizations to Solve Multi-Valued Discrete Problems

다수의 값을 갖는 이산적 문제에 적용되는 Particle Swarm Optimization

  • Yim, Dong-Soon (Department of Industrial and Management Engineering, Hannam University)
  • 임동순 (한남대학교 산업경영공학과)
  • Received : 2013.08.08
  • Accepted : 2013.09.06
  • Published : 2013.09.30


Many real world optimization problems are discrete and multi-valued. Meta heuristics including Genetic Algorithm and Particle Swarm Optimization have been effectively used to solve these multi-valued optimization problems. However, extensive comparative study on the performance of these algorithms is still required. In this study, performance of these algorithms is evaluated with multi-modal and multi-dimensional test functions. From the experimental results, it is shown that Discrete Particle Swarm Optimization (DPSO) provides better and more reliable solutions among the considered algorithms. Also, additional experiments shows that solution quality of DPSO is not lowered significantly when bit size representing a solution increases. It means that bit representation of multi-valued discrete numbers provides reliable solutions instead of becoming barrier to performance of DPSO.


  1. Michaelwicz, Z., Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, 1992.
  2. Goldberg, D.E. and Lingle, R., Alleles, Loci, and the TSP, Proceedings of the First International Conference on Genetic Algorithms, Lawrence Erlbaum Associates, Hillsdale, NJ, 1985, p 154-159.
  3. Kennedy, J., Eberhart, R.C., Particle Swarm Optimization, Proceeding of the 1995 IEEE International Conference on Neural Networks, 1995, p 1942-1948.
  4. Kennedy, J. and Eberhart, R.C., A Discrete Binary Version of the Particle Swarm Algorithm, IEEE International Conference on Systems, Man, and Cybernetics, 1997, p 4104-4108.
  5. Laskari, E.C., Parsopoulos, K.E., and Vrahatis, M.N., Particle Swarm Optimization for Integer Programming, Proceedings of the IEEE 2002 Congress on Evolutionary Computations, 2002, p 1582-1587.
  6. Pugh, J. and Martinoli, A., Discrete Multi-Valued Particle Swarm Optimization, Proceedings of IEEE Swarm Intelligence Symposium, 2006, p 103-110.
  7. Song, H., Diolata, R., and Joo, Y., Photovaltaic System Allocation Using Discrete Particle Swarm Optimization with Multi-level Quantization. Journal of Electrical Engineering and Technology, Vol. 4, No. 2, 2009, p 185-193.
  8. Vesterstrom, J. and Thomsen, R., A Comparative Study of Differential Evolution, Particle Swarm Optimization, and Evolutionary Algorithms on Numerical Benchmark Problems, Proceedings of the IEEE 2004 congress on Evolutionary Computation, 2004, p 1980-1987.
  9. Veeramachaneni, K., Osadciw, L., and Kamath, G., Probabilistically Driven Particle Swarms for Optimization of Multi Valued Discrete Problems: Design and Analysis, Proceedings of IEEE Swarm Intelligence Symposium, 2007, p 141-149.
  10. Yang, Xie-She, Test Problems in Optimization in Engineering Optimization : An Introduction with Metaheuristic Applications (Eds Xin-She Yang), John Wiley and Sons, 2010.
  11. Yim, D.S, Park, C.H., Cho, N.C, and Oh, H.S., A Case Study on the Scheduling for a Tube Manufacturing System. Journal of the Society of Korea Industrial and Systems Engineering, Vol. 32, No. 3, 2009, p 110-117.