My question is about how the concept of accepted solution in AMOSA? to elaborate more, in AMOSA the acceptance probability of a new solution vis-a-vis the current solution is determined by the amount of dominance as described in [1] where they give different cases how to calculate this probability.
So is it right to chose a random number uniformly distributed in the interval (0,1) and compare it to the calculated probability, and then we see if it's less than the probability the new solution is rejected otherwise we accept the solution? are there any better methods used in this case ?
[1] S. Bandyopadhyay, S. Saha, U. Maulik, and K. Deb, “A Simulated Annealing-Based Multiobjective Optimization Algorithm: AMOSA,” IEEE Trans. Evol. Comput., vol. 12, no. 3, pp. 269–283, Jun. 2008. http://www.isical.ac.in/~sriparna_r/amosa_final_indraft_twoc.pdf
Dear Hichem,
The typical approach is, as you have mentioned, generating random numbers in the range [0, 1] by following a uniform distribution.
For instance, imagine you have calculated the probability of acceptance of the solution new-pt, being this equal to 0.65, i.e. prob(new-pt) = 0.65, if we use the nomenclature of the paper. In addition, suppose that you have obtained a random number r = 0.4.
Since r prob(new-pt), solution new-pt would not be accepted.
There is a lot of literature regarding the generation of random numbers. For instance, you can use Pseudo-random Number Generators (PRNGs) or Chaotic Number Generators (CNGs). Mersenne Twister [1] and Tent Map [2] respectively are good examples of both types of techniques.
I hope the above has helped you.
Regards,
Eduardo
[1] Matsumoto, M., Nishimura, T.: Mersenne Twister: A 623-dimensionally Equidistributed Uniform Pseudo-random Number Generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)
[2] Crampin, M., Heal, B.: On the Chaotic Behaviour of the Tent Map. Teaching Mathematics and its Applications. 13(2), 83--89 (1994)
http://dl.acm.org/citation.cfm?id=272995
Article On the Chaotic Behaviour of the Tent Map
Thank you very much for your clarification it's helpful
Best regards
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