Maybe something of hel here: https://or-tools.googlecode.com/svn/trunk/documentation/user_manual/manual/tsp/tsptw.html

• Archive size: by experimentation, also in [1] they have more references about the archive size.
• Ri: in the original paper [1] it saids: "…, and Ri is the range of the i-th objective. Note that in several cases, Ri may not be known a priori. In these situations, the solutions present in the Archive along with the new and the current solutions are used for computing it."
• Alpha: it lays between 0.95 and 0.99
• Max temperature, min temperature, markov chain, etc: in [2,3] they use an analytical method to tune the simulated annealing parameters. (Note: they use ci and cf as initial temperature and final temperature.)

[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

[2] J. Frausto-Solis, E. F. Román, D. Romero, X. Soberon, and E. Liñán-García, “Analytically Tuned Simulated Annealing Applied to the Protein Folding Problem,” in Computational Science--ICCS 2007, Springer, 2007, pp. 370–377. https://scholar.google.com.mx/scholar?cluster=4672886717455176649&hl=en&as_sdt=0,5&as_vis=1

[3] J. Frausto-Solís, H. Sanvicente-Sánchez, and F. Imperial-Valenzuela, “ANDYMARK: An Analytical Method to Establish Dynamically the Length of the Markov Chain in Simulated Annealing for the Satisfiability Problem,” in Simulated Evolution and Learning, Springer, 2006, pp. 269–276.

Thank you both for your answers

@josé carlos, thank you for your detailed answer, about the range Ri i have read the paper but i didn't understand the part where they say "...the solutions present in the Archive along with the new and the current solutions are used for computing it." does that mean that we can simply compute the difference between the max and the min value of the i-th objective or there is another way to do it ?

@Hichem, yes, of course there are more ways to do it, I have done three different approaches. 

1) Including two more vectors, one to store the minimum values found in each objective and other to store the maximum values, global min and max found. Ri is updated using these vectors.

2) Including another two vectors to store the minimum and maximum values found in each objective for the current temperature cycle, as a local min and max found. Ri is updated using this vectors. (as it said in the original paper).

3) Ri only contains the maximum values found in each objective (global max).

From this three approaches, I get better results using the first approach (for my problem). You have to test your ideas to see which works better for your problem.

That is the part of the research. Don't get stuck, and propose new ideas.

Ok thank you very much for your answer it is very helpful and good luck with your research