What's happening, solutions are too far from real Pareto frontier, or there is no convergence at all? How are you dealing with constraints, is it by penalties?

Thank you Sir. I just use the constraint dominance concept to deal with constraint:

A solution x(1) is said to ‘constraint-dominate’ a solution x(2), if any of the following conditions are true:

• Solution x(1) is feasible and solution x(2) is not.

• Solution x(1) and solution x(2) are both infeasible, but solution x(1) has a smaller constraint violation.

• Solution x(1) and solution x(2) are feasible and solution x(1) dominates solution x(2) in the usual sense”.

The first attachment is the true Pareto front, while the second is the Pareto front produced by SMPSO. It just can't find the complete Pareto front.

What are the other parameters, such as c1, c2, w, Vmin and Vmax? How do you chose the best solution, is it randomly chosen between the non-dominated solutions? Are you using an archive?

c1 and c2 are random numbers in the range [1.5, 2.5]. w = 0.1. Vmax = (upper_limit - lower_limit)/2 and Vmin = -Vmax. 

I use an archive, and the leader is chosen from the archive based on crowded distance.Other detail about SMPSO can be found in the paper:

[1]A. J. Nebro, J. J. Durillo, J. Garcia-Nieto, C. A. C. Coello, F. Luna, and E. Alba, “SMPSO: A new PSO-based metaheuristic for multi-objective optimization,” in ieee symposium on Computational intelligence in miulti-criteria decision-making, 2009. mcdm ’09, 2009, pp. 66–73.

Thank you for your advise. I will try the penalty mechanism and try to find better parameters.

Kai, I'm not sure if using random c1 and c2 is a good thing. Besides, I think  w is too small. Have you tested other parameters?

Dear Kai

please check the attached article, I hope it will help you.

regards

Aydin

https://www.researchgate.net/publication/306048088_Optimizing_radio_frequency_identification_network_planning_through_ring_probabilistic_logic_neurons?ev=prf_pub

Article Optimizing radio frequency identification network planning t...