There are many varying theories for what each variable in Particle Swarm Optimization should look like. There are the theoretically acceptable values, and then there are the values determined over time with testing. The following are some of the recommendations I am making for your consideration.

The original (canonical) version of the Particle Swarm Optimization algorithm used values of 1, 2, and 2 respectively for Inertia, C1, and C2. These values do seem to work quite well. I have also found through testing, as have others, that values of 0.5, 1.5, and 1.5 respectively work even better, providing the best convergence rate depending upon the function and strategy used. Other values lead to slower or complete non-convergence. You, the reader, should perform your own testing based upon the strategy and function you prefer and determine which values you find suitable for your purpose.

Please note that, depending upon the strategy and function you select, your values should be different to provide proper convergence. For instance, using a minimization strategy and a Step function, I have seen optimal convergence happen using a global value of 0.729 for inertia. The cognitive intelligence (C1) is usually the same as the social intelligence (C2) with a pre-determined value of 2. I should point out however that, as you will see when we get to the chapter on building and using the visual workbench, the default value I use for C1 and C2 is 1.49445.

It is important to note that any of the values shown here are not pulled out of thin air. They come from a tremendous amount of optimization testing. In addition, they closely align with those tested by Clerc and Kennedy (2002) for implementation of constriction coefficients. Please feel free to use your own values and always keep in mind the No Free Lunch theorem.

The following is an example of how swarm optimization is affected by weight, social, and cognitive parameters:

Iteration=31,w=0,c1=c2=2	Iteration=31,w=0.59,c1=c2=2	Iteration=31,w=1,c1=c2=2