What does "more interest" mean? Let me know more, and I might be able to answer.

In the original PSO, the quality of the results depends significantly on the constant parameters of the algorithm (such as inertia weight). However, in recent years, many modified algorithms have been proposed. I have been working in this area for a while, and you are invited to see the following papers. The modified algorithms are usually much less dependent on the initial constants.

1- A Kaveh, A Nasrollahi, A new probabilistic particle swarm optimization algorithm for size optimization of spatial truss structures

2- A Kaveh, A Nasrollahi, A new hybrid meta-heuristic for structural design: ranked particles optimization

3- A Kaveh, A Nasrollahi, Engineering design optimization using a hybrid PSO and HS algorithm

Need to perform some sorts of statistical analyses to find out the optimal case and the performance of the optimizer. The meta-heuristic algorithms works with little or more amount of randomness. So, while you run the algorithm for several times, each time it would result in different types of solution. That's why you should take the mean of the results, find out the standard deviation, etc to ensure the optimal result. 

Dear Michael Patriksson

How can I understand that the pso opt point is unique and is not wherever another else? 

Dear Dastmalchi

A heuristic method does not ensure finding a global optimal solution but it gives acceptable solutions at affordable computational cost

In general, AI techniques do not guarantee finding optimal solutions

If I understand your question correctly, you should define a fitness function to measure the goodness of each solution. So, you can compare different solution to determine which is better.

Dear M. Dastmalchi,

In my opinion,  It depends on the optimal value of a fitness function as Mr. Bahram Zaeri refered. If the algorithm finds the optimal value it will show that the algorithm achieve the unique point.

Regards.

The more important point in your question seems to be the fitness function definition, if you are doing a multi-objective analysis you might want to change the weight of the the several parts has the algorithm evolves, that normally gives you an interesting result. The other solution to ensure that you are not in a week local minima/the algorithm got stuck for some reason, is to use a RPSO. Which means (among other things) that upon convergence to a certain criteria a random kick to the population.

It depends on the applications of the problem.

It depends on how you define the cost function (and the constraints related to the problem). Since the best particles (local, global, personal) are defined upon the cost function, the proper design of the cost function strongly influences the convergence toward 'meaningful' solutions (where meaningful means that these solution satisfy your goal).

It depends on the fitness function that you define.