Dear researchers, I applied "Clerk's constriction factor based PSO [1]" to a numerical minimization problem, where a nearly flat basin constitutes most part of the fitness landscape. The minimum is in the order of 10-6 and stands in the center of the basin. The fitness values decrease very slowly from the values in the order of 10-4 at the border, to the values in the order of 10-6 at the center.
Occasionally, the algorithm converged to the minimum, but most times, it only converged to values in the order of 10-4~10-5.
Can anyone help me with this problem? What happened and what kind of methods may I resort to? Thanks very much!
[1] Clerc, Maurice, and James Kennedy. "The particle swarm-explosion, stability, and convergence in a multidimensional complex space." Evolutionary Computation, IEEE Transactions on 6.1 (2002): 58-73.
Dear Xin Yu, flat basins and small variations in the fitness value is known to affect some evolutionary algorithms such as Genetic Algorithms with proportionate selection operator (also known as roulette wheel selection). However, I believe PSO shouldn't be strongly affected by this feature. Nevertheless, you may modify the function’s landscape by multiplying it by a large number to make more noticeable the fitness differences between solutions (although I believe it won’t change your results on the original function). You should also try other heuristics and see how they perform; the error you refer may actually be a good solution to your problem. In which programing language are you working (perhaps I can share some codes with you).
Hi, Xin Yu. Since PSO is a heuristic, there is no configuration that can guarantee that it will return the optimal result in any search space. However, in the search space that you described, it is probably a good idea to encourage the particles to explore more, by making the coefficients (to be multiplied to the random numbers) a bit bigger than what you currently have. You can also add an inertia component, if your velocity update step does not include it yet. Additionally, you can have more particles. These techniques will generally allow your PSO to explore more areas in the search space, but will also probably require more time before giving you an answer.
Hello Xin Yu,
Hurstic Algo did not give accurate optimal result they give approximate result. You can reduce the standard deviation. There are many way to deal with this, you can check with variable parameters of algo or you can divide search area etc. This is the simplest way you can apply. Or else you can use other algo and check there response on this problem, or you can go for hybrid technique.
Replace fitness with some strictly increasing function of fitness. In your case the substitution
fitness
On a unimodal problem, one key is to ensure that you don't stall (aka converge prematurely). In the linked paper, the author talks about making sure that all velocities stay non-zero in all dimensions.
Hope that helps.
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4983184
Dear Xin Yu,
In meta-heuristic algorithms like PSO ,particles converge prematurely and get trapped in a local minima due to the lack of fine-tuned parameter configuration and also lack of global search ability. if you are sure about the parameter configurations, the best way to overcome this problem is to add a restart strategy to the standard PSO algorithm. For an example, please see the original Ant Bee colony source code implementation.
Some times a sensitivity analysis of the parameters can calibrate appropiatly the elements of the algorithm
Have you tried chaotic initialization of the social and cognitive coefficients like a Lorentz map?