Strengths: coarsely plateaued f’, no startup cost for simple functions
Weaknesses: Local optimizations to distant minima, weaknesses of LO procedure
As far as comparative results, I'll just briefly say that these methods performed very well. In this table, the axes are global optimization methods and objective functions. The upper left and lower right numbers of each entry are the number of successful trials and average function evaluations, respectively.
These methods were especially effective for (1) functions which are expensive to evaluate, justifying the computational cost of the information-based approach, and (2) functions which are coasely plateauxed after local optimization.
The primary weakness is that the method is limited by its weakest layer. For example, if a local optimization procedure doesn't optimize to the nearest local minimua, the next layer up can be faced with an f' landscape which is difficult to search because beneficial structure in the search space is lost.