FPBIL: A Parameter-free Evolutionary Algorithm

It can be affirmed, in conclusion to this chapter, that the FPBIL is an evolutionary algorithm, competitive with the best current optimization techniques, compact, relatively modest in the use of computational resources--like PBIL--, well founded, efficient, robust, self-adaptable, simple and parameterless. Furthermore, the examples show that the FPBIL is efficient at both numerical and combinatorial problems. Here we should highlight the Four Peaks Problem, a highly deceptive problem handled very well by FPBIL. FPBIL is conceptually simple and intuitive, since it does not require much sophisticated knowledge; it is compact, in the sense that it can be programmed with a few lines of code; and uses little amount of memory, since there is no need to store individuals of a population in some data structure. The radically different way the mutation is handled in FPBIL is based on the probabilitie distribution inherent of the probability vector itself. This is updated using all the available information in each generation. These modifications enable the FPBIL to acquire selfadjustable features--such as the mechanism of variable population size--making the algorithm more efficient and more robust. Efficient in the sense that it finds solutions in less time; robust, meaning it has more resources to escape from local optimums. With the proposition of FPBIL, we expect to have added relevant theoretical and practical tools, presenting feasible improvements with a considerable economic return, in both cost and benefit. There still are, however, improvements which might be incorporated into FPBIL. After escaping from a local optimum, the FPBIL tends to approach the global optimum more slowly than other algorithms--PBIL, for example. Considering the process as a whole, the FPBIL takes advantage (since PBIL get caught more easily), but maybe it is possible to combine FPBIL with some other fast search algorithm, resulting in an even more efficient algorithm. Other improvements can appear by constructing a multi-objective FPBIL-- adapting the techniques from (Machado, 2005)--or even a parallel FPBIL--based on the techniques of (de Lima, 2005). One can still try to incorporate some kind of heuristic to the FPBIL perhaps some described in (de Lima, 2005). Works in these directions prove that these complementary techniques tends to produce better solutions.