FPBIL: A Parameter-free Evolutionary Algorithm

Abstract

The purpose of this chapter is to describe a new algorithm named FPBIL (parameter-Free PBIL), an evolution of PBIL (Population-Based Incremental Learning). FPBIL, as well as PBIL (Baluja, 1994), Genetic Algorithms (GAs) (Holland, 1992) and others are general purpose population-based evolutionary algorithms. The success of GAs is unquestionable (Goldberg, 1989). Despite that, PBIL has shown to be superior in many aspects. PBIL is a evolutionary algorithm developed as an attempt to mimic the behavior of the Genetic Algorithms in an advanced stage of its execution, “in equilibrium”. The result shows unexpectedly that the PBIL surpasses (Baluja, 1995) the genetic algorithms in almost all aspects. The PBIL is faster and finds better results (Machado, 1999). However, PBIL depends on five parameters which need to be adjusted before each application. For example, variations in the learning rate produce completely different behaviors (Baluja, 1994). Up to today, every evolutionary algorithm, like PBIL, just mentioned, depends on at least one parameter which, if not adjusted properly, can cause the algorithm to be very inefficient. Consequently, the less parameters an algorithm has, the minor the risk of it not reaching all its potential in some particular application; and the less the time spent in finding the appropriate parameter’s values. One of the benefits of FPBIL—perhaps the most important—is that it is a parameter free algorithm (the origin of the F in FPBIL), which means that a parameter optimization, an application-dependent procedure required by other algorithms in order to achieve better results, is not necessary in FPBIL. Parameter optimization demands intense computational effort, a precious time often not taken into account when somebody claims that an algorithm finds a better result in a shorter amount of time. Based on PBIL, FPBIL is built with the guarantee of a better performance than that of PBIL, which also means (whenever the PBIL has a good outcome) a better performance in comparison to other algorithms, besides the advantage of none additional computational cost in adjusting parameters. We begin this chapter by describing the PBIL algorithm and, then, we present the main steps to the FPBIL algorithm it self. Afterwards, we compare the performance of FPBIL against other algorithms in typical benchmark problems and finally we propose some concluding remarks.