$${\lambda }$$ λ -LGP: an improved version of linear genetic programming evaluated in the Ant Trail problem

Abstract

The Ant Trail problem has been widely investigated as a benchmark for automatic design of algorithms. One must design the program of a virtual ant to collect all pieces of food located in different places of a map, which may have obstacles, in a predefined limit of steps. This is a challenging problem, but several evolutionary computation (EC) researchers have reported methods with good results. In this paper, we propose an EC method called \({\lambda }\)-linear genetic programming (\({\lambda }\)-LGP), a variation of the well-known linear genetic programming (LGP) algorithm. Starting with an LGP based only on effective macro- and micro-mutations, the \({\lambda }\)-LGP proposed in this work consists in extending how the individuals are chosen for reproduction. In this model, a number (\({\lambda }\)) of mutations is applied to each individual, trying to explore its neighboring fitness regions; such individual might be replaced by one of its children according to different criteria. Several configurations were tested over three different trails: the Santa Fe, the Los Altos Hill, and the John Muir. Results show a very significant improvement over LGP by using this proposed variation. Also, \({\lambda }\)-LGP outperformed not only LGP, but also other state-of-the-art methods from the literature.