A kind of epistasis‐tunable test functions for genetic algorithms

Abstract

Summary Genetic algorithm (GA) is one of the most popular algorithms of evolutionary computation. To evaluate the performance of GAs, test functions with different levels of epistasis have been included in most of the commonly used benchmark platforms. Such test functions have been produced in general by assuming an underlying linear model for the fitness of a string, in which variable interaction should be known beforehand. This paper proposes to compose epistasis‐tunable test functions via linear combinations of simple basis functions so as to avoid explicit dependence on the knowledge of variable interaction. It is remarked that, for a GA with a binary encoding, a linearly separable fitness function, ie, a zero‐epistasis fitness function, can be decomposed into a superposition of periodical basis functions whose frequencies are exponential to 2. A kind of epistasis‐tunable test functions is accordingly produced by summing up sinusoidal basis functions with such frequencies and proper phases. The merits of thus constructed test functions are: Both the locations and values of the global maxima are trivially known; their degrees of epistasis are smoothly tunable simply by changing the locations of the global maxima. Finally, illustration examples are studied, and the results confirm the claims about the merits.

Exploring SLUG: Feature Selection Using Genetic Algorithms and Genetic Programming

“…In [14], epistasis was used to select the appropriate basis for basis change space transformations in GA, and in the same year [15] proposed a method to decipher the exact combinations of genes that trigger the epistatic effects, focusing on multi-effect and multi-way epistasis detection. Recently, a new benchmark was proposed [16] where epistasis-tunable test functions are constructed via linear combinations of simple basis functions. A different way of interpreting epistasis in ML is by studying the interactions between features in data.…”

SLUG: Feature Selection Using Genetic Algorithms and Genetic Programming

“…In [19], epistasis was used to select the appropriate basis for basis change space transformations in GA, and in the same year [3] proposed a method to decipher the exact combinations of genes that trigger the epistatic effects, focusing on multi-effect and multi-way epistasis detection. Recently, a new benchmark was proposed [24] where epistasis-tunable test functions are constructed via linear combinations of simple basis functions. A different way of interpreting epistasis in ML is by studying the interactions between features in data.…”