TY  - JOUR
A1  - Quinzan, Francesco
A1  - Göbel, Andreas
A1  - Wagner, Markus
A1  - Friedrich, Tobias
T1  - Evolutionary algorithms and submodular functions
BT  - benefits of heavy-tailed mutations
JF  - Natural computing : an innovative journal bridging biosciences and computer sciences ; an international journal
N2  - A core operator of evolutionary algorithms (EAs) is the mutation. Recently, much attention has been devoted to the study of mutation operators with dynamic and non-uniform mutation rates. Following up on this area of work, we propose a new mutation operator and analyze its performance on the (1 + 1) Evolutionary Algorithm (EA). Our analyses show that this mutation operator competes with pre-existing ones, when used by the (1 + 1) EA on classes of problems for which results on the other mutation operators are available. We show that the (1 + 1) EA using our mutation operator finds a (1/3)-approximation ratio on any non-negative submodular function in polynomial time. We also consider the problem of maximizing a symmetric submodular function under a single matroid constraint and show that the (1 + 1) EA using our operator finds a (1/3)-approximation within polynomial time. This performance matches that of combinatorial local search algorithms specifically designed to solve these problems and outperforms them with constant probability. Finally, we evaluate the performance of the (1 + 1) EA using our operator experimentally by considering two applications: (a) the maximum directed cut problem on real-world graphs of different origins, with up to 6.6 million vertices and 56 million edges and (b) the symmetric mutual information problem using a four month period air pollution data set. In comparison with uniform mutation and a recently proposed dynamic scheme, our operator comes out on top on these instances.
KW  - Evolutionary algorithms
KW  - Mutation operators
KW  - Submodular functions
KW  - Matroids
Y1  - 2021
U6  - https://doi.org/10.1007/s11047-021-09841-7
SN  - 1572-9796
VL  - 20
IS  - 3
SP  - 561
EP  - 575
PB  - Springer Science + Business Media B.V.
CY  - Dordrecht
ER  -