  Harnessing pulse generation from an ultrafast laser is a challenging task as
reaching a specific mode-locked regime generally involves adjusting multiple
control parameters, in connection with a wide range of accessible pulse
dynamics. Machine-learning tools have recently shown promising for the design
of smart lasers that can tune themselves to desired operating states. Yet,
machine-learning algorithms are mainly designed to target regimes of
parameter-invariant, stationary pulse generation, while the intelligent
excitation of evolving pulse patterns in a laser remains largely unexplored.
Breathing solitons exhibiting periodic oscillatory behavior, emerging as
ubiquitous mode-locked regime of ultrafast fibre lasers, are attracting
considerable interest by virtue of their connection with a range of important
nonlinear dynamics, such as exceptional points, and the Fermi-Pasta-Ulam
paradox. Here, we implement an evolutionary algorithm for the self-optimisation
of the breather regime in a fibre laser mode-locked through a four-parameter
nonlinear polarisation evolution. Depending on the specifications of the merit
function used for the optimisation procedure, various breathing-soliton states
are obtained, including single breathers with controllable oscillation period
and breathing ratio, and breather molecular complexes with a controllable
number of elementary constituents. Our work opens up a novel avenue for
exploration and optimisation of complex dynamics in nonlinear systems.
