Table 1. The set of cost functions used in the genetic algorithm.

In all these expressions, the electric field is measured in the desired focal point, i.e. E ₀( t) ≡ E( x ₀, y ₀, t). The statistical moments of the electric field μ, σ, and S are defined in Equation (5). For the fitness function C, the variables α, β, γ, and ξ are weights controlling the relative importance of each component of the multi-objective fitness function. For the fitness function D, c.c. stands for complex conjugate.

Fitness function	Definition	Type of Optimisation
A	$\frac{\max (E_0(t))}{\sigma [E_0(t)]}$	Spatiotemporal focusing
B	$-\frac{\mathit{min}(E_0(t))}{\sigma [E_0(t)]}$	Spatiotemporal focusing and phase inversion
C	$\text{α}\max (E_0(t))-\beta |\mu [E_0(t)]-t_0|-\gamma |\sigma [E_0(t)]-{\sigma }_0|-\zeta |S[E_0(t)]-S_0|$	Achieving a desired time delay t 0, temporal deviation σ 0 and skeweness S 0
D	$\frac{{\displaystyle \int d\omega E_0(\omega )E_{target}^{*}(\omega )+c.c.}}{\sigma [E_0(t)]}$	Phase-sensitive spectral shaping, where the aim is to obtain a measured field E 0( ω) as close as possible to a target field E target ( ω)