. 2023 Feb 13;2:32. Originally published 2022 Mar 8. [Version 3] doi: 10.12688/openreseurope.14508.3

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	$\frac{\max (E_{0} (t))}{σ [E_{0} (t)]}$	Spatiotemporal focusing
B	$- \frac{\min (E_{0} (t))}{σ [E_{0} (t)]}$	Spatiotemporal focusing and phase inversion
C	$α \max (E_{0} (t)) - β \| μ [E_{0} (t)] - t_{0} \| - γ \| σ [E_{0} (t)] - σ_{0} \| - ζ \| S [E_{0} (t)] - S_{0} \|$	Achieving a desired time delay t ₀, temporal deviation σ ₀ and skeweness S ₀
D	$\frac{\int d ω E_{0} (ω) E_{t a r g e t}^{*} (ω) + c . c .}{σ [E_{0} (t)]}$	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)