Multiobjective genetic approach for optimal control of photoinduced processes

We have applied a multiobjective genetic algorithm to the optimization of multiphoton-excited fluorescence. Our study shows the advantages that this approach can offer to experiments based on adaptive shaping of femtosecond pulses. The algorithm outperforms single-objective optimizations, being totally independent from the bias of user defined parameters and giving simultaneous access to a large set of feasible solutions. The global inspection of their ensemble represents a powerful support to unravel the connections between pulse spectral field features and excitation dynamics of the sample.

Figure 1

Comparison between the evolution of a single-objective optimization of $[I_{\mathit{fluo}}∕(ϵ+I_{\mathit{SHG}})+\alpha I_{\mathit{fluo}}]$ with $\alpha =0$, $ϵ=0.3$, and that of a run of the NSGA-II algorithm maximizing simultaneously $[I_{\mathit{fluo}}∕I_{\mathit{SHG}};I_{\mathit{fluo}}]$. Evolution of the discrimination ratio $I_{\mathit{fluo}}∕I_{\mathit{SHG}}$ in the single-objective (a) and in the multiobjective (b) cases. (c) Evolution of $I_{\mathit{fluo}}$ in the multiobjective run.

Figure 2

Global output of the multiobjective optimization of Fig. 1. Dots: individuals tested during the evolution. Circles: final feasible population (Pareto front). Dashed line: undiscriminating solution $I_{\mathit{fluo}}=I_{\mathit{SHG}}$, retrieved by an unmodulated pulse at different intensities, as demonstrated by the experimental data points lying along the diagonal.

Figure 3

Comparison between the results of several independent multiobjective (open shapes) and single-objective (solid shapes) optimizations. The single-objective GA results are obtained using different $[\alpha ;ϵ]$ parameter pairs. The crosses correspond to maximizing the opposite goal with NSGA-II, namely $[I_{\mathit{SHG}}∕I_{\mathit{fluo}};I_{\mathit{SHG}}]$. The dotted curve indicates the experimental error at different signal intensities.

Figure 4

(a) FROG traces corresponding to pulses maximizing FMN fluorescence (left), undiscriminating (center), and maximizing SHG (right). (b) Spectral cuts at zero time delay extracted from the FROG traces in the top panel. (c) Behavior of the multiobjective optimization targets $I_{\mathit{fluo}}$ and $I_{\mathit{fluo}}∕I_{\mathit{SHG}}$ as a function of the first spectral moment of the optimal pulses retrieved by the algorithm.