Simultaneous optimization of the cavity heat load and trip rates in linacs using a genetic algorithm

In this paper, a genetic algorithm-based optimization is used to simultaneously minimize two competing objectives guiding the operation of the Jefferson Lab’s Continuous Electron Beam Accelerator Facility linacs: cavity heat load and radio frequency cavity trip rates. The results represent a significant improvement to the standard linac energy management tool and thereby could lead to a more efficient Continuous Electron Beam Accelerator Facility configuration. This study also serves as a proof of principle of how a genetic algorithm can be used for optimizing other linac-based machines.

Figure 1

Plots of the two conserved quantities given in Eq. (8)—$G_i/Q_i$ shown in red and $B_i\exp [A+B_i(G_i-F_i)]$ shown in blue—for the heat load only minimization (top row) and the trip rate minimization (bottom row) for the CEBAF’s North Linac (left column) and South Linac (right column). Solid lines represent the analytically computed values of the conserved quantities.

Figure 2

The Pareto-optimal front for the simultaneous optimization of the linac’s cooling cost and trip rate (multiobjective optimization). Asymptotically, the solutions at the extremes of the Pareto-optimal curve represent the single-objective minimization of the cooling cost (top left portion of the curve) and the single-objective minimization of the trip rates (bottom right portion of the curve). Solutions A and B are on the Pareto-optimal front, while solution C is not because it is dominated by solution A (A is within the rectangle defined by C’s coordinates).

Figure 3

Effect on the quality of the Pareto-optimal front of constraining the objective functions as in Eq. (9). Both North linac (left panel) and South linac (right panel) are constrained by $T_{\max }=10$ trips per hour and $P_{\max }=1200\mathrm{W}$.

Figure 4

Effect on turning off one cavity (left panel) or two cavities (right panel) and restarting the simulation from the previous solution with all cavities on. The blue points denote the Pareto-optimal front produced by 8000 generations of the GA simulation started from a random sampling of the search space, and the red points show the 4000 generations of the GA simulation restarted from the solution to the full cavity problem with 4000 generations.

Figure 5

Pareto-optimal front for North linac obtained using the GA simulation with 512 individuals evolved for 16000 generations (top left panel). Two of the three solutions marked are closely related to the asymptotic solutions obtained by single-objective minimization of the heat load only (solution A) and trip rates only (solution C). Also shown is a solution from the Pareto-optimal front which has a trip rate of exactly five (solution B). The remaining panels show the single-objective conserved quantities for solutions A, B, and C, as in Fig. 1. Note the red outliers in the bottom right panel.

Figure 6

Same as Fig. 5, except for the South linac. Note the red outliers in solutions A and B.

Figure 7

Pareto-optimal front computed using a GA-based multiobjective optimization with 16000 generations and 512 individuals versus the single-objective GA-based optimization reported in [12].

Figure 8

Convergence of the Pareto-optimal fronts for the North (left) and South (right) linacs, as a function of the number of generations in a GA simulation.

Figure 9

Sensitivity on the Pareto-optimal front to a 10% measurement error in the cavity quality factor $Q_i$ for the North (top left) and South linacs (top right) and a 5% measurement error in gradients $G_i$ for the North (bottom left) and South linacs (bottom right). The blue (energy constraint not satisfied) and green (energy constraint satisfied) represent 10000 different machine configurations with measurement errors artificially introduced. The (unperturbed) Pareto-optimal fronts (red) are the same as those in Figs. 5 and 6, generated with 512 individuals evolved for 16000 generations.

Figure 10

Left: Relationship between the Pareto-optimal front for the multiobjective optimization of two objective functions $f_1$ and $f_2$, and the single-objective optimization of their linear combination $c_1{f}_1+c_2{f}_2$. Three different combinations of $(c_1,c_2)$ parameters are shown in green, blue and red. Right: Comparison of the Pareto-optimal fronts from the multiobjective GA simulations (blue and green points) with the results of the corresponding set of single-objective optimizations of $c_{1}P+c_{2}T$ with varying values of $(c_1,c_2)$ (red points). The simulation is for the CEBAF’s South linac.