Over a closed thermodynamic cycle, free energies should sum to 0. However, over a closed cycle in FEP (illustrated in Fig. ), errors may result in a nonzero sum, referred to as the hysteresis of the cycle. The theoretical cycle closure condition can be used as an informative constraint to solve for changes in free energy over the design . A node may also be included in multiple cycles, allowing for further redundancy in free energy solutions. To analyze this, we quantified how A or D optimization changes the number of cycles in designs. A study may then select the optimization type that produces the most cycles if cycle closure corrections will be applied to solve for Δ𝐺 values. The calculation of the number of cycles is an NP-complete problem, meaning that in practical terms, as 𝑛 or 𝑘 increase, the computational difficulty of finding the number of cycles becomes markedly higher or eventually intractable. So, to calculate the number of cycles in A-, D-, and random designs, we ran design optimizations over tractable combinations of (𝑛, 𝑘), with five replicates per (𝑛, 𝑘) (as compared to the 200 trials performed for MSE calculations). We ran simulations for the same set of (𝑛, 𝑘) for each design type. In Fig. , we present the results for the number of cycles using surfaces plotted with triangular mesh interpolation. We found that D-optimization results in an increased number of cycles compared to A-optimal and random designs (Fig. ). This trend that D-optimal designs produce more cycles was previously qualitatively noted .