Accelerating the computational design of multi-principle element alloys

We present a metaheuristic hybrid Cuckoo-Search (CS) algorithm that overcomes NP-hard global optimization and produces ultrafast solutions for large-dimensional combinatorial problems, using Levy flights (global) and Monte Carlo (local) searches, which avoids local-minima traps that stagnate solutions. The hybrid-CS removes a roadblock to computational materials design of arbitrary MPEAs by enabling ``on-the-fly'' construction of optimized Super-Cell Random Approximates (SCRAPS) with extraordinary reduction in solution times, scaling linear with cell size and exhibiting strong scaling for parallel solution. For example, a 4-element, 128-atom cell [10⁷³⁺ space] in 45s or 5-element, 500-atom cell [10⁴¹⁵⁺ space] in 270s. For a 4-component 128-atom model, we find a factor of 12,600+ reduction in parallel [400+ in serial] execution over current limited strategies. SCRAPS has specified point and pair probabilities with proper Gaussian distributions. We present several example applications using electronic-structure-based energetics and phonons.