Physics-grounded optimization via interpretable process mapping

Abstract This work presents the Purification Water Process Algorithm (PWPA), a metaheuristic framework grounded in the physical principles of industrial water treatment rather than metaphorical inspiration. The algorithm explicitly models three canonical stages—sedimentation, filtration and final purification—as distinct search operators: a gravity-based mechanism for global exploration, a stochastic filtering process to sustain diversity and a refinement phase that promotes convergence towards high-quality solutions. This direct physical correspondence yields a transparent and analytically tractable optimization process. Empirical evaluation on 30 benchmark functions, including high-dimensional instances up to 1000 variables, demonstrates that PWPA consistently matches or exceeds the performance of established metaheuristics in terms of solution quality, convergence behaviour and robustness. In particular, it achieves the known global optimum on the 1000-dimensional Schwefel function with negligible variance, highlighting its scalability. In a real-world application, PWPA was applied to hyperparameter optimization of a support vector machine (SVM) for the modified national institute of standards (MNIST) digit classification, reducing cross-validation error by 61.1% and attaining a test accuracy of 94.60% (σ=0.0041). The results suggest that anchoring metaheuristic design in well-understood physical processes can offer a viable path towards more interpretable and reliable optimization algorithms.