Hybrid chaotic differential evolution–BFGS algorithm for efficient parameter estimation in confined and leaky confined aquifer systems

Abstract Accurate estimation of aquifer parameters is crucial for sustainable groundwater management and hydrogeological modelling. This study presents a novel hybrid optimization framework, the Chaotic Differential Evolution–BFGS (CDE–BFGS) algorithm, to enhance both convergence efficiency and numerical stability in inverse modelling for aquifer parameter estimation. The proposed technique merges the global exploration capability of the Chaotic Differential Evolution (CDE) algorithm with the rapid local refinement of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method, establishing a complementary balance between exploration and exploitation within the search space. The CDE–BFGS algorithm was tested on three types of pumping-test datasets: (i) small-diameter wells in confined aquifers (Theis model), (ii) small-diameter wells in leaky confined aquifers (Hantush and Jacob model), and (iii) large-diameter wells in confined aquifers (Papadopulos and Cooper model). To assess robustness under realistic field conditions, controlled Gaussian noise was introduced into the drawdown observations at different noise levels. Results were compared with those obtained from conventional Differential Evolution (DE), Chaotic Differential Evolution (CDE), and other methods documented in the literature. Across all datasets, including perturbed scenarios with measurement noise, the hybrid approach consistently converged to the global optimum with significantly fewer iterations and function evaluations. It achieved a sum of squared errors (SSE) and standard deviation values up to four orders of magnitude lower than those reported previously, confirming its superior accuracy and robustness under noisy conditions. Further comparative analyses demonstrate that CDE–BFGS not only accelerates convergence but also yields highly stable and reliable parameter estimates across various hydrogeological conditions. As a result, the CDE–BFGS algorithm provides a computationally efficient and dependable alternative to traditional and heuristic approaches, with strong potential for automated aquifer parameter estimation and broader applications in groundwater inverse modelling.