Chaos–Quantum Particle Swarm Optimized Kriging for Symmetric Response Modeling and Multi-Objective Marketing Optimization in E-Commerce Systems

In the highly competitive e-commerce landscape, platforms must strategically balance complex operational and marketing parameters. These real-world systems inherently involve high-dimensional nonlinear interactions and strongly coupled variables, leading to complex consumer response behaviors and highly non-convex optimization landscapes. Traditional optimization approaches usually suffer from high computational costs in business environments, while conventional surrogate models are prone to premature convergence during hyperparameter estimation. To address these management and operational challenges, this study proposes a Chaos-initialized Quantum-behaved Particle Swarm Optimization Kriging (CQPSO–Kriging) framework. Chaotic mapping is introduced to enhance population diversity, while quantum-behaved particle dynamics improve global exploration capability. Utilizing large-scale real-world transaction data from the Brazilian e-commerce industry, high-fidelity surrogate response surfaces are constructed for three core business indicators: profitability, customer loyalty, and value density. Experimental results show that the proposed CQPSO–Kriging model significantly outperforms conventional approaches, such as support vector regression and radial basis function networks, achieving an exceptional coefficient of determination of R2 = 0.9586 in profit prediction. Furthermore, Sobol variance-based global sensitivity analysis is employed to extract critical managerial insights, revealing that financial variables act as interaction-driven utility multipliers in consumer decision-making. Multi-objective Pareto analysis further demonstrates that profit maximization naturally converges toward a balanced operational configuration, providing a robust quantitative tool for e-commerce precision marketing.