Self-Balanced Cart Optimization Algorithm

In e-commerce systems, the shopping cart is a concentrated reflection of user decision-making behavior. Its dynamic characteristics reflect the complex relationship between multidimensional information interaction, psychological balance, and economic constraints. Traditional shopping cart optimization models often focus on static combinations or price discount maximization, failing to fully reflect the dynamic equilibrium characteristics of shopping behavior. This paper proposes a novel algorithm based on shopping behavior characteristics: the Self-Balanced Cart Optimization (SBCO) algorithm driven by shopping cart interaction. This algorithm, based on the "shopping force field" and "potential energy balance" mechanisms, remodels the dynamic evolution of the shopping cart from the perspective of a physical system. By defining shopping force, shopping potential energy functions, and interaction forces between items, the algorithm achieves adaptive optimization and stable convergence of the shopping cart state. This paper systematically derives the complete theoretical structure of the algorithm from a mathematical perspective, establishing analyzable dynamic equations, potential energy functions, and optimization constraints. Results demonstrate that the algorithm can theoretically and naturally describe the self-organizing characteristics of shopping systems, providing a new algorithmic foundation for intelligent decision-making and dynamic recommendation in e-commerce.