In this research, two new methods for solving the Internet shopping optimization problem with sensitive prices are proposed, incorporating adaptive adjustment of control parameters. This problem is classified as NP-hard and is relevant to current electronic commerce. The first proposed solution method corresponds to a Memetic Algorithm incorporating improved local search and adaptive adjustment of control parameters. The second proposed solution method is a particle swarm optimization algorithm that adds a technique for diversification and adaptive adjustment of control parameters. We assess the effectiveness of the proposed algorithms by comparing them with the Branch and Bound algorithm, which presents the most favorable outcomes of the state-of-the-art method. Nine instances of three different sizes are used: small, medium, and large. For performance validation, the Wilcoxon and Friedman non-parametric tests are applied. The results show that the proposed algorithms exhibit comparable performance and outperform the Branch and Bound algorithm.