When the exact probability distribution of input conditions cannot be obtained in practical engineering problems, interval analysis methods are often used to analyze the upper and lower bounds of output responses. Essentially, this can be regarded as an optimization problem, solvable by optimization algorithms. This paper proposes a novel interval analysis method, i.e., multi-body dynamic evolution sequence-assisted PSO (abbreviated as DES-PSO), which combines a dynamical evolutionary sequence with the heterogeneous comprehensive learning particle swarm optimization algorithm (HCLPSO). By introducing the dynamical evolutionary sequence instead of the random sequence, the proposed method addresses the difficulty HCLPSO faces in covering the search space, making it suitable for interval analysis problems. To verify the accuracy and efficiency of the proposed DES-PSO method, this paper solves two case studies using both the DES-PSO and HCLPSO methods. The first case study employs an optimization algorithm to solve the solution domain of a linear interval equation system, and the second case study analyzes the collision and heat conduction of a smartwatch using an optimization method. The results of the case studies demonstrate that DES-PSO can significantly improve the computational speed of interval analysis while ensuring accuracy, providing a new approach to solving complex interval analysis problems.