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Various metaheuristic algorithms inspired by nature have been designed to deal with a variety of practical optimization problems. As an excellent metaheuristic algorithm, the improved particle swarm optimization algorithm based on grouping (IPSO) has strong global search capabilities. However, it lacks a strong local search ability and the ability to solve constrained discrete optimization problems. This paper focuses on improving these two aspects of the IPSO algorithm. Based on IPSO, we propose an improved particle swarm optimization algorithm based on variable neighborhood search (VN-IPSO) and design a 0-1 integer programming solution with constraints. In the experiment, the performance of the VN-IPSO algorithm is fully tested and analyzed using 23 classic benchmark functions (continuous optimization), 6 knapsack problems (discrete optimization), and 10 CEC2017 composite functions (complex functions). The results show that the VN-IPSO algorithm wins 18 first places in the classic benchmark function test set, including 6 first places in the solutions for seven unimodal test functions, indicating a good local search ability. In solving the six knapsack problems, it wins four first places, demonstrating the effectiveness of the 0-1 integer programming constraint solution and the excellent solution ability of VN-IPSO in discrete optimization problems. In the test of 10 composite functions, VN-IPSO wins first place four times and ranks the first in the comprehensive ranking, demonstrating its excellent solving ability for complex functions. [ABSTRACT FROM AUTHOR]