Multi-scale Quantum Oscillator Harmonic Algorithm (MQHOA) has good characteristics of global convergence and adaptability. For analyzing the specific performance of MQHOA on solution precision and speed, the comparisons of theoretical models and experiments were completed among the MQHOA, the classic Quantum Particle Swarm Optimization (QPSO) algorithm adopting the quantum-behaved model and having been widely used, and the QPSO with Random Mean best position (QPSO-RM) through solving the integer nonlinear programming problems. In simulation experiments, MQHOA achieved 100% success rate in solving seven unconstrained integer nonlinear programming problems, and was faster than QPSO and QPSO-RM in most cases. MQHOA was a little slower than QPSO and QPSO-RM in solving the two constrained integer nonlinear programming problems, but could obtain 100% success rate which was higher than the latter. Through the comparison of the convergence process of QPSO, QPSO-RM, MQHOA was faster and earlier on converging to the global optimal solution. The experimental results show that MQHOA can effectively adapt to solving the integer programming problems, and can avoid falling into the local optimal solution so as to obtain the global optimal solution. MQHOA is better than the contrast algorithms of QPSO and QPSO-RM in accuracy and convergence rate.