Concerning the shortcomings of unbalanced search， easy to fall into local optimum and weak comprehensive solution performance of Teaching-Learning-Based Optimization （TLBO） algorithm in dealing with optimization problems， an improved TLBO based on equilibrium optimization and Lévy flight strategy， namely ELMTLBO （Equilibrium-Lévy-Mutation TLBO）， was proposed. Firstly， an elite equilibrium guidance strategy was designed to improve the global optimization ability of the algorithm through the equilibrium guidance of multiple elite individuals in the population. Secondly， a strategy combining Lévy flight with adaptive weight was added after the learner phase of TLBO algorithm， and adaptive scaling was performed by the weight to the step size generated by Lévy flight， which improved the population's local optimization ability and enhanced the self-adaptability of individuals to complex environments. Finally， a mutation operator pool escape strategy was designed to improve the population diversity of the algorithm by the cooperative guidance of multiple mutation operators. To verify the effectiveness of the algorithm improvement， the comprehensive convergence performance of the ELMTLBO algorithm was compared with 7 state-of-the-art intelligent optimization algorithms such as the Dwarf Mongoose Optimization Algorithm （DMOA）， as well as the same type of algorithms such as Balanced TLBO （BTLBO） and standard TLBO on 15 international test functions. The statistical experiment results show that compared with advanced intelligent optimization algorithms and TLBO algorithm variants， ELMTLBO algorithm can effectively balance its search ability， not only solving both unimodal and multimodal problems， but also having significant optimization ability in complex multimodal problems. It can be seen that with the combined effect of different strategies， ELMTLBO algorithm has outstanding comprehensive optimization performance and stable global convergence performance. In addition， ELMTLBO algorithm was successfully applied to the Multiple Sequence Alignment （MSA） problem based on Hidden Markov Model （HMM）， and the high-quality aligned sequences obtained by this algorithm can be used in disease diagnosis， gene tracing and some other fields， which can provide good algorithmic support for the development of bioinformatics.