Reptile Search Algorithm （RSA） has strong global exploration ability， but its exploitation ability is relatively weak and it cannot converge well in the late stage of the iteration. To address the above issues， combined with the Teaching-Learning-Based Optimization （TLBO） algorithm， the Beetle Antennae Search （BAS） algorithm based on quadratic interpolation and the lens opposite-based learning strategy， Reptile Search Algorithm based on Multi-Hunting Coordination Strategy （MHCS-RSA） was proposed. In MHCS-RSA， the position update formula of the hunting cooperation in the encircling phase （global exploration） and hunting phase （local exploitation） of RSA was retained. And in the hunting coordination of the hunting phase， the learning phase of TLBO algorithm and the BAS based on quadratic interpolation were integrated to perform position update in order to improve the exploitation ability and convergence ability of the algorithm. In addition， the lens opposite-based learning strategy was introduced to enhance the algorithm ability of jumping out of the local optimum. Experimental results on CEC 2020 test functions show that MHCS-RSA has good optimization， convergence abilities and robustness. By solving the tension/compression spring design problem and the speed reducer design problem， the validity of MHCS-RSA is further verified in solving practical problems.

The optimization process of Remora Optimization Algorithm （ROA） includes three modes： attaching to host， empirical attack and host foraging， and the exploration ability and exploitation ability of this algorithm are relatively strong. However， because the original algorithm switches the host through empirical attack， it will lead to the poor balance between exploration and exploitation， slow convergence and being easy to fall into local optimum. Aiming at the above problems， a Modified ROA （MROA） based on chaotic host switching mechanism was proposed. Firstly， a new host switching mechanism was designed to better balance the abilities of exploration and exploitation. Then， in order to diversify the initial hosts of remora， Tent chaotic mapping was introduced for population initialization to further optimize the performance of the algorithm. Finally， MROA was compared with six algorithms such as the original ROA and Reptile Search Algorithm （RSA） in the CEC2020 test functions. Through the analysis of the experimental results， it can be seen that the best fitness value， average fitness value and fitness value standard deviation obtained by MROA are better than those obtained by ROA， RSA， Whale Optimization Algorithm （WOA）， Harris Hawks Optimization （HHO） algorithm， Sperm Swarm Optimization （SSO） algorithm， Sine Cosine Algorithm （SCA）， and Sooty Tern Optimization Algorithm （STOA） by 28%， 33%， and 12% averagely and respectively. The test results based on CEC2020 show that MROA has good optimization ability， convergence ability and robustness. At the same time， the effectiveness of MROA in engineering problems was further verified by solving the design problems of welded beam and multi-plate clutch brake.