In this paper we optimize several algorithms for the computation of reaction rates based on information calculated along minimum energy reaction paths and we evaluate the efficiencies of the optimized algorithms. The investigations are based on the calculation of chemical reaction rate constants using variational transition state theory and multidimensional semiclassical transmission coefficients including reaction path curvature. Several methods are evaluated and compared by a systematic set of applications to test cases involving the hydrogen-atom transfer reactions CH3 + H2 → CH4 + H and OH + H2 → H2O + H. For each method we present general recommendations for all algorithmic choices other than gradient step size so that future calculations may be carried out reasonably efficiently by varying only one parameter. In the process of these optimizations we have found that the accuracy of the Euler stabilization method can be significantly increased by choosing the auxiliary parameters differently than in previous work; the optimized algorithm is called ES1*. Our final recommendations for future work are (i) when the Hessian/gradient computational cost ratio is low (≲3): the Page-McIver algorithm with the Hessian recalculated at every step, with a cubic starting step, and with curvature calculated from the derivative of the gradient, and (ii) when the Hessian/gradient computational cost ratio is moderate or large: the ES1* algorithm with a Hessian step size three times larger than the gradient step size, with a quadratic starting step, and with curvature calculated from the derivative of the gradient.