In this paper, we are looking for a solution to optimize the path generation of an eel-like robot. Previous works have shown that a successful approach to generate path is to control explicitly the local system curvature. This control design based on Lyapunov methods warrants the convergence of the system shape towards the desired curvature profile. Then the purpose of this work is to determine a local optimized couple of curvature parameters which are able to guarantee a fast system response, an efficient propulsion which minimizes the spent energy or both of them. This is made through three criteria which are able to give us a local solution. Finally, we present results from simulations in motion planning for a ten-link-eellike robot, to illustrate the performance of the proposed solution.