It depends on the nature of your problem formulation. It can solved by both conventional and meta-heuristic algorithms. If the problem formulation involves too many nonlinear equations meta-heuristics is the best option as you no need to derive the derivatives. But if you can derive them, conventional is always the best option.
Alternatively, you can code the problem easily in one of the Algebraic modelling languages (AML) (e.g. AIMMS, AMPS, GAMS) which will derive all the background matrices and call the corresponding nonlinear solvers.