I have two-stage stochastic programming, including equations with high levels of complexity. The objective function is related to the first-stage variables and should be maximized. Also, one of the complex constraints is as follows: $$ P(i,j,s) = w(i) \cdot w(j) \cdot d(i,j) \cdot (k(i,s)+o(i,s)) $$ In this equation, $w$ and $d$ are first-stage binary variables, and $k$ and $o$ are second-stage continuous variables. What metaheuristic algorithm or other methods do you propose?
Also, if I use Benders' decomposition, in the subproblem the binary variables become fixed, and the problem becomes virtually linear, but of course it should be solved by a minlp solver. Do you think benders decomposition is useful? I mean, if I use it, can it generate efficient cuts due to the minlp solver?