Pareto Optimal Solutions for Stochastic Dynamic Programming Problems via Monte Carlo Simulation

Algorithm 1

algorithm

 read input;

 for  𝑖=1  until  sampleSize  do

         generate randomly a sequence of disturbances with a

           given probability distribution function;

         find a sequence of decision variables that optimizes

           the objective-function, as if it were a

           deterministic dynamic programming problem;

  end for

 mount the Pareto front of the decision variables,

         weighted by its quantiles;

 take the box-plot, the average, or any other quantile of

         these variables as the answer of the problem.

end algorithm