Piece-by-piece approach to solving large nonlinear water resources management models

Most large nonlinear optimization models are composed of "pieces" -subsets of decision variables-and constraints whose union is the entire model. Each piece represents an additional aspect of the situation being modeled. This opens the possibility, of solving the simplest piece first, adding the con straints and variables of another piece, and solving this submodel from a s tarting point provided by the first solution. This process is repeated unti l the original model is solved. This "piece-by-piece" approach provides eac h submodel with a good starting point, which greatly increases the probabil ity that a good nonlinear solver will find an optimal solution. We apply it to a large multiperiod nonlinear programming (NLP) model with 13,700 varia bles, 10,000 equations, and a high degree of nonlinearity (54.3% of the non zero Jacobian elements are nonconstant), arising from water resources plann ing and operation in. a river basin. Using the GAMS modeling language and t he CONOPT2 NLP solver, the piece-by-piece method is able to solve this mode l, while all attempts to solve the complete model from various starting poi nts fail to find a feasible solution.