Computational techniques for optimization of problems involving non-lineartransient simulations

Many optimization problems in engineering require coupling a mathematical p rogramming process to a numerical simulation. When the latter is non-linear , the resulting computer time may become unaffordably large because three s equential procedures are nested: the outer loop is associated to the optimi zation process, the middle one corresponds to the time marching scheme and the innermost loop is required for solving iteratively the non-linear syste m of equations at each time step. We propose four techniques for reducing C PU time. First, derive the initial values of state; variables at each time (innermost loop) from those computed at the previous optimization iteration (outermost loop). Second, select time increment on the basis of those used for the previous optimization iteration. Third, define convergence criteri a for the simulation problem on the basis of the optimization process, so t hat they are only as stringent as really needed. Finally, computations asso ciated to the optimization are shown to be greatly reduced by adopting Newt on-Raphson, or a variant, for solving the simulation problem. The effective ness of these techniques is illustrated through application to three exampl es involving automatic calibration of non-linear groundwater flow problems. The total number of iterations is reduced by a factor ranging between 1.7 and 4.6. Copyright (C) 1999 John Wiley & Sons, Ltd.