A Gradient Algorithm for Chance Constrained Nonlinear Goal Programming
Decision environments involve high degrees of uncertainty as well as multiple, conflicting objectives. Often sampling information is available as a means of describing uncertainty. This description can be utilized in the form of chance constraints. Goal programming offers a means of considering multiple, conflicting objectives. A nonlinear goal programming algorithm is presented based upon the gradient method, utilizing an optimal step length for chance constrained goal programming models. The resulting algorithm requires assumptions of convex solution sets, differentiable and monotonic nonlinear constraints, and normally distributed variance of stochastic parameters. The algorithm is evaluated for generality, reliability, and precision; sensitivity to parameters and data; preparational and computational effort; and convergence. Model sensitivity to parameters is identified, as well as appropriate adjustment. The algorithm was found to require minimal preparational effort, favorable computation time, and rapid convergence to optimal solution with the exception of models containing high degrees of nonlinearity.
||A Gradient Algorithm for Chance Constrained Nonlinear Goal Programming
European Journal of Operational Research (1985)
Vol. 22, No. 3
||Lee, Sang M; Olson, D.