Stochastic granule discontinuous deformation(SGDD) model is presented from mesomechanical view;random distribution model of rockfill granule is built by Monte Carlo method;and nonlinear contact algorithm is presented based on modified augmented Lagrangian algorithm.

Solution oscillation caused by identical units when using Lagrangian relaxation based algorithm for hydro thermal scheduling is analyzed in this paper.

Once a dual unit commitment obtained within Lagrangian relaxation framework is judged by this feasibility condition to be infeasible,reselect the dynamic planning route with non ramp rate constraints by using the information of the dual solution,i.

This paper discusses the jobshop scheduling under the circumstances of stochastic processing time, uncertain delayed time between two operations, induces the problem into a stochastic multi phrase decision by using scenario modeling and utilize the method of Lagrangian relaxation, scenario decomposition to solve the large scale problem.

A relaxation algorithm is developed to simulate sphere packing with arbitrary diameter distribution.