The structuring of process optimization

The efficiency of process optimization by mathematical programming can be increased by tearing, that is, rearranging the design equations so as to reduce the number of equality constraints. The structure of a system of equations may be depicted as an undirected bipartite graph; algorithm I‐T utilizes this graph to determine an order of solution for the equations which requires no tears. If this is impossible, then algorithm II‐T uses indexing in conjunction with algorithm I‐T to produce an order which minimizes the number of torn equations. This procedure is extended to the problem of minimum recycle parameters, and the two‐way interaction between tearing and algebraic simplification is illustrated.