Models of multycriterial step by step choice decisions, their use in the sugar industry

Optimal control of existing systems can be reduced to the problem of multi-criteria step by step choice of effective solutions in discrete systems. Their structure can be described as a directed graph with a given vector weights in its arches. The problem of choice can be reduced to the problem of search of optimal ways on the graph. Available methods of search are used only for linear systems whose structure is described by acyclic graphs. Nonlinear structures contain branches and/or return process streams. The methods of multi-criteria step by step choice are not applicable for them. To solve such problems we propose the model of decomposition of a graph that describes the structure of the system, into acyclic subgraphs and the synthesis model of effective integrated ways. The latter will be implemented by the consistent integration of their fragments i.e. effective ways found in acyclic subgraphs, and narrowing down through the choice function by taking into account the conditions of the system integrity. Further on, the article dwells upon a numerical realization of decomposition model and synthesis of integrated solutions. The proposed models were tested on the example of optimization of crystallization process in the sugar industry. The task was to select from a variety of possible control actions some set of alternatives, optimal in 3 additive performance criteria. At each stage of the process the appropriate control actions were selected and graph options of control actions with the given its arches quantitative estimates of the efficiency criteria was developed. As a result of application of the developed models numerous effective integrated ways, consisting of 38 options were received. Each such decision was corresponding to the option value of control impacts on the stages of the process.