Adaptive sensitivity analysis in optimization model by artificial neural network

Abstract

In most optimization model-based planning systems, additional information tends to be accumulated since the initial model building and its partial implementation. When an additional information results in changes in coefficients, sensitivity analysis is unavoidable. Particularly, if such changes require a set of desired values on the designated decision variables which are not feasible with the initial coefficients, a choice left is the adjustment of controllable coefficients. The controllable coefficients should be adjusted so that the desired values on the infeasible decision variables can be obtained. We call such an analysis an adaptive sensitivity analysis. Since there is no known analytical method for the general mapping between the "desired decision values" and the "controllable coefficients," we propose a neural network approach and attempt to validate with a scheduling problem in a refinery plant.

While we perform the adaptive sensitivity analysis, one-to-many problem is occurred in the data set. To resolve such one-to-many relationships in the data set, we develop a general purpose resolution algorithm. The algorithm is applied to the refinery case, and its validity is empirically confirmed.

According to the experimental performance of the neural network for the adaptive sensitivity analysis, the approach seems applicable to a wide real world industrial problem. To systematically support the adaptive sensitivity analysis procedure, we develop a tool UNIK-OPT/NN which integrates the neural network model with the semantically represented linear programming model that are generated by the knowledge-assisted optimization modeler UNIK-OPT. UNIK-OPT/NN is also applied to the refinery case. By using UNIK-OPT/NN, user can quickly develop an adaptive sensitivity analysis model for an optimization model, and can easily adjust the controllable coefficients in the optimization model.