A Graph-based Method to Solve the Economical Dispatch Problem Disregarding Slack Variables

One of the greatest challenges to confront Nonlinear Programming Problems, it is the selection of the active and non active set of constraints of the system. For this reason many optimization applications prefer to use barrier or penalty methods with their related ineffciencies. This paper describes a graph-based solution for these models which facilitates the handling of such constraints and, therefore, the solution process for the model. To this end some parts of the graph are considered active or non active, depending on the actual model solution as well as the values of the Lagrange multipliers. At every solution step, there will probably be some changes on the graph topology to reflect the current conditions of the problem whose solution is in progress. These solutions besides being efficient, provide an optimal storage scheme as only the fundamental information of the problem is stored.