(An) intelligent system for automatic structural identification and relaxation in integer programming : UNIK-RELAX

Abstract

Model management has been the concern of Decision Support Systems researchers for a long time. One of their major research points is the representation of problems. Since representing the general problems is not only difficult but also impractical, a group of researchers have narrowed its focus on the representation of a specific category of problems such as optimization problems. The Intelligent Information Systems laboratory at Korea Advanced Institute of Science and Technology (KAIST) is in line with this research paradigm and has developed the tool UNIK (UNIfied Knowledge), which captures the optimization models at a semantic level. The first attempt was focused on linear programming, but the scope is expanded to include integer programming and a class of nonlinear programming problems. Currently, their research covers the unification of optimization with rule based systems and the unification of constraint satisfaction problems with rule based systems, both of which are intended to support the multiple criteria decision makings. In addition, the neural network could be used on top of the optimization model for control purposes. So far, the research scope was the semantic representation of such unified problems and the aiding model formulation process under the assumption that one of the standard solvers such as Simplex algorithm, Interior Point algorithm, and Branch and Bound algorithm can be used. In the second phase of UNIK project, representing the solution procedures of NP-hard problems is investigated. As a first step toward this goal, the automatic identification of typical embedded structures in the model and the automatic transformation of the problem to a solvable Lagrangian problem are attempted. In this line of research, we give shape to the general purpose automatic generation of solution procedure based on the characteristics of the problem. To implement the automatic identification of embedded structures and relaxation to Lagrangain problem...