Development of an object oriented mathematical modeling system

Abstract

In this study, ICRON, which is a tool supporting object oriented mathematical programming, is partially developed in order to reduce the workload during the modeling and solving process of large scale optimization problems. The effectiveness of decomposition techniques in solving large scale optimization problems have led to the development of several modeling environments and tools having their own functionalities in order to increase the performances. These environments and tools in the literature have both some advantages and some disadvantages with respect to the support of easy modeling and fast solving. The new proposed mathematical programming tool is developed to allow better modeling environment to the user and to get shorter solution time relative to the previous version of ICRON by eliminating the repetitions both on models and on solver iterations which are of a considerable number especially when implementing a decomposition technique. One of the important aspects of the tool is its object oriented architecture that provides object oriented modeling of mathematical programming problems by using real world object descriptions instead of writing codes depending on sets and indexes. More importantly, it allows the user to construct a structure keeping the whole model and solver information throughout running of algorithms which provides flexibility to the user to define objective functions, decision variables or constraints and, to update the current solver information via special constructs to add column, to add row, to relax constraints, and to change types of decision variables in anywhere of the algorithm. The strong relationship between business objects and mathematical programming objects in the environment is due to the tight integration of the modeler and the solver which brings the tool beyond of the others.