Ontologies for Continuous Global Optimization

Global Optimization tackles the problem of finding all feasible points of a set of constraints that optimize an objective function. In the following, we restrict our attention to Continuous Global Optimization, and more specifically to Global Optimization over interval domains [6, 9]. We believe that Software Design for Continuous Global Optimization has things in common with Astronomy of Sixteenth Century. Many powerful systems implementing various solving techniques have already been developed. However, there exists no general cooperation architecture [4] describing knowledge sharing among solvers. More precisely, a cooperation model would define representations and specifications of shared knowledge, and protocols of communication. In Knowledge Engineering, the problem of representing shared and reusable knowledge among software agents has heavily been studied in the recent past. This problem can be addressed by ontologies. An ontology [5] is a specification of concepts of a given domain and relationships among them. One of the objectives is to lay foundations for libraries of reusable components and knowledge sharing functionalities. Knowledge based systems (KBS) are often modeled by means of three concepts: task, PSM (Problem Solving Method) and domain [8]: