| Abstract [eng] |
In this dissertation, the concept of a universal mathematical optimization system consisting of an algebraic modeling language and an open source tool capable of building an optimization model and solving it with potentially multiple underlying optimization solvers is presented. First, the main principles of algebraic modeling are presented, the essential characteristics of modern algebraic modeling languages (AMLs) are reviewed, the most prominent AMLs are identified, and a bibliometric analysis of the research field is conducted by analyzing publications from the year 2000 to the present day. Next, an extensive theoretical and experimental analysis of the characteristics of four of the most prominent algebraic modeling languages (AMPL, GAMS, JuMP ir Pyomo) and the modeling systems supporting them is performed. A purpose-built test model library is used to perform extensive benchmarks in experimental analysis. Afterwards, the main gaps within the existing algebraic modeling languages and tools are distilled and a concept of a state-of-the-art universal optimization system for algebraic modeling languages and mathematical optimization is proposed. To assess the feasibility of the proposal, a prototype of such a web-based tool is implemented. The prototype is used to compare its characteristics with other AMLs and provide an overview of how it addresses the gaps identified earlier. Lastly, clear extension points and ideas on how such a tool could be further improved are provided. |
