Modeling and solving large-scale optimization problems: case studies in renewable energy and mining

Abstract

Large-scale optimization modeling is becoming more prevalent in industry practices.As computational hardware and software continue to improve, the problems practitioners attempt to solve increase in complexity. We explain in detail how to improve the tractability and efficiency of large-scale models with the use of the following techniques: (i) Data management, (ii) efficient formulations, (iii) numerical analysis, (iv) heuristics, (v) specialized algorithms, and (vi) decomposition techniques. We apply these techniques to real-world problems in heavy-industry applications: renewable-energy and mining. The former consists of a design and dispatch model that incorporates renewable energy technologies, combined heat and power, and conventional generation. The latter is an underground production scheduling model that considers ventilation and refrigeration while managing heat load output. We highlight the importance and benefits of the modeling techniques in each of the applications, and discuss improvements with respect to the applications we model. The energy application exhibits savings of millions of dollars using an optimized solution. The underground production scheduling model admits feasible solutions where they had not previously been generated. In both applications, we significantly expedite solutions, allowing for optimization approaches to be used where they would otherwise be considered too slow for operational use.