(575c) Bi-Level Mixed-Integer Optimization for Planning and Scheduling Integration Using the Domino Framework

Traditionally, planning and scheduling problems in process systems engineering are tackled sequentially, where the process plan is decided first, and its respective scheduling decisions are taken later. However, this sequential approach may lead to sub-optimal strategies as variables are shared between the two optimization problems. Planning and scheduling problems can be tackled in a holistic approach with bi-level programming formulations, where the scheduling optimization problem is posed as a constraint on the upper level planning optimization problem [1, 2]. Such a formulation yields a mixed-integer bi-level programming problem with a high number of integer variables at the lower level, making this particular type of problem difficult to solve using deterministic bi-level approaches.

In this presentation, a novel data-driven optimization framework (Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems, DOMINO) [3] is going to be demonstrated to address problems of this nature. In this framework, mixed-integer bi-level optimization problems are approximated as single level optimization problems, by collecting samples of the upper level objective, while the lower level problem is solved to global optimality at those sampling points. This is done through integrating the DOMINO framework with a grey-box optimization solver to perform design of experiments on the upper level objective, and to consecutively approximate and optimize bi-level mixed-integer programming problems that are challenging to solve using deterministic methods. Using this data-driven framework, the planning and scheduling problem is investigated for small and large-scale scheduling problems with varying dimensionalities and for a range of planning horizons.

References

[1] S. Avraamidou and E.N. Pistikopoulos. A novel algorithm for the global solution of mixed-integer bi-level multi-follower problems and its application to Planning & Scheduling integration. 2018 European Control Conference (ECC) June 12-15, 2018. Limassol, Cyprus, pp. 1056-1061.

[2] Z. Li and M. Ierapetritou. Integrated production planning and scheduling using a decomposition framework. Chemical Engineering Science, 64(16):3585–3597, 2009.

[3] B. Beykal, S. Avraamidou, I.P.E. Pistikopoulos, M. Onel, E.N. Pistikopoulos. DOMINO: Data-driven Optimization of MultI-level NOnlinear Problems. Journal of Global Optimization (Under Review).