(23a) Constrained Grey-Box Multi-Objective Optimization Framework for Optimal Design of Energy Systems

Energy systems are characterized by large, diverse number of components in which they form an integrated complex multi-scale network. The complexity of these multi-scale models is further amplified with the generation of large number of data, which makes them harder to express with mechanistic formulations. In such models, derivative information is often unavailable or unreliable, and the direct use of optimization methods is usually rather prohibitive. [1] Thus, the global optimization of complex energy systems from an economic and sustainability perspective poses a formidable challenge.

Derivative-Free Optimization (DFO) methods are commonly utilized for the optimization of models that lack the closed-form equations or models that strongly rely on input-output data. We have previously introduced the constrained grey-box optimization algorithm called ARGONAUT [2] that couples tractable surrogate approximations, which accurately represent any unknown correlations, with the state-of-the art Mixed-Integer Nonlinear Programming (MINLP) global optimization solver ANTIGONE. [3] In this work, we further expand the existing algorithm to handle mixed-integer programming and multi-objective optimization problems, and test the proposed framework on a case study based on the energy system design for commercial buildings such as a supermarket. [4] We provide solutions to two cases; (a) optimal design based on the single-objective economic behavior or the environmental impact (b) optimal design based on the multi-objective design criteria, simultaneous optimization of economic and environmental behavior. We demonstrate that our framework enables optimization of expensive simulation-based models under multiple competing objectives in a computationally efficient way. The results are presented in the form of Pareto-frontier, compare favorably to the model-based solution in [4].

References:

[1] Boukouvala, F.; Misener, R.; Floudas, C. A., Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO. European Journal of Operational Research 2016, 252, (3), 701-727.

[2] Boukouvala, F.; Floudas, C. A., ARGONAUT: AlgoRithms for Global Optimization of coNstrAined grey-box compUTational problems. Optimization Letters 2016, 1-19.

[3] Misener, R.; Floudas, C., ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations. Journal of Global Optimization 2014, 59, (2-3), 503-526.

[4] Liu, P.; Pistikopoulos, E.N.; Li, Z., An energy systems engineering approach to the optimal design of energy systems in commercial buildings, Energy Policy 2010, 38, (8), 4224–4231.