(475b) Multi-Objective Bayesian Optimization of Process Flowsheets Using Trust Regions and Quality Set Metrics.

In the context of chemical processes, the reduction of their environmental impact in the form of climate change contributions, water and non-renewable resources usage, requires a transition towards more sustainable feedstocks and energy sources. In addition to this, the social and economic aspects must be considered for the processes and products to be viable [1].

Optimization methods aim to provide systematic decision-making tools to identify operating conditions and process configurations that consider the inherent trade-offs between sustainability indicators, i.e., economic, environmental, and social. This transforms the optimization process into a multi-objective optimization (MOO) problem [2, 3]. The transition to renewable feedstocks and energy sources will demand the chemical industry to reconsider process and product designs to include sustainability criteria as key performance indicators. Thus, the role of MOO will potentially be increased, making it one of the current challenges in process systems engineering.

Several prerequisites need to be fulfilled in MOO [1]: i) a robust and validated simulation model should be available, ii) sustainability criteria have to be defined, and iii) the availability of reliable and efficient multi-criteria decision support and optimization methods. This work deals with these three points. Herein, a Bayesian-based framework for solving MOO flowsheets problems is proposed using Gaussian processes as surrogate models obtained from high-fidelity process simulators with embedded sustainability indicators. Trust regions are used for constraining the approximation area to ensure that enough accuracy from the surrogates is preserved.

Chemical process simulators have been used extensively in industry and academia to quantify and test the benefits of process designs. These simulators have numerical algorithms that offer solutions with high levels of precision and accuracy [4]. However, they present two main challenges from an optimization perspective [5]. First, there is no direct access to closed-form mathematical expressions which prevents access to reliable derivative information; therefore, they have to be treated as black boxes. This makes its optimization process difficult as the most advanced and reliable solvers require this information in order to find optimal solutions. Second, robust simulations have associated complex functions to evaluate which are prohibited expensive for optimization solvers.

In our Bayesian-based approach the epsilon-constraint method [6] for solving MOO is used. This involves minimizing a primary objective, and expressing the rest of objective functions as inequality constraints within the problem. Different acquisition functions (e.g. lower confidence bound, expected improvement and probability of improvement) are used to balance the exploitation-exploration trade-off during the optimization [7]. This allows for a sample efficient optimization that can deal with complex flowsheets.

As MOO problems generate Pareto rather than unique solutions, in decision making it is as important as the MOO solution method per se, to quantify and analyze the quality of the Pareto solution obtained by the MOO method employed. In this work, we include a quality metric based on hypervolumes differences [8] that allows to measure the “goodness” of Pareto solutions of multi objective flowsheet optimization problems. This method compares the size of the space associated to a dominated (or inferior) Pareto solution with the space size of an ideal (or dominant) Pareto set. We demonstrate the capabilities of our framework with a case study involving a flowsheet optimization.

References:

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[3] Pieragostini, Carla, Miguel C. Mussati, and Pío Aguirre. 2012. “On Process Optimization Considering LCA Methodology.” Journal of Environmental Management 96 (1). Elsevier Ltd:43–54.

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[6] Haimes, Yacov. "On a bicriterion formulation of the problems of integrated system identification and system optimization." IEEE transactions on systems, man, and cybernetics 1.3 (1971): 296-297.

[7] del Rio Chanona, E. A., et al. "Real-time optimization meets Bayesian optimization and derivative-free optimization: A tale of modifier adaptation." Computers & Chemical Engineering 147 (2021): 107249.

[8] Wu, Jin, and Shapour Azarm. 2001. “Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set.” J. Mech. Des. 123 (1):18–25.