# Evolutionary Multi-Objective Optimisation of a Complex Steady-State Process Flowsheet – The ‘Surrogate-Assisted’ Approach

thesis

posted on 07.02.2017, 23:49 by Ishan SharmaDecision
making, in case of multiple objectives, involves analysing the trade-offs.
Evolutionary Multi-Objective Optimisation (MOO) is a derivative-free search
method, which tries to mimic the natural evolutionary process. It has the
advantage of yielding a set of Pareto-optimal or equally-good solutions in a
single run. This eliminates the need for the Decision Maker (DM) to a-priori
articulate his/her preferences among the different objectives. Generating
multiple solutions may be considered unnecessary, as ultimately the DM is going
to implement only one of the multiple non-dominated solutions generated by
evolutionary MOO. A large number of the potential, or candidate, solutions just
‘die-off’ during the course of optimization. This is specifically detrimental
in case of high fidelity objective functions/models, which are often
computationally expensive and thus, generally require a significantly high
computation time.

However, making an informed decision about the preferences a-priori is not always possible. In a large number of instances, a set of non-dominated solutions can aid the DM to make an informed decision. It is in these situations that the computation effort could be used as a ‘resource’ to fit relatively lower fidelity surrogate approximations, which can be solved in a fraction of the time needed to solve the high fidelity function/model. In the field of process design, some example of high fidelity models include; 3D, 2D and 1D Computational Fluid Dynamics (CFD) based models, cyclic or batch process models which need to be integrated with steady-state models.

The surrogate models can then be subsequently used, if expected to be of sufficient accuracy. The surrogate may also be needed to be updated periodically. This is done with the dual objective of ensuring better surrogate model accuracy/fidelity in the promising subdomain and to use the additional information that is now available due to the high fidelity model evaluations done since the last surrogate fitting step. The fidelity of the surrogate model is expected to only selectively improve because the evolutionary algorithm is more likely to generate candidate solutions from the promising subdomain, during the course of optimisation. When the surrogates are to be used for optimisation, improving the global fidelity of the surrogates makes little sense as this would inevitably require the high fidelity model to be evaluated for non-promising data points. The aim of surrogate-assisted evolutionary MOO should thus be to converge as close to the global optimum, as possible; while evaluating the high fidelity model as few number of times, as possible.

This thesis includes a review of the recent application of surrogate-assisted evolutionary MOO in the field of chemical engineering, with a specific interest in process design applications. The Multiple Adaptive Spatially Distributed Surrogates (MASDS) algorithm has been modified in order to better suit practical chemical engineering process design problems, where the final solution space is often a small subset of the initial search space. In such a scenario, periodic evolution of search space could also be done to ensure that the data points lying in the non-promising regions do not contribute to surrogate model fitting, thereby, potentially improving the surrogate accuracy (or fidelity) in the promising regions. A preliminary investigation has been done to assess this hypothesis by applying the modified MASDS or mMASDS algorithm to two numerical test problems. The results, thus obtained, are compared with those obtained from MASDS algorithm by performing two separate runs, when starting from the same initial population, while keeping all the other parameters the same.

The mMASDS algorithm is then demonstrated for a chemical engineering process design and optimisation problem, involving simultaneous optimisation of economic and environmental objectives in a coal to ammonia process with carbon capture. Two CO2 capture mechanisms have been compared by performing two separate surrogate-assisted evolutionary MOO runs. Physical absorption in chilled methanol and Activated Carbon based Pressure Swing Adsorption (PSA) that have been investigated for CO2 capture. Both the chilled methanol and PSA models are computationally expensive. For the chilled methanol case, the simulation model has a recycle; this requires the simulation to be solved iteratively. While the PSA model needs to be solved dynamically for a finite number of cycles, until a Cyclic Steady State (CSS) is achieved. This makes the entire exercise computationally prohibitive. The CO2 capture unit models are thus replaced with a set of surrogate models, predicting the CSS outputs. For the chilled methanol case, the results from the surrogate-assisted run have been compared to those obtained from Business-As-Usual (BAU) approach, where only the actual flowsheet model was used for functional evaluation. Results show significant savings, measured in terms of the hypervolume spanned by the Pareto-fronts obtained from the two approaches, for a fixed computational budget.

The surrogate-assisted strategy thus allows for better integration of computationally complex units into large-scale plant simulations. It also yields an array of surrogates, which can be used for any future prediction of the objective function values.

To decide whether to update the surrogates or not, the use of rank correlation coefficient between the surrogate and the actual models has been suggested for future implementation. This avoids the extra computational effort wasted in unnecessarily updating the surrogates.

Both the MASDS and mMASDS algorithms involve comparing the surrogate model based outputs with those obtained from the high fidelity models, during domination score computation. This may result in the accurately evaluated promising, high fidelity data points dying-off during the optimisation, due to erroneous surrogate predictions. It is thus suggested to maintain a separate Actual Evaluated Pareto (AEP) which contains only the solutions obtained from high fidelity model evaluations.

The surrogate-assisted evolutionary MOO is a powerful tool to be used for determining the trade-offs, when the mathematical model/simulation is computationally expensive to be used with conventional evolutionary algorithms. It allows the user to quickly hone in on the solution, without spending too much time in evaluating the model/simulation. It has multiple applications in chemical engineering and in particular, process design. As demonstrated in this work, it allows the user to better integrate and optimise a computationally expensive subsection with the rest of the plant.

However, making an informed decision about the preferences a-priori is not always possible. In a large number of instances, a set of non-dominated solutions can aid the DM to make an informed decision. It is in these situations that the computation effort could be used as a ‘resource’ to fit relatively lower fidelity surrogate approximations, which can be solved in a fraction of the time needed to solve the high fidelity function/model. In the field of process design, some example of high fidelity models include; 3D, 2D and 1D Computational Fluid Dynamics (CFD) based models, cyclic or batch process models which need to be integrated with steady-state models.

The surrogate models can then be subsequently used, if expected to be of sufficient accuracy. The surrogate may also be needed to be updated periodically. This is done with the dual objective of ensuring better surrogate model accuracy/fidelity in the promising subdomain and to use the additional information that is now available due to the high fidelity model evaluations done since the last surrogate fitting step. The fidelity of the surrogate model is expected to only selectively improve because the evolutionary algorithm is more likely to generate candidate solutions from the promising subdomain, during the course of optimisation. When the surrogates are to be used for optimisation, improving the global fidelity of the surrogates makes little sense as this would inevitably require the high fidelity model to be evaluated for non-promising data points. The aim of surrogate-assisted evolutionary MOO should thus be to converge as close to the global optimum, as possible; while evaluating the high fidelity model as few number of times, as possible.

This thesis includes a review of the recent application of surrogate-assisted evolutionary MOO in the field of chemical engineering, with a specific interest in process design applications. The Multiple Adaptive Spatially Distributed Surrogates (MASDS) algorithm has been modified in order to better suit practical chemical engineering process design problems, where the final solution space is often a small subset of the initial search space. In such a scenario, periodic evolution of search space could also be done to ensure that the data points lying in the non-promising regions do not contribute to surrogate model fitting, thereby, potentially improving the surrogate accuracy (or fidelity) in the promising regions. A preliminary investigation has been done to assess this hypothesis by applying the modified MASDS or mMASDS algorithm to two numerical test problems. The results, thus obtained, are compared with those obtained from MASDS algorithm by performing two separate runs, when starting from the same initial population, while keeping all the other parameters the same.

The mMASDS algorithm is then demonstrated for a chemical engineering process design and optimisation problem, involving simultaneous optimisation of economic and environmental objectives in a coal to ammonia process with carbon capture. Two CO2 capture mechanisms have been compared by performing two separate surrogate-assisted evolutionary MOO runs. Physical absorption in chilled methanol and Activated Carbon based Pressure Swing Adsorption (PSA) that have been investigated for CO2 capture. Both the chilled methanol and PSA models are computationally expensive. For the chilled methanol case, the simulation model has a recycle; this requires the simulation to be solved iteratively. While the PSA model needs to be solved dynamically for a finite number of cycles, until a Cyclic Steady State (CSS) is achieved. This makes the entire exercise computationally prohibitive. The CO2 capture unit models are thus replaced with a set of surrogate models, predicting the CSS outputs. For the chilled methanol case, the results from the surrogate-assisted run have been compared to those obtained from Business-As-Usual (BAU) approach, where only the actual flowsheet model was used for functional evaluation. Results show significant savings, measured in terms of the hypervolume spanned by the Pareto-fronts obtained from the two approaches, for a fixed computational budget.

The surrogate-assisted strategy thus allows for better integration of computationally complex units into large-scale plant simulations. It also yields an array of surrogates, which can be used for any future prediction of the objective function values.

To decide whether to update the surrogates or not, the use of rank correlation coefficient between the surrogate and the actual models has been suggested for future implementation. This avoids the extra computational effort wasted in unnecessarily updating the surrogates.

Both the MASDS and mMASDS algorithms involve comparing the surrogate model based outputs with those obtained from the high fidelity models, during domination score computation. This may result in the accurately evaluated promising, high fidelity data points dying-off during the optimisation, due to erroneous surrogate predictions. It is thus suggested to maintain a separate Actual Evaluated Pareto (AEP) which contains only the solutions obtained from high fidelity model evaluations.

The surrogate-assisted evolutionary MOO is a powerful tool to be used for determining the trade-offs, when the mathematical model/simulation is computationally expensive to be used with conventional evolutionary algorithms. It allows the user to quickly hone in on the solution, without spending too much time in evaluating the model/simulation. It has multiple applications in chemical engineering and in particular, process design. As demonstrated in this work, it allows the user to better integrate and optimise a computationally expensive subsection with the rest of the plant.