(461g) On the Impact of Solution Representations for Stochastic Optimisation of Control Trajectories of Industrial Fermentation Processes

Despite their widespread use, limitations may arise when using deterministic dynamic optimisation methods in optimal control problems. Required CPU time may be significant and solution trajectories may display extremely strong sensitivity to initialisation. Stochastic optimisation methods have versatility advantages which can be explored towards overcoming such limitations when observed (Xiao, Zhou and Zhang, 2003). Nevertheless, systematic guidelines for formulating a control trajectory representation in order to ensure compatibility with stochastic optimisation algorithms have not been hitherto developed. The present paper considers an industrial control vector optimisation problem, namely the temperature manipulation during beer fermentation (Rodman and Gerogiorgis, 2016), and applies a multi-objective plant propagation algorithm in order to investigate the influence of problem formulation and solution representation on algorithmic efficiency.

Fermentation is a key step in the production of all beer products, and a possible production bottleneck due to its significant duration (often exceeding 1 week). Therein lies a strong incentive for process optimisation and batch duration reduction; nevertheless, a clear trade-off is evident beween attainable ethanol concentration and required batch time (Carrillo-Ureta et al., 2001). Biochemical system operation and fermentation progress is sensitive to yeast cellular activity, which in turn depends on fermenter operating conditions. Consequently, it is desirable to compute and determine temperature manipulations protocols (control profiles) for improved plant performance. The complexity of the chemical system (>600 species: Vanderhaegen et al., 2006) renders comprehensive parameter estimation infeasible and dynamic optimisation (even for reduced models) quite cumbersome. A validated reduced-order dynamic model of the fermentation process (de Andrés-Toro, 1998) has been previously analysed (Rodman and Gerogiorgis, 2016) and confirmed to be adequately descriptive to capture the key chemical pathways and facilitate a stochastic optimisation study.

The Plant Propagation Algorithm employed is The Strawberry Algorithm (Salhi and Fraga, 2011), which emulates the behaviour of strawberry plants by encompassing the two key aspects of effective global optimisation algorithms: solution exploration and intensification. In nature, plants which are in a favourable environment will reproduce with greater frequency, within their local vicinity. Conversely, plants which are not as well situated will reproduce through longer distances. This inspires the Strawberry evolutionary algorithm: each member of the population (an individual solution) is evaluated (objective function computed) and a fitness function is used to rate the performance of each (Fraga and Amusat, 2016). A fitness-based selection procedure is used to identify those solutions for propagation. More fit solutions generate new solutions in the local neighbourhood; less fit solutions generate fewer solutions but further away.

The present beer fermentation control problem is formulated so that a vector of decision variables corresponds to a member of the population at each generation. The decision variable vector must be suitably formulated to allow for an expressive as well as inexpensive portrayal of the (temperature manipulation) profile for beer fermentation control: accordingly, a range of different solution representation strategies have postulated, implemented and evaluated. We hereby demonstrate that the specific formulation of the decision vector has strong influence on stochastic algorithm performance: the probability of returning favourable solutions after a fixed number of generations as well as the required number of generations to consistently achieve convergence vary significantly, as evidenced by the required CPU time as well as the quality of computed solutions. Additional benefits of select solution representations include inherent suitability for industrial application of the corresponding temperature manipulation profiles. These new stochastic optimisation results allow us to elucidate and present heuristics for effective implementation of stochastic algorithms, particularly in achieving optimal biochemical process performance under reduced-order dynamic models.

LITERATURE REFERENCES

Carrillo-Ureta, G., P. Roberts, and V. Becerra, 2001. Genetic algorithms for optimal control of beer fermentation. Proc. IEEE Int. Symp. Intell. Control, 391-396.

de Andrés-Toro, B., et al., 1998. A kinetic model for beer production under industrial operational conditions. Math. Comput. Simulat. 48(1): 65-74.

Vanderhaegen, B., et al., 2006. The chemistry of beer aging – a critical review. Food Chem. 95(3): 357-381.

Xiao, J., Zhou, Z., Zhang, G., 2003. Ant colony system algorithm for the optimization of beer fermentation control. J. Zhejiang Univ. 5(12): 1597-1603.

Rodman, A. D., Gerogiorgis, D.I., 2016. Multi-objective process optimisation of beer fermentation via dynamic simulation, Food Bioprod. Proc. 100(A): 255-274.

Salhi, A., Fraga, E. S., 2011, Nature-inspired optimisation approaches and the new Plant Propagation Algorithm, The International Conference on Numerical Analysis and Optimization (IceMATH 2011), Yogyakarta, Indonesia, K2-1-8.

Fraga, E., and Amusat, O. 2016. Understanding the impact of constraints: A rank-based fitness function for evolutionary methods. Advances in Stochastic and Deterministic Global Optimization. Springer, 243-254.