Multi-objective optimization of anaerobic digestion process using a gradient-based algorithm

•Improved mathematical anaerobic digestion model for biogas production.•Introduction of design-dependent pH value and temperature time functions.•Investigation of various objective functions involving one or two objectives.•Successful engagement of this model as a state equation in the optimization problem.•Biogas production is significantly increased by gradient-based optimization. This paper focuses on optimization of the anaerobic digestion (AD) process by using gradient-based algorithm in order to determine the optimal values of process conditions and cattle manure characteristics. For this purpose, a simple AD mathematical model, which involves pH value- and temperature-dependent parameters of biochemical reactions and batch performance equations, has been developed. By using the proposed AD model, the optimization procedure is tested by three different objective functions and two types of pH value and temperature functions of time, which also depend on design variables: piecewise linear and Bezier function. The best results are obtained by using an objective function, which involves two conflicting objectives: maximization of biogas production in the shortest time possible and minimization of heating-related cost. In this case the optimized histories of pH and temperature as well as optimal initial bacteria concentrations enable a 4 times higher biogas volume production within a time interval being 3 times shorter than at the initial AD state. This can be achieved by using either the piecewise linear or Bezier type of the pH and temperature histories. The optimization process proved to be stable and efficient, especially by the parallelized derivatives computation. The results obtained confirm the usefulness of the proposed approach, which can easily be adapted or upgraded for complex substrates and other reactor types.