Bi-objective dynamic optimization of a nonlinear time-delay system in microbial batch process

In this paper, we propose a bi-objective dynamic optimization model involving a nonlinear time-delay system to optimize the 1,3-propanediol (1,3-PD) production in a microbial batch process, where the productivity of 1,3-PD and the consumption rate of glycerol are taken as the two objectives. The initial concentrations of biomass and glycerol, and the terminal time of the process are the decision variables. By a time-scaling transformation, we first transform the problem to the one with fixed terminal time but involving a new system with variable time-delay. The normalized normal constraint method is then used to convert the resulting problem into a sequence of single-objective dynamic optimization problems. A gradient-based optimization method incorporating the constraint transcription technique is developed to solve each of these single-objective dynamic optimization problems. Finally, numerical results are provided to demonstrate the effectiveness of the proposed solution method.