## 3 Methodology  
### Multiobjective Process Optimization  
The model of the integrated biobutanol production process in Figure 1 was developed and coded in Fortran programming language. Optimizing this process boils down to determining the set of input variables that will lead to the optimal set of objective criteria. In this investigation, the input or decision variables consist of: (1) the dilution rate, defined as the volumetric input flow rate divided by the volume of the fermenter; (2) the feed glucose concentration; (3) the cell retention factor, defined as the ratio of the flow rate of Stream 8 to the flow rate of Stream 12 (Figure 1), which serves to maintain a steady microbial cell concentration in the fermentation broth; (4) the number of pervaporation modules in series, each module being preceded by a heat exchanger to increase the feed module stream to favor higher permeation flux; and (5) the number of stacked membranes in each membrane module where the stream entering the module is split equally to flow through each individual membrane unit within a stack. For the butanol production process, four objective functions were optimized simultaneously: (1) butanol productivity; (2) overall butanol concentration exiting the process, which represents the combined concentration of Streams 5, 8 and 12; (3) glucose conversion; and (4) number of membrane modules in series, i.e., the fourth decision variable. A summary of the decision variables and the objectives to be optimized is presented in Figure 2. The first three objective functions need to be maximized, whereas the fourth objective needs to be minimized. Many of these objectives conflict, and a judicious trade-off among them needs to be found. To solve the optimization problem, i.e., circumscribing the Pareto domain associated with the five decision variables and the four objective functions for the butanol production process, the dual population evolutionary algorithm (DPEA) was used [15]. For the first generation, a set of random values of the five decision variables was obtained within their feasible ranges. A total of 5000 sets of decision variables formed the initial population. For each decision variable set, the steady-state solution of the butanol production process was determined, which allowed for calculation of the four objectives. Upon creation of the first generation, containing 5000 vectors of the objective functions associated with each set of decision variables, a pairwise comparison of the objectives of all solutions in the population was performed to determine the number of times a solution was dominated. A solution is dominated if another solution within the population is better for all four objectives. All nondominated solutions and a fraction of the least-dominated solutions were retained as parents for the next generation. For all subsequent generations, two parents from the previous generation were used to give rise to a new individual using the Blend crossover operator and the Gaussian mutation operator. These two operators are essential to obtain a well-circumscribed Pareto domain and allow the diversity of the population to be maintained. This procedure, performed at each generation to keep the population size constant, was repeated until the desired number of nondominated solutions in the population was achieved. In this investigation, the Pareto domain was assumed to have converged when the number of nondominated solutions reached 4900. A good approximation of the Pareto domain, containing only nondominated solutions, is thereby obtained. The Pareto domain is determined without any biases or preferences by the decision-maker. To rank all solutions in the Pareto domain, the NetFlow method was used, where preferences of an expert, encapsulated in terms of four parameters for each objective, are used [16]. The four parameters for each objective necessary to rank the whole Pareto domain are the relative weight and three threshold parameters: the indifference threshold, the preference threshold, and the veto threshold.