Pareto-optimal front

Penicillin V Bioreactor Train Three cases maximization of (a) both penicillin yield and concentration at the end of fermentation, (b) penicillin yield and batch cycle time, and (c) penicillin yield and concentration at the end of fermentation as well as profit. NSGA-II Glucose feed concentration is the decision variable contributing to the Pareto-optimal front. Multiple solution sets producing the same Pareto-optimal front were observed. Lee et al (2007)... 

Three cases using two or three objectives from (1) maximization of number-average molecular weight, (2) minimization of reaction time, and (3) minimization of polydispersity index. In all three cases, Pareto-optimal front was found to be non-convex. Real-coded NSGA-11 was observed to be slightly better than binary-coded NSGA-11. Deb et al. (2004)... 

Problem ZDTl has a convex Pareto optimal front and is defined as shown in Eq. (5.12). 

Problem ZDT2 has a concave Pareto optimal front. The problem is presented in Eq. (5.13). 

Fig. 8.12 Pareto-optimal front for nitrogen cooling process.

Fig. 8.13 Number of stages corresponding to the Pareto-optimal front in Fig. 8.12.

Fig. 8.14 Values of the decision variables and constraint corresponding to the Pareto-optimal front in Fig. 8.12 (a) heat exchanger Ar un (b) initial refrigerant pressure, Po,n2 (c) final refrigerant pressure, Pi, n2 and (d) final product temperature, T .

Fig. 8.18 Pareto-optimal front for the optimization of dual independent expander refrigeration process.

For process optimization with respect to several economic criteria such as net present worth, payback period and operating cost, the classical Williams and Otto (WO) process and an industrial low-density polyethylene (LDPE) plant are considered. Results show that either single optimal solution or Pareto-optimal solutions are possible for process design problems depending on the objectives and model equations. Subsequently, industrial ecosystems are studied for optimization with respect to both economic and environmental objectives. Economic objective is important as companies are inherently profit-driven, and there is often a tradeoff between profit and environmental impact. Pareto-optimal fronts were successfully obtained for the 6-plant industrial ecosystem optimized for multiple objectives by NSGA-ll-aJG. The study and results reported in this chapter show the need and potential for optimization of processes for multiple economic and environmental objectives. 

The Pareto-optimal front in Figure 10.3a confirms that NPW and PBT are conflicting NPW increases rapidly and then slowly from 6.48 to 7.31 million US as the PBT decreases from 2.43 to 2.29 million US /year. Three decision variables (T, V and q 2) contribute to the optimal Pareto... 

The Pareto-optimal front in Figure 10.4a shows that NPW and PBP can vary significantly by a factor 2 for the WO process. NPW increases from... 

Fig. 13.3A Pareto-optimal fronts for gene manipulations (1-enzyme 2-enzyme A 3-enzyme o) in simultaneous maximization of DAHPS and PEPCxylase flux ratios (Case A).

Goel, T., Vaidyanathan, R., Haftka, R., Shyy, W., Queipo, N., and Tucker, K. Response surface approximation of pareto optimal front in multi-objective optimization. 

Figure 4.9 MOO results for simultaneous maximization of CH recovery and CH4 purity Pareto-optimal front (left plot), and optimal values of decision variables (right plot).

The MOO was carried out with a population size of 100, and the non-dominated solutions found at generations 100, 250, 500 and 1000 are presented in Figure 7.8. As can be seen, there is significant improvement in the front from generation 100 to 250, and acceptable Pareto-optimal front is obtained at generation 250 in about 60 s of computational time. As expected, MOO results in Figure 7.8 confirm that the two objectives are conflicting... 

Optimal values of decision variables corresponding to the Pareto-optimal front after 100 generations are shown in Figurel0.9b-e. Optimal values of membrane feed flowrate... 

Figure lO.lOe) are scattered around the lower bound initially before jumping to the upper bound. Hence, it can be concluded that all the decision variables affect the Pareto-optimal front to a certain extent. 

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