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at this point (615.75 $/hr). On the other hand, the minimum value for the total cost rate of product occurs at design point A which is about 592.6 $/hr. Design point A is the optimal situation when total cost rate of product is the sole objective function, while design point D is the optimum point when exergy efficiency is the sole objective function. In multi-objective optimization, a process of decision-making for selection of the final optimal solution from the available solutions is required. The process of decision-making is usually performed with the aid of a hypothetical point in Fig. 6.33 (the ideal point), at which both objectives have their optimal values independent of the other objectives. It is clear that it is impossible to have both objectives at their optimum point simultaneously and, as shown in Fig. 6.33, the ideal point is not a solution located on the Pareto Frontier. The closest point of the Pareto frontier to the ideal point might be considered as a desirable final solution. Nevertheless, in this case, the Pareto optimum frontier exhibits weak equilibrium i.e., a small change in exergy efficiency from varying the operating parameters causes a large variation in the total cost rate of product. Therefore, the ideal point cannot be utilized for decision-making in this problem. In selection of the final optimum point, it is desired to achieve a better magnitude for each objective than its initial value for the base case problem. Note that in multi-objective optimization and the Pareto solution, each point can be utilized as the optimized point. Therefore, the selection of the optimum solution depends on the preferences and criteria of the decision maker, suggesting that each may select a different point as for the optimum solution depending on his/her needs. Table 6.5 shows all the design parameters for points A-D. As shown in Fig. 6.33, the optimized values for exergy efficiency on the Pareto frontier range between 60 % and 68 %. To provide a good relation between exergy efficiency and total cost rate, a curve is fitted on the optimized points obtained from the evolutionary algorithm. This fitted curve is shown in Fig. 6.33. The expression for this fitted curve is given as follows: ̇ (6.4) To study the variation of thermodynamic characteristics, four different points (A to D) on the Pareto frontier are considered. Table 6.6 shows total cost rate of the system, the total exergy destruction, the system efficiency, the heating and cooling loads of the system and the CO2 emission of the system. 143PDF Image | Energy Systems for Multigeneration Purposes
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