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more than one objective function. In a single-objective optimization problem, the task is to find the value for the objective function which optimizes a sole objective function. When more than one objective function is considered in the optimization, we refer to the procedure as multi- objective optimization. One of the common approaches for dealing with multiple objective functions is to combine them into a single objective function that is to be minimized or maximized. For example, in the design of heat exchangers and cooling systems for electronic equipment, it is desirable to maximize the heat transfer rate. However, this often comes at the cost of increased fluid flow rates and corresponding frictional pressure losses. Another approach which has attracted much attention in recent years is multi-objective optimization. With this approach, two or more objective functions that are of interest in a given problem are considered and a strategy is developed to balance or trade off each objective function relative to the others [14]. To illustrate, we consider two objective functions OF1 and OF2. We assume that these are to be minimized (although maximization can be similarly handled since it is equivalent to minimization of the negative of the function). Fig. 5.2.a shows values for the two objective functions at five design points. As shown in this figure, design 2 is clearly preferable to design 4 because both objective functions are smaller for design 2 compared to design 4. Similarly, design 3 is preferable to design 5. However, designs 1, 2 and 3 are not preferable, or dominated, by any other designs. The set of non-dominated designs is introduced as the Pareto frontier, representing the best collection of design points. This is shown in Fig. 5.2.b. Note that any point on the Pareto frontier can be considered as an optimal design condition. The selection of a specific design from the set of points constituting the Pareto frontier is at the discretion of the decision maker, which may be an engineer or designer. Figure 5. 2: Multi-objective optimization with two objective functions OF1 and OF2 that are to be minimized, showing the (a) dominant designs and (b) the Pareto frontier. 67PDF Image | Energy Systems for Multigeneration Purposes
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