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Graphical methods plot the function on a graph and can be used when there are one to two independent variables. When plotting on a graph (when f(x) is dependent on only one variable) within a specific range the maxima and minima of a function become apparent easily. When dealing with two independent variables (x1, x2) a contour plot is made where the variables are set on the x and y axes and the function evaluated for various values of x1 and x2. An optimum set of variables is chosen based on the criteria of finding the maximum or minimum. Experimental methods involve changing certain variables one by one and recording the system performance. With this method there are limitations, such that changing one variable interacts with another leading to unreliable results and difficulties achieving optimization of the system. The most important approach to optimization used in this thesis is based on numerical methods. Numerical methods use iterative steps to progressively get closer to an improved solution starting with an initial guess. This method completes when changes in the independent variables from iteration to iteration become insignificant. Numerical methods can solve highly complex problems and are programmed into a computer to be solved. This makes the approach adaptable to many situations and thus is very popular for all kinds of problems. In general optimization problems involve an objective function which is dependent on xn number of independent variables. There can be a certain number of constraints, mainly equality constraints and inequality constraints. An example of an equality constraint is the area of a space needs to be exactly 300 square meters. An inequality constraint can be that the length has be less than or equal to 2 times 27PDF Image | Exergoeconomic Analysis and Optimization of ORC
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