3Optimization.pptx

#,Optimization,Greg Nellis,Professor of Mechanical Engineering,University of Wisconsin,Madison,gfnellisengr.wisc.edu,608-265-6626,Optimization,Systematic variation of one or more input parameters in order to minimize or maximize an objective function,Allows models to be used for design,Also useful for other things like solving particularly difficult sets of equations or accomplishing curve fits,This seminar will discuss,One-dimensional optimization,Multi-dimensional optimization,Constrained optimization,Other uses for optimization,One-Dimensional Optimization,Optimization1.ees,A simple example involving one-dimensional optimization-sizing a heat exchanger,Select the,UA,that maximizes the net savings,System operates for,time,=100 days/year for 5 years,Energy costs,EC,=0.73$/therm,Heat exchanger costs,HXC,=2.5$-K/W,Heat Exchanger Net Savings,Inputs,The value of the energy savings is:,where,The cost of the heat exchanger is:,The net savings is:,Heat Exchanger Sizing,Before performing optimization,setup model to provide objective function given specified values of the independent parameter(s),Set a value of,UA,and calculate the net savings,Heat Exchanger Sizing,Optimization,In order to carry out optimization EES requires at least one free parameter(i.e.,one degree of freedom),Comment out the specified values of the independent variables,Select Min/Max from the Calculate menu,Min/Max Dialog,Optimization target,Independent variable(s),Optimization method,Stopping criteria,Guess values&bounds must be set for each independent variable,#free parameters,Golden Section Search,Successively narrows the range in which the maximum must exist,Three points are evaluated(bounds&1 in between),A fourth point is selected(the guess)&the range narrowed by comparison,Carry out the Optimization,Optimal solution is contained in the Solutions Window,Quadratic Approximations Method,Three points are selected and used to generate a quadratic approximation to the objective function,The optimal value based on the quadratic is evaluated,The smallest point is discarded and the process is repeated,Quadratic Approximations Method,