Objectives Design Variables The objective can be a vector J of z system responses Design vector x contains n variables that form the design space or characteristics we are trying to maximize or minimize During design space exploration or optimization we change the [S] Often the objective is a entries of x in some rational fashion to achieve a desired effect cost scalar function,but for X;can be… range [km] real systems often we aspect ratio [- attempt multi-objective weight [kg] 2 transmit power [W] optimization: Real: xi∈R J= X3 #of apertures[日] data rate [bps] X= x→J(☒ Integer: ri∈Z orbital altitude [km] : Binary: c∈{0,1} Some objectives can be ROI [%] Boolean:xiE {true,false} conflicting. control gain [V/V] System Engineering by J.J.Gao ③cLao 国 17 System Engineering by J.J.Gao ③cLco 国 18 Parameters Constraints Constraints act as boundaries of the design space x and typically occur due to finiteness of resources or Parameters p are quantities that affect the objective technological limitations of some design variables. J,but are considered fixed,i.e.they cannot be changed by the designers. Often.but not always.optimal designs lie at the intersection of several active constraints Sometimes parameters p can be turned into design variables x to enlarge the design space. Inequality constraints: gX≤0j=1,2…,m1 Sometimes parameters p are former design variables that were fixed at some value because they were Equality constraints:x=0k=1,2....,m found not to affect any of the objectives or because Bounds::xB≤x,≤xgi=l,2,n their optimal level was predetermined. Objectives are what we are trying to achieve Constraints are what we cannot violate Design variables are what we can change System Engineering by J.Gao ③ctGe 19 System Engineering by J.J.Gao ③ct6e 20+ - System Engineering by J. J. Gao 17 Objectives + - System Engineering by J. J. Gao 18 Design Variables + - System Engineering by J. J. Gao 19 Parameters Parameters p are quantities that affect the objective J,but are considered fixed, i.e. they cannot be changed by the designers. Sometimes parameters p can be turned into design variables x to enlarge the design space. Sometimes parameters p are former design variables that were fixed at some value because they were found not to affect any of the objectives J or because their optimal level was predetermined. + - System Engineering by J. J. Gao 20 Constraints