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Introductory examples Description
Further explanation of this example:
'Applications of optimization with Xpress-MP', Introductory examples (Chapters 1 to 5) of the book 'Applications of optimization with Xpress-MP'
Source Files By clicking on a file name, a preview is opened at the bottom of this page. Data Files approx.mos (!****************************************************** Mosel Example Problems ====================== file approx.mos ``````````````` Function approximation with SOS2 SOS2s are generally used for modeling piecewise approximations of functions of a single variable. In this example, we aim to represent f as a function of x and we consider four line segments between five points. The five points are (R1, F1), (R2, F2), (R3, F3), (R4, F4) and (R5, F5) and associated with each point i is a weight variable y(i). Binary variable b(i) is associated with each of the intervals (R1, R2), (R2, R3), (R3, R4) and (R4, R5), so 'b(i)' takes value 1 if the value of x lies between 'R(i)' and 'R(i+1)'. The SOS2 property of having at most two non-zero 'y(i)', and if there are two non-zero then they must be adjacent, implies that we are always on the piece-wise linear function. (c) 2008 Fair Isaac Corporation author: S. Heipcke, Sep. 2006 *******************************************************!) model "Approximation" uses "mmxprs" declarations NB = 5 BREAKS = 1..NB R,F: array(BREAKS) of real ! Coordinates of break points x,f: mpvar ! Decision variables y: array(BREAKS) of mpvar ! Weight variables end-declarations R:: [1, 2.2, 3.4, 4.8, 6.5] F:: [2, 3.2, 1.4, 2.5, 0.8] RefRow:= sum(i in BREAKS) R(i)*y(i) x = RefRow f = sum(i in BREAKS) F(i)*y(i) ! Convexity constraint sum(i in BREAKS) y(i) = 1 ! SOS2 definition RefRow is_sos2 ! Alternative SOS definition (to be used for 0-valued RefRow coefficients): ! makesos2(union(i in BREAKS) {y(i)}, RefRow) (! Alternative formulation using binaries instead of SOS2: declarations b: array(1..NB-1) of mpvar end-declarations sum(i in 1..NB-1) b(i) = 1 forall(i in 1..NB-1) b(i) is_binary forall(i in BREAKS) y(i) <= if(i>1, b(i-1), 0) + if(i<NB, b(i), 0) !) ! Bounds 1<=x; x<=6.5 ! Solve the problem minimize(f) writeln("Objective value: ", getobjval) writeln("x: ", getsol(x)) end-model | |||||||||||||||||||||||||||||||||||||

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