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Basis and Stability Description We solve a simple 2x2 LP problem to optimality, which serves as a showcase for basis handling methods and sensitivity analysis. Further explanation of this example:
Xpress Python Reference Manual
Source Files By clicking on a file name, a preview is opened at the bottom of this page.
example_basis_sensitivity.py # Example using the Xpress Python interface # # Basis handling and sensitivity methods # # We solve a simple 2x2 LP problem to optimality, # which serves as a showcase for basis handling methods and # sensitivity analysis. # # (C) Fair Isaac Corp., 1983-2024 import xpress as xp # create and name the problem, and add variables p = xp.problem("firstexample") x1 = p.addVariable(name="x_1") x2 = p.addVariable(name="x_2", vartype = xp.continuous, lb = 0, ub = xp.infinity) # create two constraints cons1 = 5* x1 + x2 >= 7 cons2 = x1 + 4 * x2 >= 9 # add objective function, constraints p.setObjective(x1 + x2) p.addConstraint(cons1, cons2) # save the problem to a file p.write("firstexample", "lp") # load a basis by specifying row and column basis status # below, the optimal basis status will be printed p.loadbasis([2,2], [1,1]) # solve the problem and print the solution p.optimize() print("The solution is x_1 = {}, x_2 = {}".format(p.getSolution(x1), p.getSolution(x2))) # write the solution to a file p.writeslxsol("firstexample.slx") # print the row and column basis status rowstat = [] colstat = [] p.getbasis(rowstat, colstat) print("Rows basis status:", rowstat) print("Column basis status:", colstat) # write basis to a file p.writebasis("basis") print("sensitivity Analysis of the objective:") l = []; u = [] p.objsa([x1,x2], l,u) for i,x in enumerate([x1, x2]): print("The objective coefficient of {} can be varied between [{}, {}]".format(x, l[i], u[i])) print() print("Sensitivity Analysis of the lower and upper bounds:") lblower = []; lbupper = []; ublower = []; ubupper = [] p.bndsa([x1,x2], lblower,lbupper,ublower,ubupper) for i,x in enumerate([x1, x2]): print("The lower bounds of {} can be varied between [{}, {}]".format(x, lblower[i], lbupper[i])) print("The upper bounds of {} can be varied between [{}, {}]".format(x, lblower[i], lbupper[i])) print() print("Sensitivity Analysis of right-hand sides:") rhslower = []; rhsupper = [] p.rhssa([cons1, cons2], rhslower, rhsupper) for i,c in enumerate([cons1, cons2]): print("The right-hand side of constraint {} can be varied between [{}, {}]".format(c, rhslower[i], rhsupper[i])) print() | |||||||||||

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