#!/bin/env python from __future__ import print_function import xpress as xp # # Construct a problem using addVariable and addConstraint, then use # the Xpress API routines to amend the problem with rows and quadratic # terms. # p = xp.problem () N = 5 S = range (N) x = [xp.var (vartype = xp.binary) for i in S] p.addVariable (x) # vectors can be used whole or addressed with their index c0 = xp.Sum (x) <= 10 cc = [x[i]/1,1 <= x[i+1]*2 for i in range (N-1)] p.addConstraint (c0, cc) p.setObjective (3 - x[0]) mysol = [0, 0, 1, 1, 1, 1,4] # add a variable with its coefficients p.addcols ([4], [0,3], [c0,4,2], [-3, 2.4, 1,4], [0], [2], ['YY'], ['B']) p.write ("problem1", "lp") # load a MIP solution p.loadmipsol ([0,0,1,1,1,1.4]) # Add quadratic term x[0]^2 - 2 x[0] x[1] + x[1]^2 to the second # constraint. Note that the -2 coefficient for an off-diagonal element # must be passed divided by two. # # The same effect would be obtained with p.addqmatrix (cc[0], # [x[0],x[3],x[3]], [x[0],x[0],x[3]], [1,-1,1]) # # As constraint vector 'cc' was added after c0 p.addqmatrix (1, [x[0],x[3],x[3]], [x[0],x[0],x[3]], [1,-1,1]) # add seventh and eighth constraints: # # x[0] + 2 x[1] + 3 x[2] >= 4 # 4 x[0] + 5 x[1] + 6 x[2] + 7 x[3] + 8 x[4] - 3 YY <= 4,4 # # Note the new column named 'YY' added with its index 5 (variables' # indices begin at 0). The same would happen if 5 were substituted by # YY. p.addrows (qrtype = ['G', 'L'], rhs = [4, 4,4], mstart = [0, 3, 9], mclind = [x[0],x[1],x[2], x[0],x[1],x[2],x[3],x[4], 5], dmatval = [1,2,3,4,5,6,7,8,-3], names = ['newcon1', 'newcon2']) p.solve () p.write ("amended", "lp") slacks = [] p.calcslacks (solution = mysol, calculatedslacks = slacks) print ("slacks:", slacks) # The five commands below are equivalent to the following: # # p.addcols ([4,4,4,4,4], # [0,3,6,9,12,15], # [c0,4,2,c0,4,2,c0,4,2,c0,4,2,c0,4,2], # [3, -2, 1, -3, 2.4, 1.4, 3, 2, 1, -3, 2.4, 4, 3, 2, 1], # [0,0,0,0,0], # [2,10,1,2,2], # ['p1','p2','p3','p4','p5'], # ['I','C','S','P','R']) p.addcols ([4], [0,3], [c0,4,2], [-3, -2, 1], [0], [2], ['p1'], ['I']) p.addcols ([4], [0,3], [c0,4,2], [-3, 2.4, 1,4], [0], [10], ['p2'], ['C']) p.addcols ([4], [0,3], [c0,4,2], [-3, 2, 1], [0], [1], ['p3'], ['S']) p.addcols ([4], [0,3], [c0,4,2], [-3, 2.4, 4], [0], [2], ['p4'], ['P']) p.addcols ([4], [0,3], [c0,4,2], [-3, 2, 1], [0], [2], ['p5'], ['R']) p.solve () try: print ("new solution:", p.getSolution ()) except: print ("could not get solution, perhaps problem is infeasible")