# Example for the use of the Python language (Burglar problem). # # Formulation of logical constraints. # # (C) 2018-2025 Fair Isaac Corporation import xpress as xp Items = set(["camera", "necklace", "vase", "picture", "tv", "video", "chest", "brick"]) # Index set for items. WTMAX = 102 # Max weight allowed for haul. VALUE = {"camera": 15, "necklace": 100, "vase": 90, "picture": 60, "tv": 40, "video": 15, "chest": 10, "brick": 1} WEIGHT = {"camera": 2, "necklace": 20, "vase": 20, "picture": 30, "tv": 40, "video": 30, "chest": 60, "brick": 10} p = xp.problem() x = p.addVariables(Items, vartype=xp.binary) # 1 if we take item i; 0 otherwise. # Objective: maximize total value. p.setObjective(xp.Sum(VALUE[i]*x[i] for i in Items), sense=xp.maximize) # Weight restriction. p.addConstraint(xp.Sum(WEIGHT[i]*x[i] for i in Items) <= WTMAX) # *** Logic constraint: # *** Either take "vase" and "picture" or "tv" and "video" # (but not both pairs). # * Values within each pair are the same. p.addConstraint(x["vase"] == x["picture"]) p.addConstraint(x["tv"] == x["video"]) # * Choose exactly one pair (uncomment one of the 3 formulations A, B, or C). # (A) MIP formulation. # p.addConstraint(x["tv"] == 1 - x["vase"]) # (B) Logic constraint. # Note: Xpress Python interface doesn't use xor. # Need to introduce extra variable. y = p.addVariable(vartype=xp.binary) # (C) Alternative logic formulation. p.addIndicator(y == 1, x["tv"] + x["video"] >= 2) p.addIndicator(y == 0, x["vase"] + x["picture"] >= 2) p.addConstraint(x["tv"] + x["video"] + x["vase"] + x["picture"] <= 3) p.optimize() # Solve the MIP-problem. # Print out the solution. print("Solution:\n Objective: ", p.attributes.objval) xsol = p.getSolution(x) for i in Items: print(" x(", i, "): ", xsol[i])