Add tips and tricks in Gurobi

_pages/IP.md

@@ -3,7 +3,7 @@ title: "IP"
 permalink: /ip/
 layout: customPostLayout
 date: 2022-03-21 02:00:00
-last_modified_at: 2024-03-31
+last_modified_at: 2024-04-05
 ---
 
 Integer programming (IP) is a powerful tool of solving problems, especially when tackling with combinatorics ones. As far as I know, all problems with finite search spaces can be translated into IP models. Even in the worst case, we can cut off each candidate once at a time until we find a feasible solution or prove the infeasibility of the problem. Besides the various uses in different scenario, IP models can be efficiently solved by [Gurobi Optimizer - the fastest solver](https://www.gurobi.com/).
@@ -26,3 +26,38 @@ As [Bland's rules](https://en.wikipedia.org/wiki/Bland%27s_rule) stated:
 > If the minimum ratio is shared by several rows, choose the row with the lowest-numbered column (variable) basic in it.
 
 In the past, I applied the rules by choosing the row of constraint with the lowest-numbered index. It turns out to be wrong.
+
+## Tips and tricks in Gurobi
+
+```py
+from gurobipy import GRB
+import gurobipy as gp
+import numpy as np
+
+# (1) disable all output messages in Gurobi
+customEnv = gp.Env(empty=True)
+customEnv.setParam('OutputFlag', 0)
+customEnv.start()
+model = gp.Model('modelName', env=customEnv)
+
+vars = model.addMVar(shape=(3, 4), vtype=GRB.BINARY)
+# a b c d
+# e f g h
+# i j k l
+
+# (2) sum by axis: axis=1 means horizontal summation
+# (3) add vector-based constraints
+model.addConstr(vars.sum(axis=1) == np.array([1, 3, 3])) # a+b+c+d=1, e+f+g+h=3, i+j+k+l=3
+
+# (4) extract variables by custom indices
+arrA = np.array([
+    [0, 2],
+    [1, 0],
+    [2, 2],
+])
+model.addConstr(vars[arrA[:,0], arrA[:,1]].sum() == 2) # c+e+k=2
+model.addConstr(vars[arrA[:,0], arrA[:,1]] == np.array([1, 0, 1])) # c=1, e=0, k=1
+
+model.optimize()
+print(vars.x)
+```