From 82a201e78b1d20250a6dfc715bff137031410e72 Mon Sep 17 00:00:00 2001
From: Evgeniy L <eli@mirantis.com>
Date: Tue, 2 Feb 2016 16:45:20 +0300
Subject: [PATCH] Add prototype of automatic allocation of raid like volumes

The prototype shows how allocation algorithm can be implemented,
using MIP (mixed integer programming), replication factor may be
specified as a range, also user can specify size of each space
on disk, all spaces for raids must be equal.
---
 lab_mip.py | 54 +++++++++++++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 49 insertions(+), 5 deletions(-)

diff --git a/lab_mip.py b/lab_mip.py
index 32ff880..787d11a 100644
--- a/lab_mip.py
+++ b/lab_mip.py
@@ -18,6 +18,7 @@ import sys
 
 x = []
 y = []
+z = []
 
 thismodule = sys.modules[__name__]
 
@@ -33,6 +34,12 @@ for i in range(6):
     setattr(thismodule, name, var)
     y.append(var)
 
+for i in range(6 / 2):
+    name = 'z{0}'.format(i + 1)
+    var = LpVariable(name, 0, 1, 'Binary')
+    setattr(thismodule, name, var)
+    z.append(var)
+
 
 # defines the problem
 prob = LpProblem("problem", LpMaximize)
@@ -40,7 +47,6 @@ prob = LpProblem("problem", LpMaximize)
 # defines the objective function to maximize
 prob += x1 + x2 + x3 + x4 + x5 + x6, 'Sum of spaces'
 
-
 # defines the constraints
 prob += x1 + x2 <= 100, 'First disk'
 prob += x3 + x4 <= 100, 'Second disk'
@@ -48,10 +54,43 @@ prob += x5 + x6 <= 100, 'Third disk'
 
 prob += y1 + y3 + y5 == 2, 'Replication factor'
 
-prob += x1 + x3 + x5 >= 20, 'First min size'
-prob += x2 + x4 + x6 >= 101, 'Second min size'
+prob += x2 + x4 + x6 >= 10, 'Second min size'
 
-prob += x1 - x5 == 0, 'Sizes equality for raid'
+# Specify min and max sizes for RAIDs using allocation size
+# of each space, not sum of all spaces
+prob += x1 >= y1 * 10
+prob += x1 <= y1 * 30
+
+prob += x3 >= y3 * 10
+prob += x3 <= y3 * 30
+
+prob += x5 >= y5 * 10
+prob += x5 <= y5 * 30
+
+# z1, z2 and z3 are going to store info about available pairs
+prob += z1 >= y1 + y3 - 1
+prob += z1 <= y1
+prob += z1 <= y3
+
+prob += z2 >= y1 + y5 - 1
+prob += z2 <= y1
+prob += z2 <= y5
+
+prob += z3 >= y3 + y5 - 1
+prob += z3 <= y3
+prob += z3 <= y5
+
+# Make sizes equal if they are set
+M = 10000000
+
+prob += x1 - x3 + M * z1 <= M
+prob += -x1 + x3 + M * z1 <= M
+
+prob += x1 - x5 + M * z2 <= M
+prob += -x1 + x5 + M * z2 <= M
+
+prob += x3 - x5 + M * z3 <= M
+prob += -x3 + x5 + M * z3 <= M
 
 # Convert from Float to Integer
 for i, x_ in enumerate(x):
@@ -66,11 +105,16 @@ status = prob.solve(GLPK(msg=1))
 def print_vector(vector, prefix, n=2):
 
     for i, v in enumerate(vector):
-        sys.stdout.write('{0}_{1} = {2}'.format(prefix, i + 1, value(v)))
+        sys.stdout.write('{0}{1} = {2}'.format(prefix, i + 1, value(v)))
         if (i + 1) % n:
             sys.stdout.write('\t')
         else:
             sys.stdout.write('\n')
 
+print
 print_vector(x, 'x')
+print
 print_vector(y, 'y')
+print
+print_vector(z, 'z', n=3)
+print