pybnb

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A parallel branch-and-bound engine for Python. (https://pybnb.readthedocs.io)

This software is copyright (c) by Gabriel A. Hackebeil (gabe.hackebeil@gmail.com).

This software is released under the MIT software license. This license, including disclaimer, is available in the 'LICENSE' file.

Quick Start

Define a problem:

.. code:: python

simple.py

import pybnb class Simple(pybnb.Problem): def init(self): self.bounds = [0.0,1.0] def sense(self): return pybnb.minimize def objective(self): return round(self.bounds[1] - self.bounds[0], 3) def bound(self): return -(self.bounds[1] - self.bounds[0])**2 def save_state(self, node): node.state = self.bounds def load_state(self, node): self.bounds = node.state def branch(self): L, U = self.bounds mid = 0.5 * (L + U) for l,u in [(L,mid), (mid,U)]: child = pybnb.Node() child.state = (l,u) yield child

Write a solve script:

.. code:: python

solve_simple.py

import simple problem = simple.Simple() results = pybnb.solve(problem, absolute_gap=1e-9)

Run the script:

.. code:: bash

$ mpirun -np 4 python solve_simple.py

Using non-default solver options:

• absolute_gap: 1e-09 (default: 0)

Starting branch & bound solve:

• dispatcher pid: 34902 (Ozymandias.local)
• worker processes: 3

---

       Nodes        |                      Objective Bounds                        |              Work              
    Expl    Unexpl  |      Incumbent           Bound     Rel. Gap         Abs. Gap | Time (s)  Nodes/Sec Imbalance   Idle
       0         1  |            inf            -inf          inf%             inf |      0.0       0.00     0.00%      0

•    1         2  |              1              -1  200.0000000%               2 |      0.0    1226.99   300.00%      1
  

•    2         3  |            0.5              -1  150.0000000%             1.5 |      0.0    2966.04   150.00%      0
  

•    4         5  |           0.25           -0.25   50.0000000%             0.5 |      0.0    8081.95    75.00%      0
  

•    8         9  |          0.125         -0.0625   18.7500000%          0.1875 |      0.0   12566.90    37.50%      0
  Expl    Unexpl  |      Incumbent           Bound     Rel. Gap         Abs. Gap | Time (s)  Nodes/Sec Imbalance   Idle
  

•   16        17  |          0.062       -0.015625    7.7625000%        0.077625 |      0.0   15352.74    18.75%      0
  

•   32        33  |          0.031     -0.00390625    3.4906250%      0.03490625 |      0.0   15981.49    18.75%      0
  

•   64        65  |          0.016   -0.0009765625    1.6976563%    0.0169765625 |      0.0   18740.68    18.75%      0
  

•  128       129  |          0.008   -0.0002441406    0.8244141%  0.008244140625 |      0.0   21573.51    11.72%      0
  

•  256       257  |          0.004   -6.103516e-05    0.4061035%  0.004061035156 |      0.0   22166.96     8.20%      0
  Expl    Unexpl  |      Incumbent           Bound     Rel. Gap         Abs. Gap | Time (s)  Nodes/Sec Imbalance   Idle
  

•  512       513  |          0.002   -1.525879e-05    0.2015259%  0.002015258789 |      0.0   21177.00     5.86%      0
  

• 1024      1025  |          0.001   -3.814697e-06    0.1003815%  0.001003814697 |      0.1   19978.42     9.38%      0
  

• 2048      2049  |              0   -9.536743e-07    0.0000954% 9.536743164e-07 |      0.1   21606.45     5.42%      0
  

  24029 24030 | 0 -1.490116e-08 0.0000015% 1.490116119e-08 | 1.1 21961.03 5.98% 0 46159 46160 | 0 -3.72529e-09 0.0000004% 3.725290298e-09 | 2.1 22120.75 5.73% 0 Expl Unexpl | Incumbent Bound Rel. Gap Abs. Gap | Time (s) Nodes/Sec Imbalance Idle 65537 65538 | 0 -9.313226e-10 0.0000001% 9.313225746e-10 | 3.0 22459.50 6.20% 0

---

Absolute optimality tolerance met Optimal solution found!

solver results:

• solution_status: optimal
• termination_condition: optimality
• objective: 0
• bound: -9.313226e-10
• absolute_gap: 9.313226e-10
• relative_gap: 9.313226e-10
• nodes: 65537
• wall_time: 2.96 s
• best_node: Node(objective=0)

Number of Workers: 3 Load Imbalance: 6.20%

• min: 21355 (proc rank=3)
• max: 22710 (proc rank=1) Average Worker Timing:
• queue: 80.78% [avg time: 109.6 us, count: 65537]
• load_state: 0.44% [avg time: 596.1 ns, count: 65537]
• bound: 0.59% [avg time: 796.1 ns, count: 65537]
• objective: 3.52% [avg time: 4.7 us, count: 65537]
• branch: 3.36% [avg time: 4.6 us, count: 65537]
• other: 11.31% [avg time: 15.3 us, count: 65537]

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