1. Ipopt and Snopt in Strong Nonlinear System Long Trajectory Length Optimization
Huawei Wang
Human Motion & Control Lab
Mechanical Engineering
Cleveland State University
Lab Meeting, July 23, 2018
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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2. Goal:
Find out a suitable optimization platform and solver in strong nonlinear system long trajectory length optimization y Fy
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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3. Optimization problem:y Fy
Optimization problem:
Mathematical model: y g
external force
(m, y, ydot)
elastic force
𝑌 2 = 𝑌 1 𝑚 𝑌 2 =−𝑚𝑔+ 𝐹 𝑒 + 𝐹 𝑘
𝐹 𝑘 = −𝐾 𝑎 ∗𝑦, 𝑦>0 𝐹 𝑘 = − 𝐾 𝑔 𝑦 3 −𝐾 𝑎 ∗𝑦, 𝑦≤0
𝑌= 𝑦, 𝑦 𝑑𝑜𝑡
𝐾 𝑎 =0.1 𝑁 𝑚
𝐾 𝑔 =5𝑒7 𝑁 𝑚 3
which:
𝑚=1 𝑘𝑔
t (s) 1 2 3 4 5 ……
(10, 0)
(-0.02, ~)
(8.2, 0)
(9.4, 0)
(8.3, 0)
(9.7, 0)
ground
Optimization problem:
Minimize external force 𝐹 𝑒 , while go through certain positions in a period of time.
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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4. Optimization setting:y
Boundary:
y :
ydot :
Fe :
[-0.1, 10] m
[-20, 20] m/s
[-100, 100] N g
external force
(m, y, ydot)
elastic force
t (s) 1 2 3 4 5 ……
(10, 0)
(-0.02, ~)
(8.2, 0)
(9.4, 0)
(8.3, 0)
(9.7, 0)
Trajectory length:
T : [20, 40, 60, …] s
(10.3)
Sampling rate:
R : 100 Hz
(5.0, 0)
ground
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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5. Optimization Methods:
Ipopt
Snopt
Interior point optimizer
Quadratic programming
Linear solver:
HSL solvers
MUltifrontal Massively Parallel sparse direct Solver (Mumps)
Parallel Sparse Direct Linear Solver (Pardiso)
Interfaces:
Snopta: friendly to new users
Snoptb: more efficient, but nonlinear objectives and constraints need be define first.
Snoptc: similar to Snoptb
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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6. Optimization results:
MA57, 20 s trajectory length
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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7. Optimization results:
Optimization time cost of each solver at different trajectory length
Trajectory time 20 40 60 80
100
120
140
200
400
600
Problem
Size
var
6,000
12,000
18,000
24,000
30,000
36,000
42,000
60,000
120,000
180,000 NJ
14,000
28,000
56,000
70,000
84,000
98,000
140,000
280,000
420,000
Ipopt (MA57)
0.1h
0.48h
0.43h
0.925h
3.6h F1 --
Ipopt (MA86)
0.37h
0.55h
0.71h 1h
3.57h
8.7h
Ipopt (Mumps)
0.47h
0.19h
0.58h
0.69h
3.42h
Snopt F2
F1: maximum CUP time reached (16.7h)
Time cost of MA86 of different trajectory length
F2: maximum iteration reached (10*var)
: CUP filled with tasks
: only one task in CUP each time
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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8. Optimization results of Ipopt F1:
Ipopt MA57, 140 s trajectory length:
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
7/8

9. Optimization results of Snopt F2:
Snopt, 20 s trajectory length:
Snopt, 2 s trajectory length:
Huawei Wang (HMC)
Ipopt and Snopt in Long Period Strong Nonlinear System Optimization
Lab Meeting 2018
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