# Results

## The Optimization Cost vs. Iteration Plot

The plot below shows the decrease in the cost function as the optimizer changes the design to minimize the deviation.
Note: The y-value is plotted on a log scale to show the lower values. The optimizer required 11 iterations.

## Initial Design vs. Optimized Design

The dynamic response of the block has been plotted for both the initial design and the optimized design. There is improvement in the displacement, velocity, and acceleration.

## The Optimization Summary Log File

OPTIMIZATION HISTORY FILE
Version 0.1

************************************************************************
**  COPYRIGHT (C) 2004-2016                 Altair Engineering, Inc.  **
** Contains trade secrets of Altair Engineering, Inc.                 **
** Decompilation or disassembly of this software strictly prohibited. **
************************************************************************

Date             : 14/03/2017
Time             : 17:09:18
Python Version   : 2.7.12 |Anaconda 4.2.0 (64-bit)| (default, Jun 29 2016, 11:07:13) [MSC v.1500 64 bit (AMD64)]

Input File       : c:\work\simulate function\pid.py
Output Directory : c:\work\simulate function\Two_Spring_with_force_170918
Summary File     : c:\work\simulate function\Two_Spring_with_force_170918\summary.log
Design Log File  : c:\work\simulate function\Two_Spring_with_force_170918\design.log

Optimizer Settings
------------------
Algorithm        : FMIN_SLSQP
Max. # iterations: 50
Accuracy         : 1.000e-03

Simulation Settings
-------------------
Analysis         : Call optimizer.sim_function
DSA              : FD

Iteration #   Cost #    Objective       Mag(Slope)
--------------------------------------------------
1             6      4.1503e+02      1.3738e+04
2            13      4.1491e+01      2.6595e+02
3            24      4.1413e+01      1.8483e+02
4            29      3.8928e+01      2.7961e+02
5            34      1.7751e+01      6.9854e+01
6            39      2.0843e+01      1.0056e+02
7            49      2.0729e+01      1.8075e+02
8            64      2.0828e+01      2.4888e+01
9            79      2.0905e+01      2.2152e+02
10            84      2.2928e+01      2.0147e+02
11            89      2.3012e+01      7.2257e+01

Results from Optimization
-------------------------
Initial Cost   = 415.030
Final Cost     = 23.012
Cost reduction = 94.455

Individual Responses
--------------------
Weight = 1.00 Final cost of objective acceleration = 0.77
Weight = 1.00 Final cost of objective velocity = 2.32
Weight = 1.00 Final cost of objective displacement = 19.92

Final Design Table
------------------

DV                Lower Bound        Upper Bound        Initial Value      Optimized Value
------------------------------------------------------------------------------------------
DV0               +0.0000e+00        +1.0000e+00        +0.0000e+00        +1.5952e-01
DV1               +0.0000e+00        +1.0000e+00        +5.0000e-01        +8.7677e-01
DV2               +0.0000e+00        +1.0000e+00        +0.0000e+00        +4.5369e-01

Elapsed Time for job                       = 261.13 seconds
Time in Cost function                    = 130.75 seconds
Time in Sensitivity function             = 124.84 seconds

Optimization process completed.

## The Design Summary Log File

Design History
Input File      : c:\work\simulate function\pid.py
Output Directory: c:\work\simulate function\Two_Spring_with_force_170918

Iteration #   Design
--------------------------------------------------------------------------------

1          [0.0, 0.5, 0.0]
2          [0.27699, 0.63833, 2.3762e-05]
3          [0.27832, 0.63779, 2.3718e-05]
4          [0.2731, 0.6548, 3.3886e-12]
5          [0.076768, 1.0, 0.64752]
6          [0.13338, 0.91154, 0.44929]
7          [0.13338, 0.9115, 0.44932]
8          [0.13338, 0.9115, 0.44932]
9          [0.13338, 0.9115, 0.44932]
10          [0.15857, 0.87803, 0.45354]
11          [0.15952, 0.87677, 0.45369]