Adaptive Response Surface Method (ARSM)

The adaptive response surface method (ARSM) works by internally building response surfaces and adaptively updating them as new evaluations become available.

The first response surface it builds is a linear regression polynomial, then it finds the optimum on this surface and validates it with the exact simulation. If the response values from the response surface and the exact simulation are not close; ARSM updates the surface with the new evaluation and finds the optimum in this updated surface. ARSM repeats this loop until it meets one of the convergence criteria.

Error treatment and termination

The ARSM terminates when one of the following conditions is met:
  • One of the convergence criteria is satisfied.
  • The maximum number of allowable analyses is reached.

The text log of the ARSM method

Section 1: General information regarding the optimisation setup.
================  L O G - FILE - OPTFEKO  ================

Version: 14.0.430-24 of 2016-08-22
Date: 2016-08-30 11:34:29
File: dipole_arsm


================= Optimisation variables =================

No.  Name                                  Beg.value          Minimum          Maximum
  1 h                                2.000000000e+00  1.600000000e+00  2.400000000e+00
  2 radius                           2.000000000e-03  5.000000000e-04  5.000000000e-03

=================== Optimisation goals ===================

No.  Name                            Expression
  1 arsm.goals.impedance_mag73ohm   mag(inputimp(impedance(source)))
Section 2: Information regarding the ARSM parameters.
=== Optimisation method: ADAPTIVE RESPONSE SURFACE METHOD (HyperOpt) ===

On failed analysis:             Ignore failed analysis (=1)
Initial linear move:            By DV initial (=1)
Maximum iterations:             22
Response surface:               SORS (=0)
Number of sample points:        3
ARSM solver:                    SQP (=1)
Use SVD:                        No; terminate at soft convergence (=0)
ARSM algorithm version:         A; normal (=0)
Absolute convergence:            1.0000000000e-04
Constraint screening (%):        5.0000000000e+01
Constraint violation tol. (%):   2.5000000000e-01
Design variable convergence:     1.0000000000e-03
Initial DV perturbation:         1.1000000000e+00
Move limit fraction:             1.5000000000e-01
Relative convergence (%):        5.0000000000e-01
Minimal move factor:             1.0000000000e-01
Constraint threshold             1.0000000000e-04
Section 3: Information regarding the parameter values and goal values at each step.
=========== ADAPTIVE RESPONSE SURFACE METHOD (HyperOpt): Intermediate results ===========

 No.    h                radius           arsm.goals.impe  Global goal      Global best aim 
     1  2.000000000e+00  2.000000000e-03  8.223708649e+01  9.237086490e+00  9.237086490e+00
     2  2.330000000e+00  2.000000000e-03  2.584129574e+02  1.854129574e+02                 
     3  2.000000000e+00  2.495000000e-03  8.276434015e+01  9.764340145e+00                 
     4  1.700000000e+00  1.550000000e-03  1.362858864e+02  6.328588642e+01                 
     5  1.930006139e+00  1.550000000e-03  6.806363939e+01  4.936360614e+00  4.936360614e+00
     6  1.927744177e+00  2.000000000e-03  6.805981842e+01  4.940181579e+00                 
     7  1.931082122e+00  1.788235587e-03  6.821262088e+01  4.787379122e+00  4.787379122e+00
     8  1.931204660e+00  1.791996361e-03  6.822294926e+01  4.777050742e+00  4.777050742e+00
     9  1.931283820e+00  1.793912982e-03  6.822946010e+01  4.770539896e+00  4.770539896e+00
Section 4: Information regarding the termination reason and best results found on the search grid.
================= ADAPTIVE RESPONSE SURFACE METHOD (HyperOpt): Finished =================

Optimisation finished (ARSM optimizer achieved convergence. Relative change in objective function over 
two last iterations is smaller than 0.500E-02 and max. constraint violation is below permitted level.)

Optimum found for these parameters:
  h                              =   1.931283820e+00
  radius                         =   1.793912982e-03

Optimum aim function value (at no. 9):   4.770539896e+00
No. of the last analysis: 9