Interface between CONDOR and XFLOS / Pre-Solve phase

We want to optimize optimizes a non-linear function

$$y= \mbox{$\cal F$} (x), \; x \in \Re^n \; y \in \Re \ \begin{cases} b_l \leq x \leq b_u, \; & b_l,b_u \in \Re^n \\ A... ...Re^{m \times n}, b \in \Re^m \\ c_i(x) \geq 0, \; & i=1,\ldots,l \end{cases}$$ (11.1)

For the Method project, the objective function $\mbox{$\cal F$}$$(x)$ is an external code (an executable program): XFLOS. I developed a simple interface between CONDOR and XFLOS. This interface is configured via a configuration text file: ``optim.cfg''. I will now describe the content of ``optim.cfg''.

• Parameter 1:
  The filename of the executable that must be launched to run XFLOS.
• Parameters 2 & 3:
  The information exchange between CONDOR and XFLOS is based on files written on the hard drive. There are two files: The first one is a file written by CONDOR to tell XFLOS what's the current point we want to evaluate. The second one is written by XFLOS and is the result of the evaluation. Parameters 2 & 3 are the name of these files.
• Parameters 4:
  Dimension of the search space (31)
• Parameters 5,6 & 7:
  The result of a run of XFLOS is a vector of 20 values which must be aggregated into one single value which is the value of the objective function at the current point. The aggregation is based on Parameters 5,6 & 7.
• Parameter 8:
  In the industry, there are two kinds of impellers:
  • 2D impellers
  • 3D impellers
  The 2D impellers are simpler to manufacture and are thus cheaper. The set of parameters describing a 2D impeller is a subset (9 parameters) of the 31 parameters needed to describe a 3D impeller. When optimizing a 2D impeller we must fix 22 parameters and only optimize 9 parameters. Config-file-Parameter 8 sets the variables to optimize (=active variable) and those which must be fixed. Let's define $\mbox{$\cal J$}$, the set of active variables.
  Warning ! If you want, for example, to optimize $n+m$ variables, never do the following:
  • Activate the first $n$ variables, let the other $m$ variables fixed, and run CONDOR (Choose as starting point the best point known so far)
  • Activate the second set of $m$ variables, let the first set of $n$ variables fixed, and run CONDOR (Choose as starting point the best point known so far).
  • If the stopping criteria is met then stop, otherwise go back to step 1.
  This algorithm is really bad. It will results in a very slow linear speed of convergence as illustrated in Figure 11.4. The config-file-parameter 8 allows you to activate/deactivate some variables, it's sometime a useful tool but don't abuse from it! Use with care!

  Figure 11.4: Illustration of the slow linear convergence when performing consecutive optimization runs with some variables deactivated.

  

• Parameter 9:
  Starting point $x_{start}$.
• Parameter 10:
  If some runs of XFLOS have already been computed and saved on the hard drive, it's possible to tell CONDOR to use the old evaluations (warm start). If a warm start is performed, the evaluations needed to build the first quadratic will be lowered. Beside, it may be interesting to use as starting point the best point known so far, instead of value specified at parameter 9. Parameter 10 tells to CONDOR which alternative it must use for the choice of the starting point.
• Parameter 11:
  Lower bound on $x$: $b_l$
• Parameter 12:
  Upper bound on $x$: $b_u$
• Parameter 13:
  Number $m$ of linear inequalities $A x \geq b \;\; A \in \Re^{m \times n}, b \in \Re^m$ for constrained optimization.
• Parameter 14:
  The linear inequalities are described here. Each line represents a constraint. On each line, you will find: $A_{ij} \;\; (j=1,\ldots,n)$ and $b_i$. Using parameter 7, we can let some variables fixed. In this case, some linear constraints may:
  • be simply removed:
    $A_{ij}=0 \;\; \;\; \;\; j \in$   $\mbox{$\cal J$}$$\;\; \;\;$ ($A_{ij}$ is zero for all the active variables)
    ( $\mbox{$\cal J$}$ is defined using config-file-parameter 8).
  • be removed and replaced by a tighter bound on the variable $x_k$ ( $k \in$   $\mbox{$\cal J$}$)
    $A_{ij}=0 \;\; \;\; \;\; j=$$\mbox{$\cal J$}$$\backslash \{ k \}\;\;$ and $\;\; A_{ik} \neq 0$.
    The $k^{th}$ component of $b_l$ or $b_u$ will maybe be updated.
  This simple elimination of some linear constraints is implemented inside CONDOR. It is called in the literature the ``pre-solve phase''.
• Parameter 15:
  The normalization factor for each variables (see Section 12.3 about normalization).
• Parameter 16:
  The stopping criteria: $\rho_{end}$. This criteria is tested inside the normalized space.
• Parameter 17:
  We consider that the evaluation of the objective function inside XFLOS has failed when the result of this evaluation is greater than parameter 17. It means that a ``virtual constraint'' has been encountered. See Section 12.2.2 for more information.
• Parameter 18:
  In the method project, some constraints are non-linear and have been hard-coded inside the class ``METHODObjectiveFunction''. Parameter 18 activates/deactivates these non-linear constraints.
• Parameter 19:
  This parameter is the name of the file which contains all the evaluations of the objective function already performed. This file can be used to warm start (see parameter 10).
• Parameter 20:
  When XFLOS is running, CONDOR is waiting. CONDOR regularly checks the hard drive to see if the result file of XFLOS has appeared. Parameter 20 defines the time interval between two successive checks.

Here is a simple example of a ``server configuration file'':

; number of CPU's (not used currently)
;1

; IP's (not used currently)
;127.0.0.1

; blackbox objective function
;/home/andromeda_2/fld_user/METHOD/TD21/splitter
/home/fvandenb/L6/splitter
;testoptim

; objective function: input file:
/home/fvandenb/L6/000/optim.out

; objective function: output file:
/home/fvandenb/L6/000/xflos.out

; number of input variables (x vector) for the objective function
31

; The objective function is ofunction= sum_over_i ( w_i * ( O_i - C_i)^(e_i) )
; of many variables. The weights (w_i) are:
; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19     20
  0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  20  0 -1     20

; C_i are:
; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17       18 19     20
  0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0.0956  0  0  0.521

; e_i are:
; 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19     20
  2 2 2 2 2 2 2 2 2  2  2  2  2  2  2  2  2  2  2      2

; optimization of only a part of the variables:
;dz zh1 rh2 zs1 rs2 sleh sles sh1 sh2 th1 th3 ss1 ss2 ts0 ts1 ts3 tkh tks b0 b2 r2  r0 delt bet2 str coel dle el11 el12 el21 el22
; 1  2   3   4   5   6    7   8   9   10  11  12  13  14  15  16  17  18  19 20 21  22   23  24   25  26   27   28   29   30   31
  0  1   1   1   1   0    0   1   1   1   1   1   1   1   1   1   1   1   0  0   0   0    1   1   1    1   1    1    1    1    1

; a priori estimated x (starting point)-
;     1     2     3     4     5     6   7   8      9       10  11  12   13     14       15    16    17      18     19    20
;   21   22       23       24    25   26    27    28    29    30   31
;    dz   zh1   rh2   zs1   rs2   sleh  sles   sh1 sh2    th1      th3 ss1 ss2  ts0    ts1      ts3   tkh   tks      b0     b2    r2
;   r0  delt     bet2      str coel  dle   el11   el12   el21   el22
0.1068 0.0010 0.055555 0.0801 0.2245 0.0096 0.000 0.3 0.37 -0.974 -1.117010721 0.297361 0.693842 -0.301069296  -0.8 -1.117010721  0.004 0.0051 0.07647 0.035 0.225 0.07223 0.0 -0.99398 0.00 4.998956  0.000  0.000  0.000  0.000  0.0000

; use previous line as starting point:
; - 1: yes
; - 0: no, use best point found in database.
1

; lower bounds for x
; 1   2   3   4   5   6   7   8   9   10   11  12   13   14   15   16   17   18  19  20  21   22    23   24   25   26   27   28   29   30   31
;dz zh1 rh2 zs1 rs2 sleh sles sh1 sh2  th1  th3 ss1 ss2  ts0  ts1  ts3  tkh   tks  b0  b2  r2  r0 delt  bet2  str coel  dle el11 el12 el21 el22
  0   0   0   0   0   0   0   0   0 -1.7 -1.7   0  0  -1.7 -1.7 -1.7 .002  .002   0   0   0 .05    0  -1.0  -.5  0.1 -0.05    0    0    0    0

; upper bounds for x
; 1   2   3   4   5   6   7   8   9   10   11  12   13   14   15   16   17   18  19  20  21   22    23   24   25   26   27   28   29   30   31
;dz zh1 rh2 zs1 rs2 sleh sles sh1 sh2  th1  th3 ss1 ss2  ts0  ts1  ts3  tkh   tks  b0  b2  r2  r0 delt  bet2  str coel  dle el11 el12 el21 el22
  1   1   2   1   2   1   1   1   1  1.7  1.7   1  1   1.7  1.7  1.7  .05   .05   2   1   2   1    2  -0.4   .5  10   0.05  0.02  0.02  0.02  0.02

; number of inequalities
15
;0

; here would be the matrix for inequalities definition if they were needed
; 1   2   3   4   5   6   7    8   9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24   25    26   27   28   29   30   31
;dz zh1 rh2 zs1 rs2 sleh sles sh1 sh2 th1 th3 ss1 ss2 ts0 ts1 ts3 tkh tks  b0  b2  r2  r0 delt bet2 str coel  dle el11 el12 el21 el22  RHS
 -1   0   0   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   0   1   0   0   0   0   1    0     0    0    0    0    0    0
  0   0   1   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   0   0  -1   0   1   0   0    0     0    0    0    0    0    0
  0   0   0   0  -1   0   0    0   0   0   0   0   0   0   0   0   0   0   1   0   0   1   0   0   0    0     0    0    0    0    0    0
  0   0   0   0   1   0   0    0   0   0   0   0   0   0   0   0   0   0   0   0  -1   0   1   0   0    0     0    0    0    0    0    0
  0   0   0   0   0   1   0    0   0   0   0   0   0   0   0   0   0   0   0   0  -1   0   0   0   0    0     0    0    0    0    0    0
  0   0   0   0   0   0   1    0   0   0   0   0   0   0   0   0   0   0   0   0  -1   0   0   0   0    0     0    0    0    0    0    0
  0   0   0   0   0   0   0    1  -1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0    0     0    0    0    0    0    0
  0   0   0   0   0   0   0    0   0   0   0   1  -1   0   0   0   0   0   0   0   0   0   0   0   0    0     0    0    0    0    0    0
  0   0   0   0   0   0   0    0   0   0   1   0   0   0   0  -1   0   0   0   0   0   0   0   0   0    0     0    0    0    0    0  .35
  0   0   0   0   0   0   0    0   0   0  -1   0   0   0   0   1   0   0   0   0   0   0   0   0   0    0     0    0    0    0    0  .35
  0   0   0   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   1   0  -1   1   1   0   0    0     0    0    0    0    0    0
  0   0   0   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   0  -1   0   0   0   0   0    0     0    1    0    0    0    0
  0   0   0   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   0  -1   0   0   0   0   0    0     0    0    1    0    0    0
  0   0   0   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   0  -1   0   0   0   0   0    0     0    0    0    1    0    0
  0   0   0   0   0   0   0    0   0   0   0   0   0   0   0   0   0   0   0  -1   0   0   0   0   0    0     0    0    0    0    1    0

; scaling factor for the normalization of the variables.
; 1     2    3    4    5    6    7    8    9   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25   26   27   28   29   30   31
; dz  zh1  rh2  zs1  rs2 sleh sles  sh1  sh2  th1  th3  ss1  ss2  ts0  ts1  ts3  tkh  tks   b0   b2   r2   r0 delt bet2  str coel  dle el11 el12 el21 el22
1e-3 1e-3 1e-3 1e-3 1e-3 1e-3 1e-3 1e-2 1e-2 1e-2 1e-2 1e-2 1e-2 1e-2 1e-2 1e-2 5e-4 5e-4 1e-3 1e-3 1e-3 1e-3 1e-3 1e-2 1e-3 1e-2 1e-3 1e-3 1e-3 1e-3 1e-3


; stopping criteria \rho_end=
1e-4
;1e-8

; bad value of the objective function
3

; Nuovo Pignone non-linear constaints hard coded into code must be
; - activated : 1
; - desactivated: 0
;1
1

; the data are inside a file called:
;/home/andromeda_2/fld_user/METHOD/TD21/data.ll
/home/fvandenb/L6/dataNEW.ll

; when waiting for the result of the evaluation of the objective
; function, we check every xxx seconds for an arrival of the file
; containing the results
3

Config file on client node

When running CONDOR inside a cluster of computers (to do parallel optimization), the user must start on each client-node the CONDOR-client-software. This software is performing the following:

1. Wait to receive from the server a sampling site (a point) (using nearly no CPU time).
2. Evaluate the objective function at this site and return immediately the result to the server. Go to step 1.

Each client node will use a different ``client configuration file''. These files contain simply the parameters 1 to 7 of the ''server configuration file'' (described in Section 11.4). The IP addresses and the port numbers of the client nodes are currently still hard coded inside the code (at the beginning of file ``parallel.cpp'').