optimization_setup

• type: setup command.
• function: define overall optimization parameters and methods.

&optimization_setup
    STRING equation = NULL;
    STRING mode = "minimize";
    STRING method = "simplex";
    double tolerance = -0.01;
    double target = 0;
    long soft_failure = 1;
    long n_passes = 2;
    long n_evaluations = 500; 
    long n_restarts = 0;
    long matrix_order = 1;
    STRING log_file = NULL;
    long output_sparsing_factor = 0;
    long balance_terms = 0;
    double restart_worst_term_factor = 1;
    long restart_worst_terms = 1;
    long verbose = 1;
    long balance_terms = 0;
    double simplex_divisor = 3;
    double simplex_pass_range_factor = 1;
    long include_simplex_1d_scans = 1;
    long start_from_simplex_vertex1 = 0;
    long restart_random_numbers = 0;
&end

• equation -- An rpn equation for the optimization function, expressed in terms of any parameters of any optimization variables and the ``final'' parameters of the beam (as recorded in the final output file available in the run_setup namelist). The optimization variables or covariables may appear in the equation in the form <element-name>.<parameter-name>, all in capital letters. In addition, initial values of variables and covariables are available in the form <element-name>.<parameter-name>0.

  Data from MARK elements with FITPOINT=1 may be used via symbols of the form <element-name>#<occurrence-number>.<parameter-name>, where <parameter-name> can be a Twiss parameter name (if the twiss command was given), a floor coordinate name (if the floor command was given, a beam-size or centroid name, a sigma-matrix element, or a closed orbit value (xco, xpco, etc) if closed orbit calculations are requested. The parameter names are the same as those used in the corresponding output files. Beam sizes, centroids, and sigma-matrix elements are from tracking the particle distribution. See the documentation for the MARK element for a more detailed listing.

  If closed orbit calculations are requested, data from MONI, HMON, and VMON elements that have CO_FITPOINT=1 is available under the names bpmName#occurence.qco, where q is x, xp, y, or yp.

  If response matrix calculation is requested, response matrix values are available in variables with names PlaneR_bpmName#occurence_corrName#occurence.corrParam, where Plane is H (horizontal) or V (vertical) and corrParam is the parameter of the corrector used for changing the orbit (e.g., HKICK or VKICK for a KICKER element).

  If the twiss command was given with output_at_each_step=1, one may also refer to statistics of Twiss parameters in the form <statistic>.<parameter-name>, where <statistic> is either min or max. One may also use the symbols nux, dnux/dp, (and corresponding symbols for y), alphac, and alphac2. These are the tune, chromaticity, and first- and second- order momentum compaction factors. The final values of the Twiss parameters are referred to simply as betax, etax, etc.

  If the twiss command was given with output_at_each_step=1 and radiation integral computation was requested, one may use ex0 and Sdelta0 for the equilibrium emittance and momentum spread, plus J<plane> and tau<plane> for the damping partition and damping time, where <plane> is x, y, or delta.

  The coupling integral and emittance ratio due to x-y coupling may be accessed using the symbols couplingIntegral and emittanceRatio. See section 3.1.4.4 of [18].

  If the coupled_twiss_output command was given with output_at_each_step=1, one may use symbols of the form <name>#<occurrence>.<property> where <name> is the name of any MARKER element with FITPOINT=1. <property> may be one of betax1, betax2, betay1, betay2, cetax, cetay, and tilt (these are the two beta functions for x and y, the coupled dispersion values for x and y, and the beam tilt).

  If the floor_coordinates command was given, one may use X, Z, and theta to refer to the final values of the floor coordinates.

  If the sasefel command was given, one may use variables of the form SASE.<property>, where <property> is one of gainLength, saturationLength, saturationPower, or lightWavelength.

  Finally, one may use any of the names from the ``final'' output file (see run_setup), e.g., Sx (x beamsize) or eny (y normalized emittance). These refer to tracked properties of the beam.

  The equation may be left blank, in which case the user must give one or more optimization_term commands. These use the same symbols, of course.

  There are several rpn functions that are useful in constructing a good optimization equation. These are ``soft-edge'' greater-than, less-than, and not-equal functions, which have the names segt, selt, and sene, respectively. The usage is as follows:

  • V1 V2 T segt. Returns a nonzero value if and only if value V1 is greater than V2. The returned value is $((V_1-V_2)/T)^2$. Typically used to constraint a quantity from above. E.g., to limit the maximum horizontal beta function to 10m with a tolerance of $T=0.1m$, one would use max.betax 10 .1 segt.
  • V1 V2 T selt. Returns a nonzero value if and only if value V1 is less than value V2. The returned value is $((V_1-V_2)/T)^2$. Typically used to constrain a value from below. E.g., to limit a beta function to greater than 3 m with a tolerance of 0.1 m, one would use betax 3 .1 selt.
  • V1 V2 T sene. Returns a nonzero value if and only if V1 and V2 differ by more than tol. If $V_1>V_2$, returns $((V_1-(V_2+T))/T)^2$. If $V_2>V_1$, returns $((V_2-(V_1+T))/T)^2$.
• mode -- May be either ``minimize'' or ``maximize''.

• method -- May be one of ``simplex'', ``grid'', ``powell'', ``randomwalk'', ``randomsample'', or ``sample''. Recommended methods are ``simplex'' and ``randomwalk''. The latter is very useful when the lattice is unstable or nearly so.

• tolerance -- The convergence criterion for the optimization, with a negative value indicating a fractional criterion.
• target -- The value which, if reached, results in immediate termination of the optimization, whether it has converged or not.
• soft_failure -- A flag indicating, if set, that failure of an optimization pass should not result in termination of the optimization.

• n_evaluations -- The number of allowed evaluations of the optimization function. If simplex optimization is used, this is the number of allowed evaluations per pass.

• n_passes -- The number of optimization passes made to achieve convergence (``simplex'' only). A pass ends (roughly) when the number of evaluations is completed or the function doesn't change within the tolerance. A new pass involves starting the optimization again using step sizes determined from the range of the simplex and the factor simplex_pass_factor.

• n_restarts -- The number of complete restarts of the optimization (simplex only). This is an additional loop around the n_passes loop. The difference is that a restart involves using the optimized result but the original step sizes. It is highly recommended that this feature be used if convergence problems are seen.

• restart_worst_term_factor, restart_worst_terms -- Often when there are convergence problems, it is because a few terms are causing difficulty. Convergence can often be obtained by increasing the weighting of these terms. If restart_worst_term_factor is positive, then elegant will multiply the weight of the restart_worst_terms largest terms by this factor at the beginning of a restart.

• matrix_order -- Specifies the highest order of matrix elements that should be available for fitting. Elements up to third order are available for the terminal point of the beamline, and up to secod order for interior fit points. Names for first-, second-, and third-order elements are of the form Rij, Tijk, and Uijkl.
• log_file -- A file to which progress reports will be written as optimization proceeds. For SDDS data, use the final output file from the run_setup namelist.

• output_sparsing_factor -- If set to a value larger than 0, results in sparsing of output to the ``final'' file (see run_setup). This can make a significant difference in the optimization speed.

• balance_terms -- If nonzero, then all terms of the optimization expression have their weights adjusted so they make equal contributions to the penalty function. This can help prevent optimization of a single term at the expense of others. It is performed only for the initial value of the optimization function.

• simplex_divisor -- The factor by which simplex step sizes are changed as the optimization algorithm searches for a valid initial simplex.

• simplex_pass_range_factor -- When starting a new pass, the simplex optimizer takes the range over the previous simplex of each variable times this factor as the starting step size for that variable. This can be useful if the optimization brings the system close to an instability. In such a case, the simplex routine may have trouble constructing an initial simplex if the range of the variables is large. Setting this control to a value less than 1 may help.

• include_simplex_1d_scans -- If nonzero, optimizer performs single-variable scans prior to starting simplex optimization. This is usually a good idea, but in some cases it will cause problems. For example, if your design is on the edge of being unstable, you may get some many errors from the initial steps that the single-variable optimizer can't continue. Disabling the single-variable scans will sometimes solve this.

• start_from_simplex_vertex1 -- If nonzero, optimizer uses the initial simplex vertex as the starting point for each new 1d scan. Otherwise, it uses the result of the previous scan.

• restart_random_numbers -- If nonzero, the random number generators used by elegant are reset for each evaluation of the optimization function. This is valuable if one is optimizing tracking results that involve random processes (e.g., ISR or scattering).