- type: setup command.
- function: define overall optimization parameters and methods.
- sequence: must precede beam definition (bunched_beam or sdds_beam)
- Command syntax, including use of equations and subcommands, is discussed in 7.2.

&optimization_setup

STRING equation = NULL;

STRING mode = "minimize";

STRING method = "simplex";

double tolerance = -0.01;

double target = 0;

long center_on_orbit = 0;

long center_momentum_also = 1;

long soft_failure = 1;

long n_passes = 2;

long n_evaluations = 500;

long n_restarts = 0;

double restart_reset_threshold = 0;

double restart_worst_term_factor = 1;

long restart_worst_terms = 1;

long matrix_order = 1;

STRING log_file = NULL;

STRING term_log_file = NULL;

long output_sparsing_factor = 0;

long balance_terms = 0;

long verbose = 1;

long balance_terms = 0;

double simplex_divisor = 3;

double simplex_pass_range_factor = 1;

double rcds_step_factor = 0.1;

long include_simplex_1d_scans = 1;

long start_from_simplex_vertex1 = 0;

long restart_random_numbers = 0;

STRING interrupt_file = "%s.interrupt";

double interrupt_file_check_interval = 10;

&end

STRING equation = NULL;

STRING mode = "minimize";

STRING method = "simplex";

double tolerance = -0.01;

double target = 0;

long center_on_orbit = 0;

long center_momentum_also = 1;

long soft_failure = 1;

long n_passes = 2;

long n_evaluations = 500;

long n_restarts = 0;

double restart_reset_threshold = 0;

double restart_worst_term_factor = 1;

long restart_worst_terms = 1;

long matrix_order = 1;

STRING log_file = NULL;

STRING term_log_file = NULL;

long output_sparsing_factor = 0;

long balance_terms = 0;

long verbose = 1;

long balance_terms = 0;

double simplex_divisor = 3;

double simplex_pass_range_factor = 1;

double rcds_step_factor = 0.1;

long include_simplex_1d_scans = 1;

long start_from_simplex_vertex1 = 0;

long restart_random_numbers = 0;

STRING interrupt_file = "%s.interrupt";

double interrupt_file_check_interval = 10;

&end

- equation — An rpn equation for the optimization function, expressed in terms of any
parameters of any optimization variables, the “final” parameters of the beam (as recorded
in the final output file available in the run_setup namelist), and selected quantities from
Twiss parameter, tune shift with amplitude, closed orbit, beam moments, driving terms, and
other computations. 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 and from beam position monitors with CO_FITPOINT=1 may be used via symbols of the form elementName#occurenceNum.parameterName. See the documentation for the MARK, MONI, HMON, and VMON elements for detailed discussion and listing.

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 cross-plane response matrix calculation is requested, response matrix values are available in variables with names BpmPlaneCorrPlaneR_bpmName#occurence_corrName#occurence.corrParam, where BpmPlane and CorrPlane are 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).

Many quantities are made available for optimization if twiss_output command is given with output_at_each_step=1:

- Final Twiss parameters, e.g., betax, alphax, etax. The names are the same as the column names in the twiss output file.
- Linear acceptances Ax and Ay for the horizontal and vertical planes, respectively.
- Statistics of Twiss parameters in the form <statistic>.<parameter-name>, where
<statistic> is min, max, ave, p99, p98, or p96. p99 is the 99
^{th}pencentile value, a similarly for p98 and p96. - Tunes and chromaticities via symbols nux, dnux/dp, (and corresponding symbols for y).
- Chromatic derivatives of beta and alpha functions, via symbols dbetax/dp, dbetay/dp, dalphax/dp, and dalphay/dp.
- First-, second-, and third-order momentum compaction factors via symbols alphac, alphac2, and alphac3, respectively.
- If radiation integral computation is 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. One may also use I1 through I5 for the individual radiation integrals.
- If compute_driving_terms=1, then the quantities h11001, h00111, h20001, h00201, h10002, h21000, h30000, h10110, h10020, h10200, h22000, h11110, h00220, h31000, h40000, h20110, h11200, h20020, h20200, h00310, h00400, dnux/dJx, dnux/dJy, and dnuy/dJy may be used. Table 2 explains the meaning of the terms.
- 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 [19].
- If higher-order chromaticity is requested, then one may use the symbols dnux/dp2, dnux/dp3, dnuy/dp2, dnuy/dp3, etax2 , etax3, etay2 , etay3, nuxChromLower, nuxChromUpper, nuyChromLower, and nuyChromUpper.
- If the tune_shift_with_amplitude command was also given and one may use the symbols dnux/dAx, dnux/dAy, dnuy/dAx, dnuy/dAy, dnux/dAx2, dnux/dAy2, dnux/dAxAy, dnuy/dAx2, dnuy/dAy2, dnuy/dAxAy, nuxTswaLower, nuxTswaUpper, nuyTswaLower, and nuyTswaUpper.
- If HMON, VMON, or MONI elements are in the beamline, the symbol sMaxTransmittedMonitor records the s position of the last monitor that sees at least one particle.

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”, “1dscans”, “rcds”, and “sample”. Recommended methods are “simplex”, “rcds” [62], 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.
- center_on_orbit — A flag indicating whether to center the beam transverse coordinates on the closed orbit before tracking.
- center_momentum_also — A flag indicating whether to center the momentum coordinate also.
- 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_reset_threshold — If positive, then before a restart, the change in each optimization variable relative to the starting value is compared to the difference between the upper and lower limits of the variable. If that ratio is less than the given threshold, the variable’s value is set to the starting value. This can help prune small, spurious changes that have little effect on the outcome.
- 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.
- term_log_file — This names a file to which the values of the optimization terms are written at the completion of optimization, which can be convenient when large numbers of terms are used. For example, by using sddssort one could find which terms are contributing most to the penalty value.
- 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.
- rcds_step_factor — Gives the step sizes as a fraction of the range of each variable. If non-zero, overrides the step sizes given in the optimization_variable commands.
- 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).
- interrupt_file — Gives the name of a file that will be monitored by the program as it runs. If the file is created or modified while optimization is running, the optimizer will complete the present step and cleanly terminate, allowing subsequent commands, if any, to proceed.
- interrupt_file_check_interval — The interval in seconds between checking the interrupt file. N.B.: Depending on the responsiveness of the file system and the time required for a function evaluation, setting this to a small value could have a significant adverse impact on the run time.

parallel_optimization_setup