APOSMM

Asynchronously Parallel Optimization Solver for finding Multiple Minima (APOSMM) coordinates concurrent local optimization runs in order to identify many local minima.

Required: mpmath, SciPy

Optional (see below): petsc4py, nlopt, DFO-LS

Configuring APOSMM

By default, APOSMM will import several optimizers which require external packages. To import only the optimization packages you are using, add the following lines in that calling script, before importing APOSMM:

import libensemble.gen_funcs
libensemble.gen_funcs.rc.aposmm_optimizers = <optimizers>

Where optimizers is a string (or list of strings) from the available options:

'petsc', 'nlopt', 'dfols', 'scipy', 'external'

To see the optimization algorithms supported, see LocalOptInterfacer.

Persistent APOSMM

This module contains methods used our implementation of the Asynchronously Parallel Optimization Solver for finding Multiple Minima (APOSMM) method. https://doi.org/10.1007/s12532-017-0131-4

This implementation of APOSMM was developed by Kaushik Kulkarni and Jeffrey Larson in the summer of 2019.

persistent_aposmm.aposmm(H, persis_info, gen_specs, libE_info)

APOSMM coordinates multiple local optimization runs, starting from points which do not have a better point nearby (within a distance r_k). This generation function uses a local_H (serving a similar purpose as H in libEnsemble) containing the fields:

  • 'x' [n floats]: Parameters being optimized over

  • 'x_on_cube' [n floats]: Parameters scaled to the unit cube

  • 'f' [float]: Objective function being minimized

  • 'local_pt' [bool]: True if point from a local optimization run

  • 'dist_to_unit_bounds' [float]: Distance to domain boundary

  • 'dist_to_better_l' [float]: Dist to closest better local opt point

  • 'dist_to_better_s' [float]: Dist to closest better sample point

  • 'ind_of_better_l' [int]: Index of point 'dist_to_better_l’ away

  • 'ind_of_better_s' [int]: Index of point 'dist_to_better_s’ away

  • 'started_run' [bool]: True if point has started a local opt run

  • 'num_active_runs' [int]: Number of active local runs point is in

  • 'local_min' [float]: True if point has been ruled a local minima

  • 'sim_id' [int]: Row number of entry in history

and optionally

  • 'fvec' [m floats]: All objective components (if performing a least-squares calculation)

  • 'grad' [n floats]: The gradient (if available) of the objective with respect to x.

Note:

  • If any of the above fields are desired after a libEnsemble run, name them in gen_specs['out'].

  • If intitializing APOSMM with past function values, make sure to include 'x', 'x_on_cube', 'f', 'local_pt', etc. in gen_specs['in'] (and, of course, include them in the H0 array given to libensemble).

Necessary quantities in gen_specs['user'] are:

  • 'lb' [n floats]: Lower bound on search domain

  • 'ub' [n floats]: Upper bound on search domain

  • 'localopt_method' [str]: Name of an NLopt, PETSc/TAO, or SciPy method (see ‘advance_local_run’ below for supported methods). When using a SciPy method, must supply 'opt_return_codes', a list of integers that will be used to determine if the x produced by the localopt method should be ruled a local minimum. (For example, SciPy’s COBYLA has a ‘status’ of 1 if at an optimum, but SciPy’s Nelder-Mead and BFGS have a ‘status’ of 0 if at an optimum.)

  • 'initial_sample_size' [int]: Number of uniformly sampled points must be returned (non-nan value) before a local opt run is started. Can be zero if no additional sampling is desired, but if zero there must be past sim_f values given to libEnsemble in H0.

Optional gen_specs['user'] entries are:

  • 'sample_points' [numpy array]: Points to be sampled (original domain). If more sample points are needed by APOSMM during the course of the optimization, points will be drawn uniformly over the domain

  • 'components' [int]: Number of objective components

  • 'dist_to_bound_multiple' [float in (0,1]]: What fraction of the distance to the nearest boundary should the initial step size be in localopt runs

  • 'lhs_divisions' [int]: Number of Latin hypercube sampling partitions (0 or 1 results in uniform sampling)

  • 'mu' [float]: Distance from the boundary that all localopt starting points must satisfy

  • 'nu' [float]: Distance from identified minima that all starting points must satisfy

  • 'rk_const' [float]: Multiplier in front of the r_k value

  • 'max_active_runs' [int]: Bound on number of runs APOSMM is advancing

If the rules in decide_where_to_start_localopt produces more than 'max_active_runs' in some iteration, then existing runs are prioritized.

And gen_specs['user'] must also contain fields for the given localopt_method’s convergence tolerances (e.g., gatol/grtol for PETSC/TAO or ftol_rel for NLopt)

See also

test_persistent_aposmm_scipy for basic APOSMM usage.

See also

test_persistent_aposmm_with_grad for an example where past function values are given to libEnsemble/APOSMM.

persistent_aposmm.decide_where_to_start_localopt(H, n, n_s, rk_const, ld=0, mu=0, nu=0)

APOSMM starts a local optimization runs from a point that:

  • is not in an active local optimization run,

  • is more than mu from the boundary (in the unit-cube domain),

  • is more than nu from identified minima (in the unit-cube domain),

  • does not have a better point within a distance r_k of it.

For further details, see the conditions (S1-S5 and L1-L8) in Table 1 of the APOSMM paper This method first identifies sample points satisfying S2-S5, and then identifies all localopt points that satisfy L1-L7. We then start from any sample point also satisfying S1. We do not check condition L8 currently.

We don’t consider points in the history that have not returned from computation, or that have a nan value. As APOSMM works on the unit cube, note that mu and nu implicitly depend on the scaling of the original domain: adjusting the initial domain can make a run start (or not start) at a point that didn’t (or did) previously.

Parameters
  • H (numpy structured array) – History array storing rows for each point.

  • n (int) – Problem dimension

  • n_s (int) – Number of sample points in H

  • r_k_const (float) – Radius for deciding when to start runs

  • ld (integer) – Number of Latin hypercube sampling divisions (0 or 1 means uniform random sampling over the domain)

  • mu (nonnegative float) – Distance from the boundary that all starting points must satisfy

  • nu (nonnegative float) – Distance from identified minima that all starting points must satisfy

Returns

start_inds – Indices where a local opt run should be started, sorted by increasing function value.

Return type

list

persistent_aposmm.initialize_APOSMM(H, user_specs, libE_info)

Computes common values every time that APOSMM is reinvoked

persistent_aposmm.update_history_dist(H, n)

Updates distances/indices after new points that have been evaluated.

LocalOptInterfacer

This module contains methods for APOSMM to interface with various local optimization routines.

class aposmm_localopt_support.LocalOptInterfacer(user_specs, x0, f0, grad0=None)

This class defines the APOSMM interface to various local optimization routines.

Currently supported routines are

  • NLopt routines [‘LN_SBPLX’, ‘LN_BOBYQA’, ‘LN_COBYLA’, ‘LN_NEWUOA’, ‘LN_NELDERMEAD’, ‘LD_MMA’]

  • PETSc/TAO routines [‘pounders’, ‘blmvm’, ‘nm’]

  • SciPy routines [‘scipy_Nelder-Mead’, ‘scipy_COBYLA’, ‘scipy_BFGS’]

  • DFOLS [‘dfols’]

  • External local optimizer [‘external_localopt’] (which use files to pass/receive x/f values)

close()

Join process and close queue

destroy()

Recursively kill any optimizer processes still running

iterate(data)

Returns an instance of either numpy.ndarray corresponding to the next iterative guess or ConvergedMsg when the solver has completed its run.

Parameters
  • x_on_cube – A numpy array of the point being evaluated (for a handshake)

  • f – A numpy array of the function evaluation.

  • grad – A numpy array of the function’s gradient.

  • fvec – A numpy array of the function’s component values.

aposmm_localopt_support.run_external_localopt(user_specs, comm_queue, x0, f0, child_can_read, parent_can_read)

Runs an external local optimization run starting at x0, governed by the parameters in user_specs.

aposmm_localopt_support.run_local_dfols(user_specs, comm_queue, x0, f0, child_can_read, parent_can_read)

Runs a DFOLS local optimization run starting at x0, governed by the parameters in user_specs.

aposmm_localopt_support.run_local_nlopt(user_specs, comm_queue, x0, f0, child_can_read, parent_can_read)

Runs an NLopt local optimization run starting at x0, governed by the parameters in user_specs.

aposmm_localopt_support.run_local_scipy_opt(user_specs, comm_queue, x0, f0, child_can_read, parent_can_read)

Runs a SciPy local optimization run starting at x0, governed by the parameters in user_specs.

aposmm_localopt_support.run_local_tao(user_specs, comm_queue, x0, f0, child_can_read, parent_can_read)

Runs a PETSc/TAO local optimization run starting at x0, governed by the parameters in user_specs.