Wrapper for the VTMOP genfuncs drivers, for solving multiobjective optimization problems with arbitrary number of objectives.

vtmop.vtmop_gen(H, persis_info, gen_specs, _)

This generator function solves multiobjective optimization problems with d design variables (subject to simple bound constraints) and p objectives using VTMOP.

This generator produces batches of simulation inputs to evaluate, using the Fortran package VTMOP. In order to facilitate an interface between Fortran and Python, wrappers have been generated for a subset of VTMOP’s functionality using fmodpy.

The first time that this generator is called on your machine, the necessary VTMOP libraries will be automatically built using gfortran. If a different compiler is desired, edit lines 16 and 20 of gen_funcs/vtmop_libe/vtmop_libe_python_wrapper.py to specify your compiler and the appropriate compiler flags, respectively.

After the Fortran and C binaries have been built, VTMOP’s Python wrapper will be automatically imported every time the generator is called without need to recompile. Note that this wrapper uses a .so file, which is only supported by Mac and Linux/Unix systems (will not work on Windows).

All inputs and arguments to VTMOP are specified through the gen_specs[‘user’] dictionary.

Required args:

gen_specs[‘user’][‘d’] (int): is the dimension of the design space.

gen_specs[‘user’][‘p’] (int): is the number of objectives.

gen_specs[‘user’][‘lb’] (np.ndarray): is a 1d array of length D,

containing the lower bound constraints on the design variables.

gen_specs[‘user’][‘ub’] (np.ndarray): is a 1d array of length D,

containing the upper bound constraints on the design variables. Note that gen_specs[‘user’][‘ub’] must be elementwise greater than gen_specs[‘user’][‘lb’] (up to the design tolerance, specified below).

gen_specs[‘user’][‘new_run’] (bool): should be True if you are

starting a new run, and False if you would like to reload an old run using the checkpoint file ‘vtmop.chkpt’ in your current working directory.

gen_specs[‘user’][‘isnb’] (int): is the preferred initial search batch

size and is used as the size of the Latin hypercube design in the zeroeth iteration (initial search). ISNB should be much greater than SNB and a multiple of the number of simulation workers. Empirically, a good starting place is gen_specs[‘user’][‘isnb’] ~ 1000. If a large initial database is given, it is possible to set gen_specs[‘user’][‘isnb’] = 0.

gen_specs[‘user’][‘snb’] (int): is the preferred search batch size

for all other search steps and is used as the size of the Latin hypercube design in the search phase. Empirically, a good starting place is gen_specs[‘user’][‘snb’] ~ 2 * d.

gen_specs[‘user’][‘onb’] (int): is the preferred batch size for all

optimization phases. VTMOP will pad out batches of candidates in order to produce a multiple of gen_specs[‘user’][‘onb’] candidates in each iteration. In almost every case, gen_specs[‘user’][‘onb’] should be equal to the number of available simulation workers.

Optional args:

gen_specs[‘user’][‘lopt_budget’] (int): specifies the budget for GPS

optimizer iteration when solving the surrogate problems. The default value is LOPT_BUDGET is 2500 surrogate evaluations.

gen_specs[‘user’][‘decay’] (float): specifies the decay rate for the

local trust region (LTR) radius. This value affects how many times an isolated point can be the center of a LTR before it i discarded. By default, DECAY = 0.5.

gen_specs[‘user’][‘des_tol’] (float): the tolerance for the design

space. A design point that is within DES_TOL of another evaluated design point will not be reevaluated. The default value for DES_TOL is the square-root of the working precision EPS (below). Note that any value that is smaller than the working precsion EPS will be ignored and EPS will be used.

gen_specs[‘user’][‘eps’] (float): specifies the working precision of the

machine. The default value for EPS is SQRT(EPSILON), where EPSILON is the unit roundoff. Note that if the value supplied is smaller than the default value then the default value will be used.

gen_specs[‘user’][‘epsw’] (float): is a small positive number, which is

used as the fudge factor for zero-valued weights. A zero-valued weight does not guarantee Pareto optimality. Therefore, all zero weights are set to EPSW. The appropriate value of EPSW is problem dependent. By default, EPSW is the fourth root of EPSILON (the unit roundoff). Note that any value that is smaller than SQRT(EPSILON) is ignored and SQRT(EPSILON) will be used.

gen_specs[‘user’][‘obj_tol’] (float): is the tolerance for the

objective space. An objective point that is within OBJ_TOL of being dominated by another objective point will be treated as such. The default value of OBJ_TOL is the square-root of EPS. This value should be strictly greater than the value of EPS. Note that any value that is smaller than the working precsion EPS will be ignored and EPS will be used.

gen_specs[‘user’][‘obj_bounds’] (np.ndarray) is an optional 2d array

of dimensions p by 2, whose first column is a list of lower bounds and whose second column is a list of upper bounds on the range of interesting objective values. When present, this value is used to prune the list of potential LTR centers, so that only objective values in the specified range are used when looking for gaps in the Pareto. In particular, an objective value F(x) will be considered for a LTR center if and only if OBJ_BOUNDS(I,1) .LE. F_I(x) .LE. OBJ_BOUNDS(I,2) for all I = 1, …, P. By default, there are no bounds on the interesting range. Note that this value is intentionally not saved during checkpointing, and must be reset by the user when recovery mode is active, whenever a non-default value is desired. This is the only input, for which changing the value after loading from a previous checkpoint is not ill-advised.

gen_specs[‘user’][‘min_radf’] (float): is the smallest value for the

fraction r defining the trust region box dimensions r * (UB - LB), before an isolated point is abandoned. By default, MIN_RADF = 0.1 * TRUST_RADF, and is also set to this default value if it is less than DES_TOL. After MIN_RADF and TRUST_RADF are set, MIN_RADF < TRUST_RADF must hold.

gen_specs[‘user’][‘trust_radf’] (float): defines the initial trust

region centered at an isolated point X as [X - TRUST_RADF * (UB - LB), X + TRUST_RADF * (UB - LB)] intersected with [LB, UB]. By default, TRUST_RADF = 0.2, and is also set to this value if the value given is outside the interval (DES_TOL, 1 - DES_TOL).

gen_specs[‘user’][‘pmode’] (bool): specifies whether or not iteration

tasks should be performed in parallel. By default, PMODE = False. If changed to True, VTMOP uses OpenMP parallelism to perform iteration tasks, and uses the environment variable OMP_NUM_THREADS to determine the number of parallel threads per generation.

Function values/simulation database; VTMOP can also be initialized with a precomputed database of n pre-evaluated simulations. To do so, initialize a history array H0 as follows:

H0[‘x’] (np.ndarray): is a 2d n-by-d history array containing a list

of precomputed design points.

H0[‘f’] (np.ndarray): is a 2d n-by-p history array containing the list

of corresponding precomputed objective values.

H0[‘sim_id’] (np.ndarray): Set H0[‘sim_id’] = range(n).

H0[[‘given’, ‘returned’]] = True

A checkpoint file (vtmop.chkpt) will be generated in the calling directory to save the status of VTMOP, and can be used to recover in the event of a crash, or can be used to reload any run after pausing.