def __init__(self, worker_id, data, response_surface, maxeval, nsamples,
                 exp_design=None, sampling_method=None, extra=None):
        """Initialize the optimization strategy.

        :param worker_id: Start ID in a multistart setting
        :param data: Problem parameter data structure
        :param response_surface: Surrogate model object
        :param maxeval: Function evaluation budget
        :param nsamples: Number of simultaneous fevals allowed
        :param exp_design: Experimental design
        :param search_procedure: Search procedure for finding
            points to evaluate
        :param extra: Points to be added to the experimental design
        """

        self.worker_id = worker_id
        self.data = data
        self.fhat = response_surface
        if self.fhat is None:
            self.fhat = RBFInterpolant(surftype=CubicRBFSurface, maxp=maxeval)
        self.maxeval = maxeval
        self.nsamples = nsamples
        self.extra = extra

        # Default to generate sampling points using Symmetric Latin Hypercube
        self.design = exp_design
        if self.design is None:
            if self.data.dim > 50:
                self.design = LatinHypercube(data.dim, data.dim+1)
            else:
                self.design = SymmetricLatinHypercube(data.dim, 2*(data.dim+1))

        self.xrange = np.asarray(data.xup - data.xlow)

        # algorithm parameters
        self.sigma_min = 0.005
        self.sigma_max = 0.2
        self.sigma_init = 0.2

        self.failtol = max(5, data.dim)
        self.succtol = 3

        self.numeval = 0
        self.status = 0
        self.sigma = 0
        self.resubmitter = RetryStrategy()
        self.xbest = None
        self.fbest = np.inf
        self.fbest_old = None

        # Set up search procedures and initialize
        self.sampling = sampling_method
        if self.sampling is None:
            self.sampling = CandidateDYCORS(data)

        self.check_input()

        # Start with first experimental design
        self.sample_initial()
class SyncStrategyNoConstraints(BaseStrategy):
    """Parallel synchronous optimization strategy without non-bound constraints.

    This class implements the parallel synchronous SRBF strategy
    described by Regis and Shoemaker.  After the initial experimental
    design (which is embarrassingly parallel), the optimization
    proceeds in phases.  During each phase, we allow nsamples
    simultaneous function evaluations.  We insist that these
    evaluations run to completion -- if one fails for whatever reason,
    we will resubmit it.  Samples are drawn randomly from around the
    current best point, and are sorted according to a merit function
    based on distance to other sample points and predicted function
    values according to the response surface.  After several
    successive significant improvements, we increase the sampling
    radius; after several failures to improve the function value, we
    decrease the sampling radius.  We restart once the sampling radius
    decreases below a threshold.
    """

    def __init__(self, worker_id, data, response_surface, maxeval, nsamples,
                 exp_design=None, sampling_method=None, extra=None):
        """Initialize the optimization strategy.

        :param worker_id: Start ID in a multistart setting
        :param data: Problem parameter data structure
        :param response_surface: Surrogate model object
        :param maxeval: Function evaluation budget
        :param nsamples: Number of simultaneous fevals allowed
        :param exp_design: Experimental design
        :param search_procedure: Search procedure for finding
            points to evaluate
        :param extra: Points to be added to the experimental design
        """

        self.worker_id = worker_id
        self.data = data
        self.fhat = response_surface
        if self.fhat is None:
            self.fhat = RBFInterpolant(surftype=CubicRBFSurface, maxp=maxeval)
        self.maxeval = maxeval
        self.nsamples = nsamples
        self.extra = extra

        # Default to generate sampling points using Symmetric Latin Hypercube
        self.design = exp_design
        if self.design is None:
            if self.data.dim > 50:
                self.design = LatinHypercube(data.dim, data.dim+1)
            else:
                self.design = SymmetricLatinHypercube(data.dim, 2*(data.dim+1))

        self.xrange = np.asarray(data.xup - data.xlow)

        # algorithm parameters
        self.sigma_min = 0.005
        self.sigma_max = 0.2
        self.sigma_init = 0.2

        self.failtol = max(5, data.dim)
        self.succtol = 3

        self.numeval = 0
        self.status = 0
        self.sigma = 0
        self.resubmitter = RetryStrategy()
        self.xbest = None
        self.fbest = np.inf
        self.fbest_old = None

        # Set up search procedures and initialize
        self.sampling = sampling_method
        if self.sampling is None:
            self.sampling = CandidateDYCORS(data)

        self.check_input()

        # Start with first experimental design
        self.sample_initial()

    def check_input(self):
        assert not hasattr(self.data, "eval_ineq_constraints"), "Objective function has constraints,\n" \
            "SyncStrategyNoConstraints can't handle constraints"
        assert not hasattr(self.data, "eval_eq_constraints"), "Objective function has constraints,\n" \
            "SyncStrategyNoConstraints can't handle constraints"

    def proj_fun(self, x):
        x = np.atleast_2d(x)
        return round_vars(self.data, x)

    def log_completion(self, record):
        """Record a completed evaluation to the log.

        :param record: Record of the function evaluation
        """
        xstr = np.array_str(record.params[0], max_line_width=np.inf,
                            precision=5, suppress_small=True)
        logger.info("Feasible {:.3e} @ {}".format(record.value, xstr))

    def adjust_step(self):
        """Adjust the sampling radius sigma.

        After succtol successful steps, we cut the sampling radius;
        after failtol failed steps, we double the sampling radius.

        :ivar Fnew: Best function value in new step
        :ivar fbest: Previous best function evaluation
        """
        # Initialize if this is the first adaptive step
        if self.fbest_old is None:
            self.fbest_old = self.fbest
            return

        # Check if we succeeded at significant improvement
        if self.fbest < self.fbest_old - 1e-3 * math.fabs(self.fbest_old):
            self.status = max(1, self.status + 1)
        else:
            self.status = min(-1, self.status - 1)
        self.fbest_old = self.fbest

        # Check if step needs adjusting
        if self.status <= -self.failtol:
            self.status = 0
            self.sigma /= 2
            logger.info("Reducing sigma")
        if self.status >= self.succtol:
            self.status = 0
            self.sigma = min([2.0 * self.sigma, self.sigma_max])
            logger.info("Increasing sigma")

    def sample_initial(self):
        """Generate and queue an initial experimental design.
        """
        if self.numeval == 0:
            logger.info("=== Start ===")
        else:
            logger.info("=== Restart ===")
        self.fhat.reset()
        self.sigma = self.sigma_init
        self.status = 0
        self.xbest = None
        self.fbest_old = None
        self.fbest = np.inf
        self.fhat.reset()
        start_sample = self.design.generate_points()
        assert start_sample.shape[1] == self.data.dim, \
            "Dimension mismatch between problem and experimental design"
        start_sample = from_unit_box(start_sample, self.data)
        # Add extra evaluation points provided by the user
        if self.extra is not None:
            start_sample = np.vstack((start_sample, self.extra))

        for j in range(min(start_sample.shape[0], self.maxeval - self.numeval)):
            start_sample[j, :] = self.proj_fun(start_sample[j, :])  # Project onto feasible region
            proposal = self.propose_eval(start_sample[j, :])
            self.resubmitter.rput(proposal)

        self.sampling.init(start_sample, self.fhat, self.maxeval - self.numeval)

    def sample_adapt(self):
        """Generate and queue samples from the search strategy
        """
        self.adjust_step()
        nsamples = min(self.nsamples, self.maxeval - self.numeval)
        new_points = self.sampling.make_points(npts=nsamples, xbest=self.xbest, sigma=self.sigma,
                                             proj_fun=self.proj_fun)
        for i in range(nsamples):
            proposal = self.propose_eval(np.ravel(new_points[i, :]))
            self.resubmitter.rput(proposal)

    def start_batch(self):
        """Generate and queue a new batch of points
        """
        if self.sigma < self.sigma_min:
            self.sample_initial()
        else:
            self.sample_adapt()

    def propose_action(self):
        """Propose an action
        """
        if self.numeval == self.maxeval:
            return self.propose_terminate()
        elif self.resubmitter.num_eval_outstanding == 0:
            self.start_batch()
        return self.resubmitter.get()

    def on_complete(self, record):
        """Handle completed function evaluation.

        When a function evaluation is completed we need to ask the constraint
        handler if the function value should be modified which is the case for
        say a penalty method. We also need to print the information to the
        logfile, update the best value found so far and notify the GUI that
        an evaluation has completed.

        :param record: Evaluation record
        """

        self.log_completion(record)
        self.numeval += 1
        record.worker_id = self.worker_id
        record.worker_numeval = self.numeval
        self.fhat.add_point(record.params[0], record.value)
        if record.value < self.fbest:
            self.xbest = record.params[0]
            self.fbest = record.value