# pragma pylint: disable=too-many-instance-attributes, pointless-string-statement """ This module contains the hyperopt logic """ import io import locale import logging import random import warnings from collections import OrderedDict from math import ceil from operator import itemgetter from pathlib import Path from pprint import pprint from typing import Any, Dict, List, Optional import progressbar import rapidjson import tabulate from colorama import Fore, Style from colorama import init as colorama_init from joblib import (Parallel, cpu_count, delayed, dump, load, wrap_non_picklable_objects) from pandas import DataFrame, isna, json_normalize from freqtrade.data.converter import trim_dataframe from freqtrade.data.history import get_timerange from freqtrade.exceptions import OperationalException from freqtrade.misc import plural, round_dict from freqtrade.optimize.backtesting import Backtesting # Import IHyperOpt and IHyperOptLoss to allow unpickling classes from these modules from freqtrade.optimize.hyperopt_interface import IHyperOpt # noqa: F401 from freqtrade.optimize.hyperopt_loss_interface import \ IHyperOptLoss # noqa: F401 from freqtrade.resolvers.hyperopt_resolver import (HyperOptLossResolver, HyperOptResolver) # Suppress scikit-learn FutureWarnings from skopt with warnings.catch_warnings(): warnings.filterwarnings("ignore", category=FutureWarning) from skopt import Optimizer from skopt.space import Dimension progressbar.streams.wrap_stderr() progressbar.streams.wrap_stdout() logger = logging.getLogger(__name__) INITIAL_POINTS = 30 # Keep no more than SKOPT_MODEL_QUEUE_SIZE models # in the skopt model queue, to optimize memory consumption SKOPT_MODEL_QUEUE_SIZE = 10 MAX_LOSS = 100000 # just a big enough number to be bad result in loss optimization class Hyperopt: """ Hyperopt class, this class contains all the logic to run a hyperopt simulation To run a backtest: hyperopt = Hyperopt(config) hyperopt.start() """ def __init__(self, config: Dict[str, Any]) -> None: self.config = config self.backtesting = Backtesting(self.config) self.custom_hyperopt = HyperOptResolver.load_hyperopt(self.config) self.custom_hyperoptloss = HyperOptLossResolver.load_hyperoptloss(self.config) self.calculate_loss = self.custom_hyperoptloss.hyperopt_loss_function self.results_file = (self.config['user_data_dir'] / 'hyperopt_results' / 'hyperopt_results.pickle') self.data_pickle_file = (self.config['user_data_dir'] / 'hyperopt_results' / 'hyperopt_tickerdata.pkl') self.total_epochs = config.get('epochs', 0) self.current_best_loss = 100 if not self.config.get('hyperopt_continue'): self.clean_hyperopt() else: logger.info("Continuing on previous hyperopt results.") self.num_epochs_saved = 0 # Previous evaluations self.epochs: List = [] # Populate functions here (hasattr is slow so should not be run during "regular" operations) if hasattr(self.custom_hyperopt, 'populate_indicators'): self.backtesting.strategy.advise_indicators = \ self.custom_hyperopt.populate_indicators # type: ignore if hasattr(self.custom_hyperopt, 'populate_buy_trend'): self.backtesting.strategy.advise_buy = \ self.custom_hyperopt.populate_buy_trend # type: ignore if hasattr(self.custom_hyperopt, 'populate_sell_trend'): self.backtesting.strategy.advise_sell = \ self.custom_hyperopt.populate_sell_trend # type: ignore # Use max_open_trades for hyperopt as well, except --disable-max-market-positions is set if self.config.get('use_max_market_positions', True): self.max_open_trades = self.config['max_open_trades'] else: logger.debug('Ignoring max_open_trades (--disable-max-market-positions was used) ...') self.max_open_trades = 0 self.position_stacking = self.config.get('position_stacking', False) if self.has_space('sell'): # Make sure use_sell_signal is enabled if 'ask_strategy' not in self.config: self.config['ask_strategy'] = {} self.config['ask_strategy']['use_sell_signal'] = True self.print_all = self.config.get('print_all', False) self.hyperopt_table_header = 0 self.print_colorized = self.config.get('print_colorized', False) self.print_json = self.config.get('print_json', False) @staticmethod def get_lock_filename(config: Dict[str, Any]) -> str: return str(config['user_data_dir'] / 'hyperopt.lock') def clean_hyperopt(self) -> None: """ Remove hyperopt pickle files to restart hyperopt. """ for f in [self.data_pickle_file, self.results_file]: p = Path(f) if p.is_file(): logger.info(f"Removing `{p}`.") p.unlink() def _get_params_dict(self, raw_params: List[Any]) -> Dict: dimensions: List[Dimension] = self.dimensions # Ensure the number of dimensions match # the number of parameters in the list. if len(raw_params) != len(dimensions): raise ValueError('Mismatch in number of search-space dimensions.') # Return a dict where the keys are the names of the dimensions # and the values are taken from the list of parameters. return {d.name: v for d, v in zip(dimensions, raw_params)} def _save_results(self) -> None: """ Save hyperopt results to file """ num_epochs = len(self.epochs) if num_epochs > self.num_epochs_saved: logger.debug(f"Saving {num_epochs} {plural(num_epochs, 'epoch')}.") dump(self.epochs, self.results_file) self.num_epochs_saved = num_epochs logger.debug(f"{self.num_epochs_saved} {plural(self.num_epochs_saved, 'epoch')} " f"saved to '{self.results_file}'.") @staticmethod def _read_results(results_file: Path) -> List: """ Read hyperopt results from file """ logger.info("Reading epochs from '%s'", results_file) data = load(results_file) return data def _get_params_details(self, params: Dict) -> Dict: """ Return the params for each space """ result: Dict = {} if self.has_space('buy'): result['buy'] = {p.name: params.get(p.name) for p in self.hyperopt_space('buy')} if self.has_space('sell'): result['sell'] = {p.name: params.get(p.name) for p in self.hyperopt_space('sell')} if self.has_space('roi'): result['roi'] = self.custom_hyperopt.generate_roi_table(params) if self.has_space('stoploss'): result['stoploss'] = {p.name: params.get(p.name) for p in self.hyperopt_space('stoploss')} if self.has_space('trailing'): result['trailing'] = self.custom_hyperopt.generate_trailing_params(params) return result @staticmethod def print_epoch_details(results, total_epochs: int, print_json: bool, no_header: bool = False, header_str: str = None) -> None: """ Display details of the hyperopt result """ params = results.get('params_details', {}) # Default header string if header_str is None: header_str = "Best result" if not no_header: explanation_str = Hyperopt._format_explanation_string(results, total_epochs) print(f"\n{header_str}:\n\n{explanation_str}\n") if print_json: result_dict: Dict = {} for s in ['buy', 'sell', 'roi', 'stoploss', 'trailing']: Hyperopt._params_update_for_json(result_dict, params, s) print(rapidjson.dumps(result_dict, default=str, number_mode=rapidjson.NM_NATIVE)) else: Hyperopt._params_pretty_print(params, 'buy', "Buy hyperspace params:") Hyperopt._params_pretty_print(params, 'sell', "Sell hyperspace params:") Hyperopt._params_pretty_print(params, 'roi', "ROI table:") Hyperopt._params_pretty_print(params, 'stoploss', "Stoploss:") Hyperopt._params_pretty_print(params, 'trailing', "Trailing stop:") @staticmethod def _params_update_for_json(result_dict, params, space: str) -> None: if space in params: space_params = Hyperopt._space_params(params, space) if space in ['buy', 'sell']: result_dict.setdefault('params', {}).update(space_params) elif space == 'roi': # Convert keys in min_roi dict to strings because # rapidjson cannot dump dicts with integer keys... # OrderedDict is used to keep the numeric order of the items # in the dict. result_dict['minimal_roi'] = OrderedDict( (str(k), v) for k, v in space_params.items() ) else: # 'stoploss', 'trailing' result_dict.update(space_params) @staticmethod def _params_pretty_print(params, space: str, header: str) -> None: if space in params: space_params = Hyperopt._space_params(params, space, 5) if space == 'stoploss': print(header, space_params.get('stoploss')) else: print(header) pprint(space_params, indent=4) @staticmethod def _space_params(params, space: str, r: int = None) -> Dict: d = params[space] # Round floats to `r` digits after the decimal point if requested return round_dict(d, r) if r else d @staticmethod def is_best_loss(results, current_best_loss: float) -> bool: return results['loss'] < current_best_loss def print_results(self, results) -> None: """ Log results if it is better than any previous evaluation """ is_best = results['is_best'] if self.print_all or is_best: print( self.get_result_table( self.config, results, self.total_epochs, self.print_all, self.print_colorized, self.hyperopt_table_header ) ) self.hyperopt_table_header = 2 @staticmethod def _format_explanation_string(results, total_epochs) -> str: return (("*" if results['is_initial_point'] else " ") + f"{results['current_epoch']:5d}/{total_epochs}: " + f"{results['results_explanation']} " + f"Objective: {results['loss']:.5f}") @staticmethod def get_result_table(config: dict, results: list, total_epochs: int, highlight_best: bool, print_colorized: bool, remove_header: int) -> str: """ Log result table """ if not results: return '' tabulate.PRESERVE_WHITESPACE = True trials = json_normalize(results, max_level=1) trials['Best'] = '' trials = trials[['Best', 'current_epoch', 'results_metrics.trade_count', 'results_metrics.avg_profit', 'results_metrics.total_profit', 'results_metrics.profit', 'results_metrics.duration', 'loss', 'is_initial_point', 'is_best']] trials.columns = ['Best', 'Epoch', 'Trades', 'Avg profit', 'Total profit', 'Profit', 'Avg duration', 'Objective', 'is_initial_point', 'is_best'] trials['is_profit'] = False trials.loc[trials['is_initial_point'], 'Best'] = '* ' trials.loc[trials['is_best'], 'Best'] = 'Best' trials.loc[trials['is_initial_point'] & trials['is_best'], 'Best'] = '* Best' trials.loc[trials['Total profit'] > 0, 'is_profit'] = True trials['Trades'] = trials['Trades'].astype(str) trials['Epoch'] = trials['Epoch'].apply( lambda x: '{}/{}'.format(str(x).rjust(len(str(total_epochs)), ' '), total_epochs) ) trials['Avg profit'] = trials['Avg profit'].apply( lambda x: '{:,.2f}%'.format(x).rjust(7, ' ') if not isna(x) else "--".rjust(7, ' ') ) trials['Avg duration'] = trials['Avg duration'].apply( lambda x: '{:,.1f} m'.format(x).rjust(7, ' ') if not isna(x) else "--".rjust(7, ' ') ) trials['Objective'] = trials['Objective'].apply( lambda x: '{:,.5f}'.format(x).rjust(8, ' ') if x != 100000 else "N/A".rjust(8, ' ') ) trials['Profit'] = trials.apply( lambda x: '{:,.8f} {} {}'.format( x['Total profit'], config['stake_currency'], '({:,.2f}%)'.format(x['Profit']).rjust(10, ' ') ).rjust(25+len(config['stake_currency'])) if x['Total profit'] != 0.0 else '--'.rjust(25+len(config['stake_currency'])), axis=1 ) trials = trials.drop(columns=['Total profit']) if print_colorized: for i in range(len(trials)): if trials.loc[i]['is_profit']: for j in range(len(trials.loc[i])-3): trials.iat[i, j] = "{}{}{}".format(Fore.GREEN, str(trials.loc[i][j]), Fore.RESET) if trials.loc[i]['is_best'] and highlight_best: for j in range(len(trials.loc[i])-3): trials.iat[i, j] = "{}{}{}".format(Style.BRIGHT, str(trials.loc[i][j]), Style.RESET_ALL) trials = trials.drop(columns=['is_initial_point', 'is_best', 'is_profit']) if remove_header > 0: table = tabulate.tabulate( trials.to_dict(orient='list'), tablefmt='orgtbl', headers='keys', stralign="right" ) table = table.split("\n", remove_header)[remove_header] elif remove_header < 0: table = tabulate.tabulate( trials.to_dict(orient='list'), tablefmt='psql', headers='keys', stralign="right" ) table = "\n".join(table.split("\n")[0:remove_header]) else: table = tabulate.tabulate( trials.to_dict(orient='list'), tablefmt='psql', headers='keys', stralign="right" ) return table @staticmethod def export_csv_file(config: dict, results: list, total_epochs: int, highlight_best: bool, csv_file: str) -> None: """ Log result to csv-file """ if not results: return # Verification for overwrite if Path(csv_file).is_file(): logger.error(f"CSV file already exists: {csv_file}") return try: io.open(csv_file, 'w+').close() except IOError: logger.error(f"Failed to create CSV file: {csv_file}") return trials = json_normalize(results, max_level=1) trials['Best'] = '' trials['Stake currency'] = config['stake_currency'] base_metrics = ['Best', 'current_epoch', 'results_metrics.trade_count', 'results_metrics.avg_profit', 'results_metrics.total_profit', 'Stake currency', 'results_metrics.profit', 'results_metrics.duration', 'loss', 'is_initial_point', 'is_best'] param_metrics = [("params_dict."+param) for param in results[0]['params_dict'].keys()] trials = trials[base_metrics + param_metrics] base_columns = ['Best', 'Epoch', 'Trades', 'Avg profit', 'Total profit', 'Stake currency', 'Profit', 'Avg duration', 'Objective', 'is_initial_point', 'is_best'] param_columns = list(results[0]['params_dict'].keys()) trials.columns = base_columns + param_columns trials['is_profit'] = False trials.loc[trials['is_initial_point'], 'Best'] = '*' trials.loc[trials['is_best'], 'Best'] = 'Best' trials.loc[trials['is_initial_point'] & trials['is_best'], 'Best'] = '* Best' trials.loc[trials['Total profit'] > 0, 'is_profit'] = True trials['Epoch'] = trials['Epoch'].astype(str) trials['Trades'] = trials['Trades'].astype(str) trials['Total profit'] = trials['Total profit'].apply( lambda x: '{:,.8f}'.format(x) if x != 0.0 else "" ) trials['Profit'] = trials['Profit'].apply( lambda x: '{:,.2f}'.format(x) if not isna(x) else "" ) trials['Avg profit'] = trials['Avg profit'].apply( lambda x: '{:,.2f}%'.format(x) if not isna(x) else "" ) trials['Avg duration'] = trials['Avg duration'].apply( lambda x: '{:,.1f} m'.format(x) if not isna(x) else "" ) trials['Objective'] = trials['Objective'].apply( lambda x: '{:,.5f}'.format(x) if x != 100000 else "" ) trials = trials.drop(columns=['is_initial_point', 'is_best', 'is_profit']) trials.to_csv(csv_file, index=False, header=True, mode='w', encoding='UTF-8') logger.info(f"CSV file created: {csv_file}") def has_space(self, space: str) -> bool: """ Tell if the space value is contained in the configuration """ # The 'trailing' space is not included in the 'default' set of spaces if space == 'trailing': return any(s in self.config['spaces'] for s in [space, 'all']) else: return any(s in self.config['spaces'] for s in [space, 'all', 'default']) def hyperopt_space(self, space: Optional[str] = None) -> List[Dimension]: """ Return the dimensions in the hyperoptimization space. :param space: Defines hyperspace to return dimensions for. If None, then the self.has_space() will be used to return dimensions for all hyperspaces used. """ spaces: List[Dimension] = [] if space == 'buy' or (space is None and self.has_space('buy')): logger.debug("Hyperopt has 'buy' space") spaces += self.custom_hyperopt.indicator_space() if space == 'sell' or (space is None and self.has_space('sell')): logger.debug("Hyperopt has 'sell' space") spaces += self.custom_hyperopt.sell_indicator_space() if space == 'roi' or (space is None and self.has_space('roi')): logger.debug("Hyperopt has 'roi' space") spaces += self.custom_hyperopt.roi_space() if space == 'stoploss' or (space is None and self.has_space('stoploss')): logger.debug("Hyperopt has 'stoploss' space") spaces += self.custom_hyperopt.stoploss_space() if space == 'trailing' or (space is None and self.has_space('trailing')): logger.debug("Hyperopt has 'trailing' space") spaces += self.custom_hyperopt.trailing_space() return spaces def generate_optimizer(self, raw_params: List[Any], iteration=None) -> Dict: """ Used Optimize function. Called once per epoch to optimize whatever is configured. Keep this function as optimized as possible! """ params_dict = self._get_params_dict(raw_params) params_details = self._get_params_details(params_dict) if self.has_space('roi'): self.backtesting.strategy.minimal_roi = \ self.custom_hyperopt.generate_roi_table(params_dict) if self.has_space('buy'): self.backtesting.strategy.advise_buy = \ self.custom_hyperopt.buy_strategy_generator(params_dict) if self.has_space('sell'): self.backtesting.strategy.advise_sell = \ self.custom_hyperopt.sell_strategy_generator(params_dict) if self.has_space('stoploss'): self.backtesting.strategy.stoploss = params_dict['stoploss'] if self.has_space('trailing'): d = self.custom_hyperopt.generate_trailing_params(params_dict) self.backtesting.strategy.trailing_stop = d['trailing_stop'] self.backtesting.strategy.trailing_stop_positive = d['trailing_stop_positive'] self.backtesting.strategy.trailing_stop_positive_offset = \ d['trailing_stop_positive_offset'] self.backtesting.strategy.trailing_only_offset_is_reached = \ d['trailing_only_offset_is_reached'] processed = load(self.data_pickle_file) min_date, max_date = get_timerange(processed) backtesting_results = self.backtesting.backtest( processed=processed, stake_amount=self.config['stake_amount'], start_date=min_date, end_date=max_date, max_open_trades=self.max_open_trades, position_stacking=self.position_stacking, ) return self._get_results_dict(backtesting_results, min_date, max_date, params_dict, params_details) def _get_results_dict(self, backtesting_results, min_date, max_date, params_dict, params_details): results_metrics = self._calculate_results_metrics(backtesting_results) results_explanation = self._format_results_explanation_string(results_metrics) trade_count = results_metrics['trade_count'] total_profit = results_metrics['total_profit'] # If this evaluation contains too short amount of trades to be # interesting -- consider it as 'bad' (assigned max. loss value) # in order to cast this hyperspace point away from optimization # path. We do not want to optimize 'hodl' strategies. loss: float = MAX_LOSS if trade_count >= self.config['hyperopt_min_trades']: loss = self.calculate_loss(results=backtesting_results, trade_count=trade_count, min_date=min_date.datetime, max_date=max_date.datetime) return { 'loss': loss, 'params_dict': params_dict, 'params_details': params_details, 'results_metrics': results_metrics, 'results_explanation': results_explanation, 'total_profit': total_profit, } def _calculate_results_metrics(self, backtesting_results: DataFrame) -> Dict: return { 'trade_count': len(backtesting_results.index), 'avg_profit': backtesting_results.profit_percent.mean() * 100.0, 'total_profit': backtesting_results.profit_abs.sum(), 'profit': backtesting_results.profit_percent.sum() * 100.0, 'duration': backtesting_results.trade_duration.mean(), } def _format_results_explanation_string(self, results_metrics: Dict) -> str: """ Return the formatted results explanation in a string """ stake_cur = self.config['stake_currency'] return (f"{results_metrics['trade_count']:6d} trades. " f"Avg profit {results_metrics['avg_profit']: 6.2f}%. " f"Total profit {results_metrics['total_profit']: 11.8f} {stake_cur} " f"({results_metrics['profit']: 7.2f}\N{GREEK CAPITAL LETTER SIGMA}%). " f"Avg duration {results_metrics['duration']:5.1f} min." ).encode(locale.getpreferredencoding(), 'replace').decode('utf-8') def get_optimizer(self, dimensions: List[Dimension], cpu_count) -> Optimizer: return Optimizer( dimensions, base_estimator="ET", acq_optimizer="auto", n_initial_points=INITIAL_POINTS, acq_optimizer_kwargs={'n_jobs': cpu_count}, random_state=self.random_state, model_queue_size=SKOPT_MODEL_QUEUE_SIZE, ) def run_optimizer_parallel(self, parallel, asked, i) -> List: return parallel(delayed( wrap_non_picklable_objects(self.generate_optimizer))(v, i) for v in asked) @staticmethod def load_previous_results(results_file: Path) -> List: """ Load data for epochs from the file if we have one """ epochs: List = [] if results_file.is_file() and results_file.stat().st_size > 0: epochs = Hyperopt._read_results(results_file) # Detection of some old format, without 'is_best' field saved if epochs[0].get('is_best') is None: raise OperationalException( "The file with Hyperopt results is incompatible with this version " "of Freqtrade and cannot be loaded.") logger.info(f"Loaded {len(epochs)} previous evaluations from disk.") return epochs def _set_random_state(self, random_state: Optional[int]) -> int: return random_state or random.randint(1, 2**16 - 1) def start(self) -> None: self.random_state = self._set_random_state(self.config.get('hyperopt_random_state', None)) logger.info(f"Using optimizer random state: {self.random_state}") self.hyperopt_table_header = -1 data, timerange = self.backtesting.load_bt_data() preprocessed = self.backtesting.strategy.ohlcvdata_to_dataframe(data) # Trim startup period from analyzed dataframe for pair, df in preprocessed.items(): preprocessed[pair] = trim_dataframe(df, timerange) min_date, max_date = get_timerange(data) logger.info( 'Hyperopting with data from %s up to %s (%s days)..', min_date.isoformat(), max_date.isoformat(), (max_date - min_date).days ) dump(preprocessed, self.data_pickle_file) # We don't need exchange instance anymore while running hyperopt self.backtesting.exchange = None # type: ignore self.backtesting.pairlists = None # type: ignore self.epochs = self.load_previous_results(self.results_file) cpus = cpu_count() logger.info(f"Found {cpus} CPU cores. Let's make them scream!") config_jobs = self.config.get('hyperopt_jobs', -1) logger.info(f'Number of parallel jobs set as: {config_jobs}') self.dimensions: List[Dimension] = self.hyperopt_space() self.opt = self.get_optimizer(self.dimensions, config_jobs) if self.print_colorized: colorama_init(autoreset=True) try: with Parallel(n_jobs=config_jobs) as parallel: jobs = parallel._effective_n_jobs() logger.info(f'Effective number of parallel workers used: {jobs}') # Define progressbar if self.print_colorized: widgets = [ ' [Epoch ', progressbar.Counter(), ' of ', str(self.total_epochs), ' (', progressbar.Percentage(), ')] ', progressbar.Bar(marker=progressbar.AnimatedMarker( fill='\N{FULL BLOCK}', fill_wrap=Fore.GREEN + '{}' + Fore.RESET, marker_wrap=Style.BRIGHT + '{}' + Style.RESET_ALL, )), ' [', progressbar.ETA(), ', ', progressbar.Timer(), ']', ] else: widgets = [ ' [Epoch ', progressbar.Counter(), ' of ', str(self.total_epochs), ' (', progressbar.Percentage(), ')] ', progressbar.Bar(marker=progressbar.AnimatedMarker( fill='\N{FULL BLOCK}', )), ' [', progressbar.ETA(), ', ', progressbar.Timer(), ']', ] with progressbar.ProgressBar( max_value=self.total_epochs, redirect_stdout=False, redirect_stderr=False, widgets=widgets ) as pbar: EVALS = ceil(self.total_epochs / jobs) for i in range(EVALS): # Correct the number of epochs to be processed for the last # iteration (should not exceed self.total_epochs in total) n_rest = (i + 1) * jobs - self.total_epochs current_jobs = jobs - n_rest if n_rest > 0 else jobs asked = self.opt.ask(n_points=current_jobs) f_val = self.run_optimizer_parallel(parallel, asked, i) self.opt.tell(asked, [v['loss'] for v in f_val]) # Calculate progressbar outputs for j, val in enumerate(f_val): # Use human-friendly indexes here (starting from 1) current = i * jobs + j + 1 val['current_epoch'] = current val['is_initial_point'] = current <= INITIAL_POINTS logger.debug(f"Optimizer epoch evaluated: {val}") is_best = self.is_best_loss(val, self.current_best_loss) # This value is assigned here and not in the optimization method # to keep proper order in the list of results. That's because # evaluations can take different time. Here they are aligned in the # order they will be shown to the user. val['is_best'] = is_best self.print_results(val) if is_best: self.current_best_loss = val['loss'] self.epochs.append(val) # Save results after each best epoch and every 100 epochs if is_best or current % 100 == 0: self._save_results() pbar.update(current) except KeyboardInterrupt: print('User interrupted..') self._save_results() logger.info(f"{self.num_epochs_saved} {plural(self.num_epochs_saved, 'epoch')} " f"saved to '{self.results_file}'.") if self.epochs: sorted_epochs = sorted(self.epochs, key=itemgetter('loss')) best_epoch = sorted_epochs[0] self.print_epoch_details(best_epoch, self.total_epochs, self.print_json) else: # This is printed when Ctrl+C is pressed quickly, before first epochs have # a chance to be evaluated. print("No epochs evaluated yet, no best result.")