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@@ -34,22 +34,27 @@ using Facade = DataFacade<Algorithm>;
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namespace
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{
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// Alternative paths candidate via nodes are taken from overlapping search spaces.
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// Overlapping by a third guarantees us taking candidate nodes "from the middle".
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const constexpr auto kSearchSpaceOverlapFactor = 1.33;
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// Unpack n-times more candidate paths to run high-quality checks on.
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// Unpacking paths yields higher chance to find good alternatives but is also expensive.
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const constexpr auto kAlternativesToUnpackFactor = 2.0;
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// Alternative paths length requirement (stretch).
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// At most 25% longer then the shortest path.
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const constexpr auto kAtMostLongerBy = 0.25;
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// Alternative paths similarity requirement (sharing).
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// At least 15% different than the shortest path.
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const constexpr auto kAtLeastDifferentBy = 0.85;
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// Alternative paths are still reasonable around the via node candidate (local optimality).
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// At least optimal around 10% sub-paths around the via node candidate.
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const /*constexpr*/ auto kAtLeastOptimalAroundViaBy = 0.10;
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// gcc 7.1 ICE ^
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struct Parameters
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{
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// Alternative paths candidate via nodes are taken from overlapping search spaces.
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// Overlapping by a third guarantees us taking candidate nodes "from the middle".
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double kSearchSpaceOverlapFactor = 1.33;
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// Unpack n-times more candidate paths to run high-quality checks on.
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// Unpacking paths yields higher chance to find good alternatives but is also expensive.
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unsigned kAlternativesToUnpackFactor = 2;
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// Alternative paths length requirement (stretch).
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// At most 25% longer then the shortest path.
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double kAtMostLongerBy = 0.25;
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// Alternative paths similarity requirement (sharing).
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// At least 25% different than the shortest path.
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double kAtMostSameBy = 0.75;
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// Alternative paths are still reasonable around the via node candidate (local optimality).
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// At least optimal around 10% sub-paths around the via node candidate.
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double kAtLeastOptimalAroundViaBy = 0.1;
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// Alternative paths similarity requirement (sharing) based on calles.
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// At least 15% different than the shortest path.
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double kCellsAtMostSameBy = 0.95;
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};
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// Represents a via middle node where forward (from s) and backward (from t)
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// search spaces overlap and the weight a path (made up of s,via and via,t) has.
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@@ -71,11 +76,104 @@ struct WeightedViaNodePackedPath
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// its total weight and the via node used to construct the path.
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struct WeightedViaNodeUnpackedPath
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{
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double sharing;
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WeightedViaNode via;
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UnpackedNodes nodes;
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UnpackedEdges edges;
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};
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// Scale the maximum allowed weight increase based on its magnitude:
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// - Shortest path 10 minutes, alternative 13 minutes => Factor of 0.30 ok
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// - Shortest path 10 hours, alternative 13 hours => Factor of 0.30 unreasonable
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double getLongerByFactorBasedOnDuration(const EdgeWeight duration)
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{
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BOOST_ASSERT(duration != INVALID_EDGE_WEIGHT);
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// We only have generic weights here and no durations without unpacking.
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// We also have restricted way penalties which are huge and will screw scaling here.
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//
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// Users can pass us generic weights not based on durations; we can't do anything about
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// it here other than either generating too many or no alternatives in these cases.
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//
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// We scale the weights with a step function based on some rough guestimates, so that
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// they match tens of minutes, in the low hours, tens of hours, etc.
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// Computed using a least-squares curve fitiing on the following values:
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//
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// def func(xs, a, b, c, d):
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// return a + b/(xs-d) + c/(xs-d)**3
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//
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// xs = np.array([5 * 60, 10 * 60, 30 * 60, 60 * 60, 3 * 60 * 60, 10 * 60 * 60])
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// ys = np.array([1.0, 0.75, 0.5, 0.4, 0.3, 0.2])
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//
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// xs_interp = np.arange(5*60, 10*60*60, 5*60)
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// ys_interp = np.interp(xs_interp, xs, ys)
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//
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// params, _ = scipy.optimize.curve_fit(func, xs_interp, ys_interp)
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//
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// The hyperbolic shape was chosen because it interpolated well between
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// the given datapoints and drops off for large durations.
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const constexpr auto a = 1.91578463e-01;
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const constexpr auto b = 1.35118442e+03;
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const constexpr auto c = 2.45437877e+09;
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const constexpr auto d = -2.07944571e+03;
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if (duration < EdgeWeight(5 * 60))
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{
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return 1.0;
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}
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else if (duration > EdgeWeight(10 * 60 * 60))
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{
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return 0.20;
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}
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// Bigger than 10 minutes but smaller than 10 hours
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BOOST_ASSERT(duration >= 5 * 60 && duration <= 10 * 60 * 60);
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return a + b / (duration - d) + c / std::pow(duration - d, 3);
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}
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Parameters parametersFromRequest(const PhantomNodes &phantom_node_pair)
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{
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Parameters parameters;
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const auto distance = util::coordinate_calculation::haversineDistance(
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phantom_node_pair.source_phantom.location, phantom_node_pair.target_phantom.location);
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// 10km
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if (distance < 10000.)
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{
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parameters.kAlternativesToUnpackFactor = 10.0;
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parameters.kCellsAtMostSameBy = 1.0;
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parameters.kAtLeastOptimalAroundViaBy = 0.2;
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parameters.kAtMostSameBy = 0.50;
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}
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// 20km
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else if (distance < 20000.)
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{
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parameters.kAlternativesToUnpackFactor = 8.0;
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parameters.kCellsAtMostSameBy = 1.0;
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parameters.kAtLeastOptimalAroundViaBy = 0.2;
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parameters.kAtMostSameBy = 0.60;
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}
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// 50km
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else if (distance < 50000.)
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{
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parameters.kAlternativesToUnpackFactor = 6.0;
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parameters.kCellsAtMostSameBy = 0.95;
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parameters.kAtMostSameBy = 0.65;
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}
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// 100km
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else if (distance < 100000.)
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{
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parameters.kAlternativesToUnpackFactor = 4.0;
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parameters.kCellsAtMostSameBy = 0.95;
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parameters.kAtMostSameBy = 0.70;
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}
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return parameters;
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}
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// Filters candidates which are on not unique.
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// Returns an iterator to the uniquified range's new end.
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// Note: mutates the range in-place invalidating iterators.
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@@ -110,49 +208,13 @@ RandIt filterViaCandidatesByRoadImportance(RandIt first, RandIt last, const Faca
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return last;
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}
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// Scale the maximum allowed weight increase based on its magnitude:
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// - Shortest path 10 minutes, alternative 13 minutes => Factor of 0.30 ok
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// - Shortest path 10 hours, alternative 13 hours => Factor of 0.30 unreasonable
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double scaledAtMostLongerByFactorBasedOnDuration(EdgeWeight duration)
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{
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BOOST_ASSERT(duration != INVALID_EDGE_WEIGHT);
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// We only have generic weights here and no durations without unpacking.
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// We also have restricted way penalties which are huge and will screw scaling here.
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//
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// Users can pass us generic weights not based on durations; we can't do anything about
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// it here other than either generating too many or no alternatives in these cases.
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//
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// We scale the weights with a step function based on some rough guestimates, so that
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// they match tens of minutes, in the low hours, tens of hours, etc.
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// Todo: instead of a piecewise constant function should this be a continuous function?
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// At the moment there are "hard" jump edge cases when crossing the thresholds.
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auto scaledAtMostLongerBy = kAtMostLongerBy;
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const constexpr auto minutes = 60.;
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const constexpr auto hours = 60. * minutes;
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if (duration < EdgeWeight(10 * minutes))
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scaledAtMostLongerBy *= 1.20;
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else if (duration < EdgeWeight(30 * minutes))
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scaledAtMostLongerBy *= 1.00;
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else if (duration < EdgeWeight(1 * hours))
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scaledAtMostLongerBy *= 0.90;
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else if (duration < EdgeWeight(3 * hours))
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scaledAtMostLongerBy *= 0.70;
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else if (duration > EdgeWeight(10 * hours))
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scaledAtMostLongerBy *= 0.50;
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return scaledAtMostLongerBy;
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}
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// Filters candidates with much higher weight than the primary route. Mutates range in-place.
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// Returns an iterator to the filtered range's new end.
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template <typename RandIt>
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RandIt
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filterViaCandidatesByStretch(RandIt first, RandIt last, EdgeWeight weight, double weight_multiplier)
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RandIt filterViaCandidatesByStretch(RandIt first,
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RandIt last,
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const EdgeWeight weight,
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const Parameters ¶meters)
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{
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util::static_assert_iter_category<RandIt, std::random_access_iterator_tag>();
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util::static_assert_iter_value<RandIt, WeightedViaNode>();
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@@ -160,9 +222,7 @@ filterViaCandidatesByStretch(RandIt first, RandIt last, EdgeWeight weight, doubl
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// Assumes weight roughly corresponds to duration-ish. If this is not the case e.g.
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// because users are setting weight to be distance in the profiles, then we might
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// either generate more candidates than we have to or not enough. But is okay.
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const auto scaled_at_most_longer_by =
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scaledAtMostLongerByFactorBasedOnDuration(weight / weight_multiplier);
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const auto stretch_weight_limit = (1. + scaled_at_most_longer_by) * weight;
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const auto stretch_weight_limit = (1. + parameters.kAtMostLongerBy) * weight;
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const auto over_weight_limit = [=](const auto via) {
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return via.weight > stretch_weight_limit;
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@@ -198,8 +258,15 @@ filterViaCandidatesByViaNotOnPath(const WeightedViaNodePackedPath &path, RandIt
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// Filters packed paths with similar cells between each other. Mutates range in-place.
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// Returns an iterator to the filtered range's new end.
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template <typename RandIt>
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RandIt filterPackedPathsByCellSharing(RandIt first, RandIt last, const Partition &partition)
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RandIt filterPackedPathsByCellSharing(RandIt first,
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RandIt last,
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const Partition &partition,
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const Parameters ¶meters)
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{
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// In this case we don't need to calculate sharing, because it would not filter anything
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if (parameters.kCellsAtMostSameBy >= 1.0)
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return last;
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util::static_assert_iter_category<RandIt, std::random_access_iterator_tag>();
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util::static_assert_iter_value<RandIt, WeightedViaNodePackedPath>();
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@@ -226,14 +293,13 @@ RandIt filterPackedPathsByCellSharing(RandIt first, RandIt last, const Partition
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return last;
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std::unordered_set<CellID> cells;
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cells.reserve(size * (shortest_path.path.size() + 1) * (1. + kAtMostLongerBy));
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cells.reserve(size * (shortest_path.path.size() + 1) * (1 + parameters.kAtMostLongerBy));
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cells.insert(get_cell(std::get<0>(shortest_path.path.front())));
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for (const auto &edge : shortest_path.path)
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cells.insert(get_cell(std::get<1>(edge)));
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const auto over_sharing_limit = [&](const auto &packed) {
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if (packed.path.empty())
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{ // don't remove routes with single-node (empty) path
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return false;
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@@ -253,7 +319,7 @@ RandIt filterPackedPathsByCellSharing(RandIt first, RandIt last, const Partition
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const auto sharing = 1. - difference;
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if (sharing > kAtLeastDifferentBy)
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if (sharing > parameters.kCellsAtMostSameBy)
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{
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return true;
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}
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@@ -277,7 +343,8 @@ RandIt filterPackedPathsByLocalOptimality(const WeightedViaNodePackedPath &path,
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const Heap &forward_heap,
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const Heap &reverse_heap,
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RandIt first,
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RandIt last)
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RandIt last,
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const Parameters ¶meters)
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{
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util::static_assert_iter_category<RandIt, std::random_access_iterator_tag>();
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util::static_assert_iter_value<RandIt, WeightedViaNodePackedPath>();
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@@ -376,7 +443,7 @@ RandIt filterPackedPathsByLocalOptimality(const WeightedViaNodePackedPath &path,
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const auto detour_length = forward_heap.GetKey(via) - forward_heap.GetKey(a) +
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reverse_heap.GetKey(via) - reverse_heap.GetKey(b);
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return plateaux_length < kAtLeastOptimalAroundViaBy * detour_length;
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return plateaux_length < parameters.kAtLeastOptimalAroundViaBy * detour_length;
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};
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return std::remove_if(first, last, is_not_locally_optimal);
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@@ -384,7 +451,11 @@ RandIt filterPackedPathsByLocalOptimality(const WeightedViaNodePackedPath &path,
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// Filters unpacked paths compared to all other paths. Mutates range in-place.
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// Returns an iterator to the filtered range's new end.
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template <typename RandIt> RandIt filterUnpackedPathsBySharing(RandIt first, RandIt last)
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template <typename RandIt>
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RandIt filterUnpackedPathsBySharing(RandIt first,
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RandIt last,
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const Facade &facade,
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const Parameters ¶meters)
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{
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util::static_assert_iter_category<RandIt, std::random_access_iterator_tag>();
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util::static_assert_iter_value<RandIt, WeightedViaNodeUnpackedPath>();
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@@ -400,27 +471,35 @@ template <typename RandIt> RandIt filterUnpackedPathsBySharing(RandIt first, Ran
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return last;
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std::unordered_set<EdgeID> edges;
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edges.reserve(size * shortest_path.edges.size() * (1. + kAtMostLongerBy));
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edges.reserve(size * shortest_path.edges.size() * (1.25));
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edges.insert(begin(shortest_path.edges), begin(shortest_path.edges));
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const auto over_sharing_limit = [&](const auto &unpacked) {
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edges.insert(begin(shortest_path.edges), end(shortest_path.edges));
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const auto over_sharing_limit = [&](auto &unpacked) {
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if (unpacked.edges.empty())
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{ // don't remove routes with single-node (empty) path
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return false;
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}
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const auto not_seen = [&](const EdgeID edge) { return edges.count(edge) < 1; };
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const auto different = std::count_if(begin(unpacked.edges), end(unpacked.edges), not_seen);
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EdgeWeight total_duration = 0;
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const auto add_if_seen = [&](const EdgeWeight duration, const EdgeID edge) {
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auto edge_duration = facade.GetEdgeData(edge).duration;
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total_duration += edge_duration;
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if (edges.count(edge) > 0)
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{
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return duration + edge_duration;
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}
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return duration;
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};
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const auto difference = different / static_cast<double>(unpacked.edges.size());
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BOOST_ASSERT(difference >= 0.);
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BOOST_ASSERT(difference <= 1.);
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const auto shared_weight =
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std::accumulate(begin(unpacked.edges), end(unpacked.edges), EdgeWeight{0}, add_if_seen);
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const auto sharing = 1. - difference;
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unpacked.sharing = shared_weight / static_cast<double>(total_duration);
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BOOST_ASSERT(unpacked.sharing >= 0.);
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BOOST_ASSERT(unpacked.sharing <= 1.);
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if (sharing > kAtLeastDifferentBy)
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if (unpacked.sharing > parameters.kAtMostSameBy)
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{
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return true;
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}
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@@ -431,14 +510,19 @@ template <typename RandIt> RandIt filterUnpackedPathsBySharing(RandIt first, Ran
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}
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};
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return std::remove_if(first + 1, last, over_sharing_limit);
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auto end = std::remove_if(first + 1, last, over_sharing_limit);
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std::sort(
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first + 1, end, [](const auto &lhs, const auto &rhs) { return lhs.sharing < rhs.sharing; });
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return end;
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}
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// Filters annotated routes by stretch based on duration. Mutates range in-place.
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|
// Returns an iterator to the filtered range's new end.
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|
template <typename RandIt>
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RandIt
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filterAnnotatedRoutesByStretch(RandIt first, RandIt last, const InternalRouteResult &shortest_route)
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|
|
RandIt filterAnnotatedRoutesByStretch(RandIt first,
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|
|
RandIt last,
|
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|
|
const InternalRouteResult &shortest_route,
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|
|
const Parameters ¶meters)
|
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|
|
{
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|
|
util::static_assert_iter_category<RandIt, std::random_access_iterator_tag>();
|
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|
|
|
util::static_assert_iter_value<RandIt, InternalRouteResult>();
|
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|
|
@@ -446,9 +530,7 @@ filterAnnotatedRoutesByStretch(RandIt first, RandIt last, const InternalRouteRes
|
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|
|
|
BOOST_ASSERT(shortest_route.is_valid());
|
|
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|
|
const auto shortest_route_duration = shortest_route.duration();
|
|
|
|
|
const auto scaled_at_most_longer_by =
|
|
|
|
|
scaledAtMostLongerByFactorBasedOnDuration(shortest_route_duration);
|
|
|
|
|
const auto stretch_duration_limit = (1. + scaled_at_most_longer_by) * shortest_route_duration;
|
|
|
|
|
const auto stretch_duration_limit = (1. + parameters.kAtMostLongerBy) * shortest_route_duration;
|
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|
|
|
|
|
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|
|
const auto over_duration_limit = [=](const auto &route) {
|
|
|
|
|
return route.duration() > stretch_duration_limit;
|
|
|
|
@@ -559,6 +641,7 @@ void unpackPackedPaths(InputIt first,
|
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|
|
|
}
|
|
|
|
|
|
|
|
|
|
WeightedViaNodeUnpackedPath unpacked_path{
|
|
|
|
|
0.0,
|
|
|
|
|
WeightedViaNode{packed_path_via, packed_path_weight},
|
|
|
|
|
std::move(unpacked_nodes),
|
|
|
|
|
std::move(unpacked_edges)};
|
|
|
|
@@ -573,7 +656,8 @@ void unpackPackedPaths(InputIt first,
|
|
|
|
|
inline std::vector<WeightedViaNode>
|
|
|
|
|
makeCandidateVias(SearchEngineData<Algorithm> &search_engine_data,
|
|
|
|
|
const Facade &facade,
|
|
|
|
|
const PhantomNodes &phantom_node_pair)
|
|
|
|
|
const PhantomNodes &phantom_node_pair,
|
|
|
|
|
const Parameters ¶meters)
|
|
|
|
|
{
|
|
|
|
|
Heap &forward_heap = *search_engine_data.forward_heap_1;
|
|
|
|
|
Heap &reverse_heap = *search_engine_data.reverse_heap_1;
|
|
|
|
@@ -605,7 +689,7 @@ makeCandidateVias(SearchEngineData<Algorithm> &search_engine_data,
|
|
|
|
|
while (forward_heap.Size() + reverse_heap.Size() > 0)
|
|
|
|
|
{
|
|
|
|
|
if (shortest_path_weight != INVALID_EDGE_WEIGHT)
|
|
|
|
|
overlap_weight = shortest_path_weight * kSearchSpaceOverlapFactor;
|
|
|
|
|
overlap_weight = shortest_path_weight * parameters.kSearchSpaceOverlapFactor;
|
|
|
|
|
|
|
|
|
|
// Termination criteria - when we have a shortest path this will guarantee for our overlap.
|
|
|
|
|
const bool keep_going = forward_heap_min + reverse_heap_min < overlap_weight;
|
|
|
|
@@ -670,7 +754,7 @@ makeCandidateVias(SearchEngineData<Algorithm> &search_engine_data,
|
|
|
|
|
return candidate_vias;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
} // anon. ns
|
|
|
|
|
} // namespace
|
|
|
|
|
|
|
|
|
|
// Alternative Routes for MLD.
|
|
|
|
|
//
|
|
|
|
@@ -691,9 +775,11 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
const PhantomNodes &phantom_node_pair,
|
|
|
|
|
unsigned number_of_alternatives)
|
|
|
|
|
{
|
|
|
|
|
Parameters parameters = parametersFromRequest(phantom_node_pair);
|
|
|
|
|
|
|
|
|
|
const auto max_number_of_alternatives = number_of_alternatives;
|
|
|
|
|
const auto max_number_of_alternatives_to_unpack =
|
|
|
|
|
kAlternativesToUnpackFactor * max_number_of_alternatives;
|
|
|
|
|
parameters.kAlternativesToUnpackFactor * max_number_of_alternatives;
|
|
|
|
|
BOOST_ASSERT(max_number_of_alternatives > 0);
|
|
|
|
|
BOOST_ASSERT(max_number_of_alternatives_to_unpack >= max_number_of_alternatives);
|
|
|
|
|
|
|
|
|
@@ -707,7 +793,8 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
Heap &reverse_heap = *search_engine_data.reverse_heap_1;
|
|
|
|
|
|
|
|
|
|
// Do forward and backward search, save search space overlap as via candidates.
|
|
|
|
|
auto candidate_vias = makeCandidateVias(search_engine_data, facade, phantom_node_pair);
|
|
|
|
|
auto candidate_vias =
|
|
|
|
|
makeCandidateVias(search_engine_data, facade, phantom_node_pair, parameters);
|
|
|
|
|
|
|
|
|
|
const auto by_weight = [](const auto &lhs, const auto &rhs) { return lhs.weight < rhs.weight; };
|
|
|
|
|
auto shortest_path_via_it =
|
|
|
|
@@ -730,6 +817,9 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
NodeID shortest_path_via = shortest_path_via_it->node;
|
|
|
|
|
EdgeWeight shortest_path_weight = shortest_path_via_it->weight;
|
|
|
|
|
|
|
|
|
|
const double duration_estimation = shortest_path_weight / facade.GetWeightMultiplier();
|
|
|
|
|
parameters.kAtMostLongerBy = getLongerByFactorBasedOnDuration(duration_estimation);
|
|
|
|
|
|
|
|
|
|
// Filters via candidate nodes with heuristics
|
|
|
|
|
|
|
|
|
|
// Note: filter pipeline below only makes range smaller; no need to erase items
|
|
|
|
@@ -738,8 +828,7 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
|
|
|
|
|
it = filterViaCandidatesByUniqueNodeIds(begin(candidate_vias), it);
|
|
|
|
|
it = filterViaCandidatesByRoadImportance(begin(candidate_vias), it, facade);
|
|
|
|
|
it = filterViaCandidatesByStretch(
|
|
|
|
|
begin(candidate_vias), it, shortest_path_weight, facade.GetWeightMultiplier());
|
|
|
|
|
it = filterViaCandidatesByStretch(begin(candidate_vias), it, shortest_path_weight, parameters);
|
|
|
|
|
|
|
|
|
|
// Pre-rank by weight; sharing filtering below then discards by similarity.
|
|
|
|
|
std::sort(begin(candidate_vias), it, [](const auto lhs, const auto rhs) {
|
|
|
|
@@ -783,10 +872,10 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
forward_heap, // paths for s, via
|
|
|
|
|
reverse_heap, // paths for via, t
|
|
|
|
|
begin(weighted_packed_paths) + 1,
|
|
|
|
|
alternative_paths_last);
|
|
|
|
|
|
|
|
|
|
alternative_paths_last,
|
|
|
|
|
parameters);
|
|
|
|
|
alternative_paths_last = filterPackedPathsByCellSharing(
|
|
|
|
|
begin(weighted_packed_paths), alternative_paths_last, partition);
|
|
|
|
|
begin(weighted_packed_paths), alternative_paths_last, partition, parameters);
|
|
|
|
|
|
|
|
|
|
BOOST_ASSERT(weighted_packed_paths.size() >= 1);
|
|
|
|
|
|
|
|
|
@@ -816,7 +905,8 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
|
|
|
|
|
auto unpacked_paths_last = end(unpacked_paths);
|
|
|
|
|
|
|
|
|
|
unpacked_paths_last = filterUnpackedPathsBySharing(begin(unpacked_paths), end(unpacked_paths));
|
|
|
|
|
unpacked_paths_last = filterUnpackedPathsBySharing(
|
|
|
|
|
begin(unpacked_paths), end(unpacked_paths), facade, parameters);
|
|
|
|
|
|
|
|
|
|
const auto unpacked_paths_first = begin(unpacked_paths);
|
|
|
|
|
const auto number_of_unpacked_paths =
|
|
|
|
@@ -850,7 +940,9 @@ InternalManyRoutesResult alternativePathSearch(SearchEngineData<Algorithm> &sear
|
|
|
|
|
|
|
|
|
|
if (routes.size() > 1)
|
|
|
|
|
{
|
|
|
|
|
routes_last = filterAnnotatedRoutesByStretch(routes_first + 1, routes_last, *routes_first);
|
|
|
|
|
parameters.kAtMostLongerBy = getLongerByFactorBasedOnDuration(routes_first->duration());
|
|
|
|
|
routes_last = filterAnnotatedRoutesByStretch(
|
|
|
|
|
routes_first + 1, routes_last, *routes_first, parameters);
|
|
|
|
|
routes.erase(routes_last, end(routes));
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|