diff --git a/test/yulPhaser/Population.cpp b/test/yulPhaser/Population.cpp
index 0cb0fe29f..12555845c 100644
--- a/test/yulPhaser/Population.cpp
+++ b/test/yulPhaser/Population.cpp
@@ -48,6 +48,14 @@ namespace solidity::phaser::test
 class PopulationFixture
 {
 protected:
+	static ChromosomePair twoStepSwap(Chromosome const& _chromosome1, Chromosome const& _chromosome2)
+	{
+		return ChromosomePair{
+			Chromosome(vector<string>{_chromosome1.optimisationSteps()[0], _chromosome2.optimisationSteps()[1]}),
+			Chromosome(vector<string>{_chromosome2.optimisationSteps()[0], _chromosome1.optimisationSteps()[1]}),
+		};
+	}
+
 	shared_ptr<FitnessMetric> m_fitnessMetric = make_shared<ChromosomeLengthMetric>();
 };
 
@@ -309,6 +317,53 @@ BOOST_FIXTURE_TEST_CASE(crossover_should_return_empty_population_if_selection_is
 	BOOST_TEST(population.crossover(selection, fixedPointCrossover(0.5)).individuals().empty());
 }
 
+BOOST_FIXTURE_TEST_CASE(symmetricCrossoverWithRemainder_should_return_crossed_population_and_remainder, PopulationFixture)
+{
+	Population population(m_fitnessMetric, {Chromosome("aa"), Chromosome("cc"), Chromosome("gg"), Chromosome("hh")});
+	PairMosaicSelection selection({{2, 1}}, 0.25);
+	assert(selection.materialise(population.individuals().size()) == (vector<tuple<size_t, size_t>>{{2, 1}}));
+
+	Population expectedCrossedPopulation(m_fitnessMetric, {Chromosome("gc"), Chromosome("cg")});
+	Population expectedRemainder(m_fitnessMetric, {Chromosome("aa"), Chromosome("hh")});
+
+	BOOST_TEST(
+		population.symmetricCrossoverWithRemainder(selection, twoStepSwap) ==
+		(tuple<Population, Population>{expectedCrossedPopulation, expectedRemainder})
+	);
+}
+
+BOOST_FIXTURE_TEST_CASE(symmetricCrossoverWithRemainder_should_allow_crossing_the_same_individual_multiple_times, PopulationFixture)
+{
+	Population population(m_fitnessMetric, {Chromosome("aa"), Chromosome("cc"), Chromosome("gg"), Chromosome("hh")});
+	PairMosaicSelection selection({{0, 0}, {2, 1}}, 1.0);
+	assert(selection.materialise(population.individuals().size()) == (vector<tuple<size_t, size_t>>{{0, 0}, {2, 1}, {0, 0}, {2, 1}}));
+
+	Population expectedCrossedPopulation(m_fitnessMetric, {
+		Chromosome("aa"), Chromosome("aa"),
+		Chromosome("aa"), Chromosome("aa"),
+		Chromosome("gc"), Chromosome("cg"),
+		Chromosome("gc"), Chromosome("cg"),
+	});
+	Population expectedRemainder(m_fitnessMetric, {Chromosome("hh")});
+
+	BOOST_TEST(
+		population.symmetricCrossoverWithRemainder(selection, twoStepSwap) ==
+		(tuple<Population, Population>{expectedCrossedPopulation, expectedRemainder})
+	);
+}
+
+BOOST_FIXTURE_TEST_CASE(symmetricCrossoverWithRemainder_should_return_empty_population_if_selection_is_empty, PopulationFixture)
+{
+	Population population(m_fitnessMetric, {Chromosome("aa"), Chromosome("cc")});
+	PairMosaicSelection selection({}, 0.0);
+	assert(selection.materialise(population.individuals().size()).empty());
+
+	BOOST_TEST(
+		population.symmetricCrossoverWithRemainder(selection, twoStepSwap) ==
+		(tuple<Population, Population>{Population(m_fitnessMetric), population})
+	);
+}
+
 BOOST_AUTO_TEST_SUITE_END()
 BOOST_AUTO_TEST_SUITE_END()
 
diff --git a/tools/yulPhaser/Population.cpp b/tools/yulPhaser/Population.cpp
index b336daf73..acdae1eb7 100644
--- a/tools/yulPhaser/Population.cpp
+++ b/tools/yulPhaser/Population.cpp
@@ -117,6 +117,37 @@ Population Population::crossover(PairSelection const& _selection, function<Cross
 	return Population(m_fitnessMetric, crossedIndividuals);
 }
 
+tuple<Population, Population> Population::symmetricCrossoverWithRemainder(
+	PairSelection const& _selection,
+	function<SymmetricCrossover> _symmetricCrossover
+) const
+{
+	vector<int> indexSelected(m_individuals.size(), false);
+
+	vector<Individual> crossedIndividuals;
+	for (auto const& [i, j]: _selection.materialise(m_individuals.size()))
+	{
+		auto children = _symmetricCrossover(
+			m_individuals[i].chromosome,
+			m_individuals[j].chromosome
+		);
+		crossedIndividuals.emplace_back(move(get<0>(children)), *m_fitnessMetric);
+		crossedIndividuals.emplace_back(move(get<1>(children)), *m_fitnessMetric);
+		indexSelected[i] = true;
+		indexSelected[j] = true;
+	}
+
+	vector<Individual> remainder;
+	for (size_t i = 0; i < indexSelected.size(); ++i)
+		if (!indexSelected[i])
+			remainder.emplace_back(m_individuals[i]);
+
+	return {
+		Population(m_fitnessMetric, crossedIndividuals),
+		Population(m_fitnessMetric, remainder),
+	};
+}
+
 namespace solidity::phaser
 {
 
diff --git a/tools/yulPhaser/Population.h b/tools/yulPhaser/Population.h
index cf82a5aa8..2d79dfef2 100644
--- a/tools/yulPhaser/Population.h
+++ b/tools/yulPhaser/Population.h
@@ -100,6 +100,10 @@ public:
 	Population select(Selection const& _selection) const;
 	Population mutate(Selection const& _selection, std::function<Mutation> _mutation) const;
 	Population crossover(PairSelection const& _selection, std::function<Crossover> _crossover) const;
+	std::tuple<Population, Population> symmetricCrossoverWithRemainder(
+		PairSelection const& _selection,
+		std::function<SymmetricCrossover> _symmetricCrossover
+	) const;
 
 	friend Population operator+(Population _a, Population _b);