To optimize the provided PostgreSQL SQL queries, we need to address several potential performance bottlenecks. These can include improving join conditions, using appropriate indexing, and optimizing the functions and expressions used in the queries. Here's a step-by-step breakdown of the optimizations we can apply:

 1 Creating Indexes: Ensure that the tables used in join conditions and where clauses have indexes on the relevant columns. This will significantly speed up the join operations and filtering.


 CREATE INDEX idx_relations_osm_id ON origin_osm.relations(osm_id);
 CREATE INDEX idx_relation_members_parent_id ON origin_osm.relation_members(parent_id);
 CREATE INDEX idx_relation_members_osm_id ON origin_osm.relation_members(osm_id);
 CREATE INDEX idx_relation_members_member_type ON origin_osm.relation_members(member_type);
 CREATE INDEX idx_ways_osm_id ON origin_osm.ways(osm_id);
 CREATE INDEX idx_ways_tags_landuse ON origin_osm.ways USING GIN (tags);
 CREATE INDEX idx_relations_tags_landuse ON origin_osm.relations USING GIN (tags);
 CREATE INDEX idx_forests_simplified_geometry ON proc_osm.forests_simplified USING GIST (geometry);
 CREATE INDEX idx_forests_simplified_area ON proc_osm.forests_simplified USING BTREE (ST_Area(geometry));


 2 Optimizing Multipolygons Query: Optimize the join conditions and predicates in the first materialized view creation.


 CREATE MATERIALIZED VIEW IF NOT EXISTS proc_osm.multipolygon_relations AS (
     SELECT r.osm_id, ST_BuildArea(ST_Collect(w.geometry)) AS geometry
     FROM origin_osm.relations r
     JOIN origin_osm.relation_members rm ON r.osm_id = rm.parent_id AND rm.member_type = 1
     JOIN origin_osm.ways w ON rm.osm_id = w.osm_id
     WHERE r.relation_type = 'multipolygon'
     GROUP BY r.osm_id
 ) WITH NO DATA;


 3 Optimizing Forests Simplified Query: Ensure the query is logically separated for better readability and performance.


 CREATE MATERIALIZED VIEW IF NOT EXISTS proc_osm.forests_simplified AS (
     WITH forest_ways AS (
         SELECT w.osm_id
         FROM origin_osm.ways w
         WHERE w.tags -> 'landuse' = 'forest' OR w.tags -> 'natural' = 'wood'
     ),
     forest_relations AS (
         SELECT r.osm_id
         FROM origin_osm.relations r
         WHERE (r.tags -> 'landuse' = 'forest' OR r.tags -> 'natural' = 'wood')
           AND r.relation_type = 'multipolygon'
     ),
     all_forests AS (
         SELECT w.osm_id,
                CASE WHEN NOT ST_IsValid(ST_BuildArea(w.geometry)) THEN
                     ST_MakeValid(ST_BuildArea(w.geometry), 'method=structure')
                ELSE ST_BuildArea(w.geometry)
                END AS geometry,
                1 AS element_type
         FROM forest_ways
         JOIN origin_osm.ways w ON forest_ways.osm_id = w.osm_id
         UNION ALL
         SELECT fr.osm_id,
                m.geometry,
                2 AS element_type
         FROM forest_relations fr
         JOIN proc_osm.multipolygon_relations m ON fr.osm_id = m.osm_id
     )
     SELECT af.osm_id,
            ST_SimplifyPreserveTopology(af.geometry, 100) AS geometry,
            af.element_type
     FROM all_forests af
     WHERE af.geometry IS NOT NULL
 ) WITH NO DATA;


 4 Optimizing Forests Simplified with Areas Query: Avoid calculating area for each cluster multiple times.


 CREATE MATERIALIZED VIEW IF NOT EXISTS proc_osm.forests_simplified_with_areas AS (
     WITH clustered_forests AS (
         SELECT fs.osm_id,
                fs.geometry,
                ST_ClusterDBSCAN(fs.geometry, 100, 2) OVER () AS cluster_id
         FROM proc_osm.forests_simplified fs
         WHERE ST_Area(fs.geometry) > 0
     ),
     forest_area_for_cluster_id AS (
         SELECT cf.cluster_id,
                SUM(ST_Area(ST_Transform(cf.geometry, 4326)::geography)) AS total_area
         FROM clustered_forests cf
         WHERE cf.cluster_id IS NOT NULL
         GROUP BY cf.cluster_id
     )
     SELECT cf.geometry,
            cf.osm_id,
            COALESCE(fa.total_area, ST_Area(ST_Transform(cf.geometry, 4326)::geography)) AS total_area,
            cf.cluster_id
     FROM clustered_forests cf
     LEFT JOIN forest_area_for_cluster_id fa ON fa.cluster_id = cf.cluster_id
 ) WITH NO DATA;


 5 Optimizing Relevant Forests Simplified Query: Shorten the query with relevant filtering.


 CREATE MATERIALIZED VIEW IF NOT EXISTS proc_osm.relevant_forests_simplified AS (
     SELECT fsa.geometry,
            fsa.osm_id,
            fsa.total_area,
            fsa.cluster_id
     FROM proc_osm.forests_simplified_with_areas fsa
     WHERE fsa.total_area > 500000
 ) WITH NO DATA;


By creating indexes on columns frequently used in joins and where clauses, and optimizing the use of logical constructs in the queries, we significantly improve query performance. These changes should address common bottlenecks and enhance the overall speed.