I'm using the pgr_astar function of Postgres and I want to personalize the optimal path proposed according to the preferences of the user. For example if the pg_astar propose the red path, I want to make this function propose the orange path if I specify that the user wants to go through the blue point.
If you know, that the route should go through the blue point, then you could use
SELECT * FROM pgr_dijkstraVia( 'SELECT id, source, target, cost, reverse_cost FROM edge_table order by id', ARRAY[1, 2, 3] );
Where 1, 2 and 3 are your vertex ID's and "2" is the blue point.
This is function uses Dijkstra and not A-Star, but I'm not aware of a strong reason not to use Dijkstra.