[1] In 2009, he tied for 1st–5th with Sergey Volkov, Andrey Rychagov, Andrei Deviatkin, and Zhou Weiqi in the Chigorin Memorial.

[2] In 2010, tied for 1st–8th with Sergey Volkov, Viorel Iordăchescu, Eduardo Iturrizaga, Gadir Guseinov, David Arutinian, Aleksej Aleksandrov, and Tornike Sanikidze in the 12th Dubai Open.

[6] In December 2011 Melkumyan tied for 1st–3rd with Alexey Dreev and Radosław Wojtaszek in the European Blitz Chess Championship and won the event on tie-break.

[7] In January 2012 he won the 2nd Armenian Chess960 Championship[8] and in February 2012 tied for 4th–8th with Alexander Khalifman, Maxim Rodshtein, Fabiano Caruana, and Dmitry Andreikin in the 11th Aeroflot Open.

In 2017, he shared 1st–3rd places with Gabriel Sargissian and Sebastien Maze in 9th CSC London Chess Classic FIDE Open.