After finishing Gymnasium in Zagreb, he studied Theoretical Physics at the University of Zagreb during 1949–1953 and studied for Ph.
Kostrena is well known by its maritime tradition, shipowners and seamen. Randic"s ancestors were sailing ship owners as well as ship captains. Doctorate degree at the University of Cambridge, England (1954–1958).
From 1960 to 1970 he was at the Ruđer Bošković Institute in Zagreb, Croatia, where he founded the Theoretical Chemistry Group.
During 1971–1980 he was visiting various universities in United States of America including Johns Hopkins, Massachusetts Institute of Technology, Harvard, Tufts, and Cornell. With 1973 his research oriented towards application of Discrete Mathematics and Graph Theory in particular to characterization of molecules and bio-molecules.
During 1980 to 1997 he was professor in the Department of Mathematics and Computer Science at Drake University, Des Moines, Iowa. During the past 15 years he is spending three months each year at the National Institute of Chemistry, Ljubljana, Slovenia collaborating with scientists from its Laboratory for Chemometrics.
He is Honorary Member of The Croatian Chemical Society, The International Academy of Mathematical Chemistry and The National Institute of Chemistry, Ljubljana, Slovenia.
Married Mirjana Jovic, October 8, 1960. 1 child Velimir.