This thesis considers the fundamental problem of "partitioning" which is all- pervasive in computer science. It has applications in "Big Data" because the vast amounts of data encountered in "Big Data" applications cannot be processed in a sin- gle block, but are better analyzed when it is partitioned in various monolithic units. It also has direct applications in numerous areas including databases, process schedul- ing, mapping and image retrieval. In this research we consider a specific instantiation of the Object Partitioning Problem, namely the Equi-Partitioning Problem (EPP), in which the partitions are equi-sized. In particular we concentrate on the various Learn- ing Automata (LA)-based solutions. In this regard, the Object Migration Automata (OMA), and its variants have been the benchmark solutions.