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Numerous traditional board games such as Backgammon, Chess, Tic-Tac-Toc, Othello, Checkers, and Go have been used as research test-beds for assessing the performance of myriad computational intelligence systems including evolutionary algorithms (EAs) and artificial neural networks (ANNs). Approaches included building intelligent search algorithms to find the required solutions in such board games by searching through the solutions space stochastically. Recently, one particular type of search algorithm has been receiving a lot of interest in solving such kinds of game problems, which is the multi-objective evolutionary algorithms (MOEAs). Unlike single-objective optimization based search algorithms, MOEAs are able to find a set of non-dominated solutions which trades-off among all the conflicting objectives. In this study, the utilization of a multi-objective approach in evolving ANNs for Go game is investigated. A simple three layered feed-forward ANN is used and evolved with Pareto Archived Evolution Strategies (PAES) for computer players to learn and play the small board Go games.