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In this paper, we proposed a multi-objective Pareto based particle swarm optimization (MOPPSO) to minimize the architectural complexity and maximize the classification accuracy of a polynomial neural network (PNN). To support this, we provide an extensive review of the literature on multi-objective particle swarm optimization and PNN. Classification using PNN can be considered as a multi-objective problem rather than as a single objective one. Measures like classification accuracy and architectural complexity used for evaluating PNN based classification can be thought of as two different conflicting criterions. Using these two metrics as the criteria of classification problem, the proposed MOPPSO technique attempts to find out a set of non-dominated solutions with less complex PNN architecture and high classification accuracy. An extensive experimental study has been carried out to compare the importance and effectiveness of the proposed method with the chosen state-of-the-art multi-objective particle swarm optimization (MOPSO) algorithm using several benchmark datasets. A comprehensive bibliography is included for further enhancement of this area.