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In recent years, a number of authors have successfully extended particle swarmoptimization to problem domains with multiple objec\-tives. This paper addresses theissue of parallelizing multi-objec\-tive particle swarms. We propose and empirically comparetwo parallel versions which differ in the way they divide the swarminto subswarms that can be processed independently on differentprocessors. One of the variants works asynchronouslyand is thus particularly suitable for heterogeneous computer clusters asoccurring e.g.\ in moderngrid computing platforms.