The parameters of foaming and nano-clay percentage on the density of polymer foam and cell size with the PVC field is studied. Cell size and density have a significant impact on the strength of foam and its insulation (including sounds and thermal insulation). By optimizing cell size and density, foam can be produced with the best mechanical properties. In foaming process of the nanocomposite samples by mass method, the design variables (input parameters) are foaming time and temperature and MMT content. The controlled elitist multi-objective GA is applied to minimize both the foam density and the cell size. To that end, the population size and the Pareto fraction are selected as 100 and 0.5, respectively. The noninferior solution obtained by the controlled elitist multi-objective GA is illustrated. When both the MMT and the temperature are high, the resulting foam does not have ideal characteristics.
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