The multi-criteria problem of shape optimization of a moving punch under integral constraint on the total force of contact pressure is considered. The punch motion is investigated in a quasistatic formulation taking into account the friction forces and wear of the material. All investigations are in the frame of optimization problem formulations with vector functionals and based on the concept of Pareto optimization. As a multi-criteria problem, the following quantities are minimized: the friction dissipation power, the wear rate of material, the wear dissipation power and the discrepancy between the given pressure distribution and the actual realization. A family of Pareto-optimal solutions is constructed for various values of weighting coefficients.
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