A simple method of parameter-free Paretian optimisation is proposed in order to explore shapes of the unknown boundary of a synthesis region, in the search for the family of optimal shapes fulfilling a prescribed set of conflicting objective functions. To this end, a velocity-time law, related to the objective functions, governs the motion of a set of nodes located along the synthesis region boundary. The proposed method of optimal shape design conserves domain connectivity; moreover, because of the kinematic formulation, there is no need to solve the motion equation of the moving boundary. This way, the computational cost of the proposed method is low, and the advantage of a broad search space – inherent in the parameter-free approach – is preserved. To assess the method, a case study of inverse induction-heating is considered; the associated field problem is solved by means of finite-element analysis.
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