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Multi-objective Optimization Approach to Malfatti's Problem
In this work, we consider the multi-objective optimization problem
based on the circle packing problem, particularly, extended Malfatti's
problem (Enkhbat, 2020) with k disks. Malfatti's problem was examined
for the first time from a view point of global optimization theory and algorithm
in (Enkhbat, 2016). Also, a game theory approach has been applied
to Malfatti's problem in (Enkhbat and Battur, 2021). In this paper, we apply
the the multi-objective optimization approach to the problem. Using the
weighted sum method, we reduce this problem to optimization problem with
nonconvex constraints. For solving numerically the weighted sum optimization
problem, we apply KKT conditions and find Pareto stationary points.
Also, we estimate upper bounds of the global value of the objective function
by Lagrange duality. Numerical results are provided