A penalty scheme for the Tchebycheff scalarization method to optimize the single screw extrusion

Abstract

The polymer single screw extruder optimal design has been involving the optimization of six objectives. Multi-objective optimization methods, in particular those based on the weighted Tchebycheff Scalarization (wTS) function, have provided reasonable solutions in a way that good trade-offs between conflicting objectives are identified. In this work, a new penalty term is added to the wTS function aiming to guide the solution toward the Pareto front. The corresponding formulation works similarly to the penalty-based boundary intersection function. The goal of the proposed penalty parameter scheme is to balance convergence and diversity. Since six objectives are simultaneously optimized, the penalty scheme provides large as well as small penalty parameter values to enlarge the improving region. The results show that the set of solutions obtained by the penalty-based wTS algorithm can reasonably well cover the Pareto front.