Robust Optimization for Multiobjective Programming Problems with Imprecise Information

AbstractA robust optimization approach is proposed for generating nondominated robust solutions for multiobjective linear programming problems with imprecise coefficients in the objective functions and constraints. Robust optimization is used in dealing with impreciseness while an interactive procedure is used in eliciting preference information from the decision maker and in making tradeoffs among the multiple objectives. Robust augmented weighted Tchebycheff programs are formulated from the multiobjective linear programming model using the concept of budget of uncertainty. A linear counterpart of the robust augmented weighted Tchebycheff program is derived. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs

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

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.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie SkłodowskaCurie grant agreement No. 734205 – H2020-MSCA-RISE-2016