This paper deals with the Alienor method to tackle multiobjective nonlinear optimization problems. In this approach, the multiple criteria of the optimization problem are aggregated into a single one using weighted su...This paper deals with the Alienor method to tackle multiobjective nonlinear optimization problems. In this approach, the multiple criteria of the optimization problem are aggregated into a single one using weighted sums. Then, the resulting single objective nonlinear optimization problem is solved using the Alienor method associated with the Optimization Preserving Operators technique which has proved to be suitable for (nonlinear) optimization problems with a large number of variables (see [1]). The proposed approach is evaluated through test problems. The results show that the approach provides good approximations of the Pareto front while requiring small computational time, even for large instances.展开更多
Purpose-A recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method.A progressive focusing on the most promising region,in combination with a variation of the density o...Purpose-A recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method.A progressive focusing on the most promising region,in combination with a variation of the density of the alpha-dense curve,is proposed.Design/methodology/approach-ALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve:the curvilinear abscissa along the curve becomes the only design parameter for any design space.As a counterpart,the transformation of the objective function in the projected space is much more difficult to tackle.Findings-A fine tuning of the procedure has been performed in order to identity the correct balance between the different elements of the procedure.The proposed approach has been tested by using a set of algebraic functions with up to 1,024 design variables,demonstrating the ability of the method in solving large scale optimization problem.Also an industrial application is presented.Originality/value-In the knowledge of the author there is not a similar paper in the current literature.展开更多
文摘This paper deals with the Alienor method to tackle multiobjective nonlinear optimization problems. In this approach, the multiple criteria of the optimization problem are aggregated into a single one using weighted sums. Then, the resulting single objective nonlinear optimization problem is solved using the Alienor method associated with the Optimization Preserving Operators technique which has proved to be suitable for (nonlinear) optimization problems with a large number of variables (see [1]). The proposed approach is evaluated through test problems. The results show that the approach provides good approximations of the Pareto front while requiring small computational time, even for large instances.
基金Acknowledgements:The author would like to thank the Italian Minister of Instruction,University and Research(MIUR)to support this research with funds coming from PRIN Project 2017(No.2017KKJP4X entitled“Innovative numerical methods for evolutionary partial differential equations and applications”).
文摘Purpose-A recursive scheme for the ALIENOR method is proposed as a remedy for the difficulties induced by the method.A progressive focusing on the most promising region,in combination with a variation of the density of the alpha-dense curve,is proposed.Design/methodology/approach-ALIENOR method is aimed at reducing the space dimensions of an optimization problem by spanning it by using a single alpha-dense curve:the curvilinear abscissa along the curve becomes the only design parameter for any design space.As a counterpart,the transformation of the objective function in the projected space is much more difficult to tackle.Findings-A fine tuning of the procedure has been performed in order to identity the correct balance between the different elements of the procedure.The proposed approach has been tested by using a set of algebraic functions with up to 1,024 design variables,demonstrating the ability of the method in solving large scale optimization problem.Also an industrial application is presented.Originality/value-In the knowledge of the author there is not a similar paper in the current literature.
