In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the mult...In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.展开更多
The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of ...The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.展开更多
Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimi...Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.展开更多
This paper proposes an optimization method for finding the optimal design of a bistable mechanism with a desired performance that is robust to structural and material uncertainties.Using interval numbers to characteri...This paper proposes an optimization method for finding the optimal design of a bistable mechanism with a desired performance that is robust to structural and material uncertainties.Using interval numbers to characterize the uncertainties in the structural parameters and materials,we present a nonprobabilistic multiobjective optimization model and transform it into a single objective optimization model using a penalty function.The sensitivity of the mechanical performance of bistable structures to uncertain parameters was analyzed,and the design parameters with notable effects on the bistable performance were identified as optimization variables.A neural network-based proxy model for the nonlinear characteristics of the bistable mechanism was established,and its accuracy was validated through finite element outcomes.Based on this model,a two-layer nested genetic algorithm was employed to solve the multiobjective robust optimization problem of the bistable structures with critical forces and a second stable position.The effectiveness of the optimization method was verified by comparing it with the finite element and experimental results.The proposed method was applied in the design of silicon-based inertial switches.展开更多
文摘In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.
基金Taif University Researchers Supporting Project number(TURSP-2020/20),Taif University,Taif,Saudi Arabia。
文摘The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.
文摘Many Optimization problems in engineering and economic involve the challenging task of pondering both conflicting goals and random data. In this paper, we give an up-to-date overview of how important ideas from optimization, probability theory and multicriteria decision analysis are interwoven to address situations where the presence of several objective functions and the stochastic nature of data are under one roof in a linear optimization context. In this way users of these models are not bound to caricature their problems by arbitrarily squeezing different objective functions into one and by blindly accepting fixed values in lieu of imprecise ones.
基金supported by the National Key Research and Development Program of China(Grant No.2022YFB3204800)the National Natural Science Foundation of China(Grant No.52375573)the Youth Innovation Team of Shanxi Universities(Grant No.2022-63)。
文摘This paper proposes an optimization method for finding the optimal design of a bistable mechanism with a desired performance that is robust to structural and material uncertainties.Using interval numbers to characterize the uncertainties in the structural parameters and materials,we present a nonprobabilistic multiobjective optimization model and transform it into a single objective optimization model using a penalty function.The sensitivity of the mechanical performance of bistable structures to uncertain parameters was analyzed,and the design parameters with notable effects on the bistable performance were identified as optimization variables.A neural network-based proxy model for the nonlinear characteristics of the bistable mechanism was established,and its accuracy was validated through finite element outcomes.Based on this model,a two-layer nested genetic algorithm was employed to solve the multiobjective robust optimization problem of the bistable structures with critical forces and a second stable position.The effectiveness of the optimization method was verified by comparing it with the finite element and experimental results.The proposed method was applied in the design of silicon-based inertial switches.
