For constrained multi-objective optimization problems (CMOPs), how to preserve infeasible individuals and make use of them is a problem to be solved. In this case, a modified objective function method with feasible-gu...
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For constrained multi-objective optimization problems (CMOPs), how to preserve infeasible individuals and make use of them is a problem to be solved. In this case, a modified objective function method with feasible-guiding strategy on the basis of NSGA-II is proposed to handle CMOPs in this paper. The main idea of proposed algorithm is to modify the objectivefunction values of an individual with its constraint violation values and true objectivefunction values, of which a feasibility ratio fed back from current population is used to keep the balance, and then the feasible-guiding strategy is adopted to make use of preserved infeasible individuals. In this way, non-dominated solutions, obtained from proposed algorithm, show superiority on convergence and diversity of distribution, which can be confirmed by the comparison experiment results with other two CMOEAs on commonly used constrained test problems. Crown Copyright (C) 2013 Published by Elsevier B.V. All rights reserved.
In this paper, we use the modified objective function method for a class of nonconvex multiobjective variational problems involving univex functions. Under univexity hypotheses, we prove the equivalence between an (we...
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In this paper, we use the modified objective function method for a class of nonconvex multiobjective variational problems involving univex functions. Under univexity hypotheses, we prove the equivalence between an (weakly) efficient solution of the considered multiobjective variational problem and an (weakly) efficient solution of the associated modified multiobjective variational problem constructed in the modified objective function method.
The purpose of this paper is to provide the linearization technique to solve the multidimensional control optimization problem (MCOP) involving first-order partial differential equation (PDEs) constraints. Firstly, we...
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The purpose of this paper is to provide the linearization technique to solve the multidimensional control optimization problem (MCOP) involving first-order partial differential equation (PDEs) constraints. Firstly, we use the modifiedobjectivefunction approach for simplifying the aforesaid extremum problem (MCOP) and show that the solution sets of the original control optimization problem and its modified control optimization problem (MCOP) Omega$$ {}_{\Omega} $$ are equivalent under convexity assumptions. Further, we use the absolute value exact penalty functionmethod to transform (MCOP) Omega$$ {}_{\Omega} $$ into a penalized control problem (MCOP) Omega & rhov;$$ {}_{\Omega \varrho } $$. Then, we establish the equivalence between a minimizer of the modified penalized optimization problem (MCOP) Omega & rhov;$$ {}_{\Omega \varrho } $$ and a saddle point of the Lagrangian defined for the modified optimization problem (MCOP) Omega$$ {}_{\Omega} $$ under appropriate convexity hypotheses. Moreover, the results established in the paper are illustrated by some examples of MCOPs involving first-order PDEs constraints.
In this article, for a given class of multi-dimensional scalar variational control problems (named (P)) with mixed constraints implying second-order partial differential equations and inequations, we introduce an auxi...
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In this article, for a given class of multi-dimensional scalar variational control problems (named (P)) with mixed constraints implying second-order partial differential equations and inequations, we introduce an auxiliary (modified) class of variational control problems (named (P)(b?,c?)), which is much easier to study, and provide some characterization results of (P) and (P)(b?,c?) by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to (P)(b?,c?). For this aim, we consider scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian.
This paper aims to find a solution of interval uncertainty to multiobjective variational problems. For this, we consider an interval -valued multiobjective variational problem. Then, by using the modified F -objective...
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This paper aims to find a solution of interval uncertainty to multiobjective variational problems. For this, we consider an interval -valued multiobjective variational problem. Then, by using the modified F -objectivefunctionmethod, we construct associated interval -valued multiobjective variational problem with the modified F -objectivefunctions. We establish a relationship between LU-pareto optimal solution of original problem and its associated modified problem by using the concept of LU-F-convexity and LU-F-pseudoconvexity. Further, we define LULagrange function and its saddle point to discuss the efficient solution of original problem through it. We provide an example to validate our results numerically.
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