In this work, some reasoning's mistakes in the paper by Kohli (doi:10.3934/jimo.2020114) are highlighted. Furthermore, we correct the flaws, propose a correct formulation of the main result (Theorem 5.1) and give ...
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In this work, some reasoning's mistakes in the paper by Kohli (doi:10.3934/jimo.2020114) are highlighted. Furthermore, we correct the flaws, propose a correct formulation of the main result (Theorem 5.1) and give alter-native proofs.
This paper proposes a bilevel improved fruit fly optimization algorithm (BIFOA) to address the nonlinear bilevel programming problem (NBLPP). Considering the hierarchical nature of the problem, this algorithm is const...
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This paper proposes a bilevel improved fruit fly optimization algorithm (BIFOA) to address the nonlinear bilevel programming problem (NBLPP). Considering the hierarchical nature of the problem, this algorithm is constructed by combining two sole improved fruit fly optimization algorithms. In the proposed algorithm, the lower level problem is treated as a common nonlinear programmingproblem rather than being transformed into the constraints of the upper level problem. Eventually, 10 test problems are selected involving low-dimensional and high-dimensional problems to evaluate the performance of BIFOA from the aspects of the accuracy and stability of the solutions. The results of extensive numerical experiments and comparisons reveal that the proposed algorithm outperforms the compared algorithms and is significantly better than the methods presented in the literature;the proposed algorithm is an effective and comparable algorithm for NBLPP. (C) 2017 Elsevier B.V. All rights reserved.
The main aim of this paper is to establish sufficient optimality conditions using an upper estimate of Clarke subdifferential of value function and the concept of convexifactor for optimistic bilevelprogramming probl...
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The main aim of this paper is to establish sufficient optimality conditions using an upper estimate of Clarke subdifferential of value function and the concept of convexifactor for optimistic bilevel programming problems with convex and non-convex lower-level problems. For this purpose, the notions of asymptotic pseudoconvexity and asymptotic quasiconvexity are defined in terms of the convexifactors.
In this paper, we consider a kind of bilevel linear programmingproblem where the coefficients of both objective functions are fuzzy numbers. In order to deal with such a problem, the original problem can be approxima...
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In this paper, we consider a kind of bilevel linear programmingproblem where the coefficients of both objective functions are fuzzy numbers. In order to deal with such a problem, the original problem can be approximated by an interval bilevel programming problem in terms of the nearest interval approximation of a fuzzy number. Based on the Karush-Kuhn-Tucker (KKT) optimality conditions for the optimization problem with an interval-valued objective function, the interval bilevel programming problem can be converted into a single-level programmingproblem with an interval-value objective function. To minimize the interval objective function, the order relations of interval numbers are used to transform the uncertain single-objective optimization into a multi-objective optimization solved by global criteria method (GCM). Finally, illustrative numerical examples are provided to demonstrate the feasibility of the proposed approach.
bilevel programming problem (BLPP) is a NP-hard problem and very difficult to be resolved by using the classical method. This paper attempts to develop an efficient method based on improved bilevel particle swarm opti...
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bilevel programming problem (BLPP) is a NP-hard problem and very difficult to be resolved by using the classical method. This paper attempts to develop an efficient method based on improved bilevel particle swarm optimization algorithm (IBPSO) to deal with BLPP. The improved algorithm adopts dynamic self-adapting inertia weight and Cauchy distribution to ensure global search ability and faster convergence speed of IBPSO. IBPSO employs two improved PSO as a main program and a subprogram respectively. According to the interactive iterations of two improved PSO algorithms, IBPSO can solve BLPP without some assumptions of BLPP, such as the gradient information of the objective functions, the convexity of constraint regions, and so on. Twelve bilevelproblems in the literatures are employed to illustrate the performance of IBPSO and some comparisons are also given. The results demonstrate that the proposed algorithm IBPSO exhibits higher accuracy than other algorithms. Then IBPSO is adopted to solve two supply chain models proposed in this paper, and some features of the proposed bilevel model are given based on the experimental data. The results support the finding that IBPSO is effective in optimizing BLPP.
In this article, we introduce two versions of nonsmooth extension of Abadie constraint qualification in terms of convexifactors and Clarke subdifferential and employ the weaker one to develop new necessary Karush-Kuhn...
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In this article, we introduce two versions of nonsmooth extension of Abadie constraint qualification in terms of convexifactors and Clarke subdifferential and employ the weaker one to develop new necessary Karush-Kuhn-Tucker type optimality conditions for optimistic bilevel programming problem with convex lower-level problem, using an upper estimate of Clarke subdifferential of value function in variational analysis and the concept of convexifactor.
Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632-651, 2012). Recently, the same author corrected his results in the note (J Optim Theory ...
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Necessary optimality conditions for a bilevel optimization problem are given in the paper by Kohli (J Optim Theory Appl 152: 632-651, 2012). Recently, the same author corrected his results in the note (J Optim Theory Appl 181:706-707, 2019). In this work, we have pointed out that some of the new modifications are wrong. We correct the flaws and present an alternative proof for the main result.
In this paper, an algorithm is developed to solve an indefinite quadratic integer bilevel programming problem with bounded variables. The problem is solved by solving the relaxed problem. A mixed integer cut for findi...
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In this paper, an algorithm is developed to solve an indefinite quadratic integer bilevel programming problem with bounded variables. The problem is solved by solving the relaxed problem. A mixed integer cut for finding the integer solution of the given problem is developed. The algorithm is explained with the help of an example.
A method of constructing test problems for linear bilevel programming problems is presented. The method selects a vertex of the feasible region, 'far away' from the solution of the relaxed linear programming p...
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A method of constructing test problems for linear bilevel programming problems is presented. The method selects a vertex of the feasible region, 'far away' from the solution of the relaxed linear programmingproblem, as the global solution of the bilevelproblem. A predetermined number of constraints are systematically selected to be assigned to the lower problem. The proposed method requires only local vertex search and solutions to linear programs.
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