In the network shortest path interdiction problem, an evader attempts to find the shortest path between the origin and the destination in a network, while an interdictor attempts to maximize the length of this shortes...
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In the network shortest path interdiction problem, an evader attempts to find the shortest path between the origin and the destination in a network, while an interdictor attempts to maximize the length of this shortest path by interdicting network arcs with limited resources. Therefore, the problem can be formulated as a bi-level programming problem. Existing methods for solving this problem have either low accuracy or slow convergence speed. To address this, in this article, we propose a new algorithm to overcome the above challenges by transforming the problem into an iterative generalized set coverage problem and then solving it by using zero-one linear programming. At each step of the iteration, we obtain a better solution than at the previous step by setting a fixed parameter to interdict a dynamic set regarding the possible interdiction paths. We rigorously prove that the iterative algorithm can converge to the optimal solution. Additionally, the convergence speed is significantly faster than those of baseline methods. For the fixed parameter setting problem, we also propose a parameter adaptive algorithm to further accelerate the convergence speed. Finally, the excellent performance of the proposed algorithms is verified in randomly generated networks and real networks.
The maximum clique problems calls for determining the size of the largest clique in a given graph. This graph problem affords a number of zero-one linear programming formulations. In this case study we deal with some ...
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The maximum clique problems calls for determining the size of the largest clique in a given graph. This graph problem affords a number of zero-one linear programming formulations. In this case study we deal with some of these formulations. We consider ways for tightening the formulations. We carry out numerical experiments to see the improvements the tightened formulations provide.
Column generation is a linearprogramming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restr...
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Column generation is a linearprogramming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restricted master problem and a column generation subproblem. The latter step is founded on dual information from the former one;often an optimal dual solution to the linearprogramming relaxation of the restricted master problem is used. We consider a zero-one linear programming problem that is approached by column generation and present a generic sufficient optimality condition for the restricted master problem to contain the columns required to find an integer optimal solution to the complete problem. The condition is based on dual information, but not necessarily on an optimal dual solution. It is however most natural to apply the condition in a situation when an optimal or near-optimal dual solution is at hand. We relate our result to a few special cases from the literature, and make some suggestions regarding possible exploitation of the optimality condition in the construction of column generation methods for integer programs. (C) 2018 Elsevier B.V. All rights reserved.
Usually, companies confront the difficulty to make the best decision about the way to invest their recourses in different project alternatives. The company acquires competitive advantages when their software developme...
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Usually, companies confront the difficulty to make the best decision about the way to invest their recourses in different project alternatives. The company acquires competitive advantages when their software development projects are well evaluated and correctly selected. Selecting projects in the Information Technology field presents challenges in many senses;e.g., the difficulty that entails assessing intangible benefits, projects are interdependent and companies impose self-constraints. In addition, the framework to make the decision is generally uncertain with many unknown factors. This paper aims to propose a model that integrates methods, techniques and tools such as the Balanced Scorecard Model, neutrosophic Analytic Hierarchy Process and zero-one linear programming. The proposed model is designed to select the best portfolio of Information Technology projects, it overcomes the obstacles mentioned above and can be coherently incorporated in the strategic plan process of any company. In addition, it eases the course of experts' decision making, because it is based on Neutrosophy and hence incorporates the indeterminacy term.
This paper is main to find the best way to make a plan about the generators operation. Firstly, we describe all conditions as constraints exactly. Secondly, we simplify the models by using zero-one liner programming. ...
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ISBN:
(纸本)9781479934348
This paper is main to find the best way to make a plan about the generators operation. Firstly, we describe all conditions as constraints exactly. Secondly, we simplify the models by using zero-one liner programming. Thirdly, we use non-liner optimization and integer programming to create the objective function. Because of a great quantity of work, we use interior-point method as an example to increase efficiency. Also, we offer a way to get the optimum solution by using Lingo. The method and solving process provides a theories analysis foundation for optimization of generators and other
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