Topic
Discrete optimization
About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.
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04 Jun 2008
TL;DR: Minmax Regret Combinatorial Optimization Problems with Interval Data.
Abstract: Minmax Regret Combinatorial Optimization Problems with Interval Data.- Problem Formulation.- Evaluation of Optimality of Solutions and Elements.- Exact Algorithms.- Approximation Algorithms.- Minmax Regret Minimum Selecting Items.- Minmax Regret Minimum Spanning Tree.- Minmax Regret Shortest Path.- Minmax Regret Minimum Assignment.- Minmax Regret Minimum s???t Cut.- Fuzzy Combinatorial Optimization Problem.- Conclusions and Open Problems.- Minmax Regret Sequencing Problems with Interval Data.- Problem Formulation.- Sequencing Problem with Maximum Lateness Criterion.- Sequencing Problem with Weighted Number of Late Jobs.- Sequencing Problem with the Total Flow Time Criterion.- Conclusions and Open Problems.- Discrete Scenario Representation of Uncertainty.
82 citations
TL;DR: In this paper, a flexible algorithm for solving nonlinear engineering design optimization problems involving zero-one, discrete, and continuous variables is presented, which restricts its search only to the permissible values of the variables, thereby reducing the search effort in converging near the optimum solution.
Abstract: A flexible algorithm for solving nonlinear engineering design optimization problems involving zero-one, discrete, and continuous variables is presented. The algorithm restricts its search only to the permissible values of the variables, thereby reducing the search effort in converging near the optimum solution. The efficiency and ease of application of the proposed method is demonstrated by solving four different mechanical design problems chosen from the optimization literature. These results are encouraging and suggest the use of the technique to other more complex engineering design problems.
81 citations
TL;DR: Analytical and discrete optimization approaches for routing an aircraft with variable radar cross‐section (RCS) subject to a constraint on the trajectory length have been developed and the impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples.
Abstract: The deterministic problem for finding an aircraft's optimal risk trajectory in a threat environment has been formulated. The threat is associated with the risk of aircraft detection by radars or similar sensors. The model considers an aircraft's trajectory in three-dimensional (3-D) space and represents the aircraft by a symmetrical ellipsoid with the axis of symmetry directing the trajectory. Analytical and discrete optimization approaches for routing an aircraft with variable radar cross-section (RCS) subject to a constraint on the trajectory length have been developed. Through techniques of Calculus of Variations, the analytical approach reduces the original risk optimization problem to a vectorial nonlinear differential equation. In the case of a single detecting installation, a solution to this equation is expressed by a quadrature. A network optimization approach reduces the original problem to the Constrained Shortest Path Problem (CSPP) for a 3-D network. The CSPP has been solved for various ellipsoid shapes and different length constraints in cases with several radars. The impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact of variable RCS on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006
81 citations
81 citations
TL;DR: This paper considers nonlinearly constrained tolerance allocation problems and the Monte Carlo simulation is introduced into the frame in order to make the frame efficient, and the genetic algorithm is improved according to the features of theMonte Carlo simulation.
81 citations