scholarly journals On the complexity of optimization problems for 3-dimensional convex polyhedra and decision trees

1997 ◽  
Vol 8 (3) ◽  
pp. 123-137 ◽  
Author(s):  
Gautam Das ◽  
Michael T. Goodrich
Keyword(s):  
Decision Trees ◽  
Optimization Problems ◽  
Convex Polyhedra ◽  
3 Dimensional

On the Topological Characterization of 3-D Polyhedral Microstrutures

2007 ◽  
Vol 537-538 ◽  
pp. 563-570 ◽  
Author(s):  
Tamás Réti ◽  
Agnes Csizmazia ◽  
Imre Felde
Keyword(s):  
Single Phase ◽  
Cellular Systems ◽  
Convex Polyhedra ◽  
Quantitative Characterization ◽  
Topological Characterization ◽  
Shape Factors ◽  
3 Dimensional ◽  
Cellular Models ◽  
Finite Set

To characterize topologically the polycrystalline microstructure of single-phase alloys computer simulations are performed on 3-dimensional cellular models. These infinite periodic cellular systems are constructed from a finite set of space filling convex polyhedra (grains). It is shown that the appropriately selected topological shape factors can be successfully used for the quantitative characterization of computer-simulated microstructures of various types.

scholarly journals A Sensitivity Analysis of Critical Genetic Algorithm Parameters

2016 ◽  
pp. 863-880
Author(s):  
Eungcheol Kim ◽  
Manoj K. Jha ◽  
Min-Wook Kang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Critical Parameters ◽  
Optimal Solutions ◽  
Genetic Operators ◽  
Solution Quality ◽  
Local Optima ◽  
3 Dimensional ◽  
Combinatorial Optimization Problems ◽  
Decision Variables

Genetic Algorithms (GAs) have been applied in many complex combinatorial optimization problems and have been proven to yield reasonably good solutions due to their ability of searching in continuous spaces and avoiding local optima. However, one issue in GA application that needs to be carefully explored is to examine sensitivity of critical parameters that may affect the quality of solutions. The key critical GA parameters affecting solution quality include the number of genetic operators, the number of encoded decision variables, the parameter for selective pressure, and the parameter for non-uniform mutation. The effect of these parameters on solution quality is particularly significant for complex problems of combinatorial nature. In this paper the authors test the sensitivity of critical GA parameters in optimizing 3-dimensional highway alignments which has been proven to be a complex combinatorial optimization problem for which an exact solution is not possible warranting the application of heuristics procedures, such as GAs. If GAs are applied properly, similar optimal solutions should be expected at each replication. The authors perform several example studies in order to arrive at a general set of conclusions regarding the sensitivity of critical GA parameters on solution quality. The first study shows that the optimal solutions obtained for a range of scenarios consisting of different combinations of the critical parameters are quite close. The second study shows that different optimal solutions are obtained when the number of encoded decision variables is changed.

BUILDING CONSISTENCIES FOR PARTIALLY DEFINED CONSTRAINTS WITH DECISION TREES AND NEURAL NETWORKS

2007 ◽  
Vol 16 (04) ◽  
pp. 683-706 ◽  
Author(s):  
ARNAUD LALLOUET ◽  
ANDREI LEGTCHENKO
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Artificial Neural Networks ◽  
Decision Trees ◽  
Optimization Problems ◽  
Machine Learning Techniques ◽  
Incomplete Knowledge ◽  
Learning Techniques ◽  
Variable Domains ◽  
Constraint Learning

Partially Defined Constraints can be used to model the incomplete knowledge of a concept or a relation. Instead of only computing with the known part of the constraint, we propose to complete its definition by using Machine Learning techniques. Since constraints are actively used during solving for pruning domains, building a classifier for instances is not enough: we need a solver able to reduce variable domains. Our technique is composed of two steps: first we learn a classifier for each constraint projections and then we transform the classifiers into a propagator. The first contribution is a generic meta-technique for classifier improvement showing performances comparable to boosting. The second lies in the ability of using the learned concept in constraint-based decision or optimization problems. We presents results using Decision Trees and Artificial Neural Networks for constraint learning and propagation. It opens a new way of integrating Machine Learning in Decision Support Systems.

A Sensitivity Analysis of Critical Genetic Algorithm Parameters

2015 ◽  
Vol 6 (1) ◽  
pp. 30-48 ◽  
Author(s):  
Eungcheol Kim ◽  
Manoj K. Jha ◽  
Min-Wook Kang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Critical Parameters ◽  
Optimal Solutions ◽  
Genetic Operators ◽  
Solution Quality ◽  
Local Optima ◽  
3 Dimensional ◽  
Combinatorial Optimization Problems ◽  
Decision Variables

Genetic Algorithms (GAs) have been applied in many complex combinatorial optimization problems and have been proven to yield reasonably good solutions due to their ability of searching in continuous spaces and avoiding local optima. However, one issue in GA application that needs to be carefully explored is to examine sensitivity of critical parameters that may affect the quality of solutions. The key critical GA parameters affecting solution quality include the number of genetic operators, the number of encoded decision variables, the parameter for selective pressure, and the parameter for non-uniform mutation. The effect of these parameters on solution quality is particularly significant for complex problems of combinatorial nature. In this paper the authors test the sensitivity of critical GA parameters in optimizing 3-dimensional highway alignments which has been proven to be a complex combinatorial optimization problem for which an exact solution is not possible warranting the application of heuristics procedures, such as GAs. If GAs are applied properly, similar optimal solutions should be expected at each replication. The authors perform several example studies in order to arrive at a general set of conclusions regarding the sensitivity of critical GA parameters on solution quality. The first study shows that the optimal solutions obtained for a range of scenarios consisting of different combinations of the critical parameters are quite close. The second study shows that different optimal solutions are obtained when the number of encoded decision variables is changed.

Design Optimization of Transonic Compressor Rotor Using CFD and Genetic Algorithm

2006 ◽  
Author(s):  
Weilin Yi ◽  
Hongyan Huang ◽  
Wanjin Han
Keyword(s):  
Genetic Algorithm ◽  
Design Optimization ◽  
Response Surface ◽  
Optimization Design ◽  
Optimization Problems ◽  
Response Surface Model ◽  
Navier Stokes ◽  
Surface Model ◽  
3 Dimensional ◽  
Transonic Compressor

The paper describes a new optimization strategy for computationally expensive design optimization problems of turbomachinery, combined with design of experiment (DOE), response surface models (RSM), genetic algorithm (GA) and a 3-D Navier-Stokes solver. Data points for response evaluations were selected by Latin hypercube design (LHD) and 3-dimensional Navier-Stokes analysis was carried out at these sample points. The quadratic response surface model was used to approximate the relationships between the design variables and flow parameters. The genetic algorithm was applied to the response surface model to perform global optimization to obtain the optimum design. The above method was applied to the optimization design of NASA rotor37. The object was to maximize the adiabatic efficiency. An optimum leading edge line was found which produced a new 3-dimensional blade combined with sweep and composite bowing. As a result of this optimization, the adiabatic efficiency was successfully increased by 1.58%. It was found that the strategy of this paper provides a reliable design optimization method for turbomachinery blades at reasonable computing cost.

OPTIMIZATION PROBLEMS FOR DECISION TREES

1994 ◽  
Vol 21 (4) ◽  
pp. 391-401 ◽  
Author(s):  
Mikhail Moshkov
Keyword(s):  
Decision Trees ◽  
Optimization Problems

A Sensitivity Analysis of Critical Genetic Algorithm Parameters

2015 ◽  
pp. 1064-1081
Author(s):  
Eungcheol Kim ◽  
Manoj K. Jha ◽  
Min-Wook Kang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Critical Parameters ◽  
Optimal Solutions ◽  
Genetic Operators ◽  
Solution Quality ◽  
Local Optima ◽  
3 Dimensional ◽  
Combinatorial Optimization Problems ◽  
Decision Variables

Genetic Algorithms (GAs) have been applied in many complex combinatorial optimization problems and have been proven to yield reasonably good solutions due to their ability of searching in continuous spaces and avoiding local optima. However, one issue in GA application that needs to be carefully explored is to examine sensitivity of critical parameters that may affect the quality of solutions. The key critical GA parameters affecting solution quality include the number of genetic operators, the number of encoded decision variables, the parameter for selective pressure, and the parameter for non-uniform mutation. The effect of these parameters on solution quality is particularly significant for complex problems of combinatorial nature. In this paper the authors test the sensitivity of critical GA parameters in optimizing 3-dimensional highway alignments which has been proven to be a complex combinatorial optimization problem for which an exact solution is not possible warranting the application of heuristics procedures, such as GAs. If GAs are applied properly, similar optimal solutions should be expected at each replication. The authors perform several example studies in order to arrive at a general set of conclusions regarding the sensitivity of critical GA parameters on solution quality. The first study shows that the optimal solutions obtained for a range of scenarios consisting of different combinations of the critical parameters are quite close. The second study shows that different optimal solutions are obtained when the number of encoded decision variables is changed.

scholarly journals On the complements of 3-dimensional convex polyhedra as polynomial images of ℝ3

2014 ◽  
Vol 25 (07) ◽  
pp. 1450071 ◽  
Author(s):  
José F. Fernando ◽  
Carlos Ueno
Keyword(s):  
Convex Polyhedron ◽  
Convex Polyhedra ◽  
Semialgebraic Sets ◽  
3 Dimensional

Let [Formula: see text] be a convex polyhedron of dimension n. Denote [Formula: see text] and let [Formula: see text] be its closure. We prove that for n = 3 the semialgebraic sets [Formula: see text] and [Formula: see text] are polynomial images of ℝ3. The former techniques cannot be extended in general to represent the semialgebraic sets [Formula: see text] and [Formula: see text] as polynomial images of ℝn if n ≥ 4.

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