scholarly journals Efficient randomized algorithms for some geometric optimization problems

1996 ◽  
Vol 16 (4) ◽  
pp. 317-337 ◽  
Author(s):  
P. K. Agarwal ◽  
M. Sharir
Keyword(s):  
Randomized Algorithms ◽  
Optimization Problems ◽  
Geometric Optimization

Origami Folding and Bar Frameworks

2014 ◽  
Author(s):  
Alejandro R. Diaz
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Optimization Problems ◽  
Undirected Graph ◽  
Geometric Optimization ◽  
Order Effects ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Higher Order Effects

One of the more computationally demanding tasks in a process of synthesizing “from scratch” origami crease patterns designed for a given purpose involve a simulation capability to track the progression of the folding process as the pattern folds. This work presents an approach to simulate origami folding based on bar frameworks. The work is related to joint frameworks and projected polyhedral, as they apply to folding. The analysis starts from a representation of a crease pattern as an undirected graph G(E,V) formed by edges E and vertices V. A framework G(p) is an instance of G where the vertex locations are assigned positions according to a vector valued function p(t), where t marks the folding progression and t=0 represents the initial, flat configuration. The strategy presented is based on finding a sequence of instances {p(1), p(2), …} corresponding to an analytic flex p, i.e., functions such that edges in all G(p(t)) have the same length. The method is based on using a finite element description of a bar framework corresponding to a truss-like structure congruent with G(p). Solutions to an eigenvalue problem associated with this structure provide the means to update from p(t) to p(t+1). Two simple (purely geometric) optimization problems adjust the update to compensate for higher order effects, guaranteeing that the length of the edges remain constant. The methodology can be used to achieve configurations close to “flat folding”, provided that no interference of the faces occurs along the way. We expected that physically-motivated constraints (stresses, deformations, etc.) and sensitivity analysis computations will be more easily represented in this framework and therefore this formulation will have an advantage over more standard “origami mathematics” approaches. The approach is illustrated with an example of folding a simple 10-crease pattern.

scholarly journals On some geometric optimization problems in layered manufacturing

1999 ◽  
Vol 12 (3-4) ◽  
pp. 219-239 ◽  
Author(s):  
Jayanth Majhi ◽  
Ravi Janardan ◽  
Michiel Smid ◽  
Prosenjit Gupta
Keyword(s):  
Optimization Problems ◽  
Layered Manufacturing ◽  
Geometric Optimization

A Rigorous Complexity Analysis of the (1 + 1) Evolutionary Algorithm for Separable Functions with Boolean Inputs

1998 ◽  
Vol 6 (2) ◽  
pp. 185-196 ◽  
Author(s):  
Stefan Droste ◽  
Thomas Jansen ◽  
Ingo Wegener
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Randomized Algorithms ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Mutation Rates ◽  
Crossover Operator ◽  
Separable Functions ◽  
Run Time

Evolutionary algorithms (EAs) are heuristic randomized algorithms which, by many impressive experiments, have been proven to behave quite well for optimization problems of various kinds. In this paper a rigorous theoretical complexity analysis of the (1 + 1) evolutionary algorithm for separable functions with Boolean inputs is given. Different mutation rates are compared, and the use of the crossover operator is investigated. The main contribution is not the result that the expected run time of the (1 + 1) evolutionary algorithm is Θ(n ln n) for separable functions with n variables but the methods by which this result can be proven rigorously.

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