Automated mirror design using an evolution strategy

Doyle, Steven; Corcoran, David; Connell, Jon

doi:10.1117/1.602091

Cited by 29 publications

(19 citation statements)

References 15 publications

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“…[45] uses a modified Newtoniteration method. On the other hand, Doyle et al [46][47][48] use a Genetic Algorithm for the optimization, and [49] uses a custom global 'Brute Force' algorithm. To the authors' knowledge, choosing one optimization method or another is quite arbitrary, and no method has proven to be the best for this sort of optimization problem.…”

Section: Discussionmentioning

confidence: 99%

“…Doyle et al present [46][47][48] an evolution strategy (a variation on the Genetic Algorithm) for 2D luminary design with point [46] and extended [47] light sources, later completed with a careful analysis of the objective function [48] (called Merit Function in the papers). As such, they defined a threeterm objective function consisting of a term that represents the absolute element-wise difference between the target and resultant distributions in an objective region, and a term representing a penalty for the rays that lie outside the desired region, plus a third term that represents a measure of the difference between the reflected and the desired light power.…”

Section: Surfaces Defined As Splinesmentioning

confidence: 98%

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A Survey of Inverse Surface Design From Light Transport Behavior Specification

Patow

Pueyo

2005

Computer Graphics Forum

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Inverse surface design problems from light transport behavior specification usually represent extremely complex and costly processes, but their importance is well known. In particular, they are very interesting for lighting and luminaire design, in which it is usually difficult to test design decisions on a physical model in order to avoid costly mistakes. In this survey, we present the main ideas behind these kinds of problems, characterize them, and summarize existing work in the area, revealing problems that remain open and possible areas of further research.

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Section: Discussionmentioning

confidence: 99%

Section: Surfaces Defined As Splinesmentioning

confidence: 98%

A Survey of Inverse Surface Design From Light Transport Behavior Specification

Patow

Pueyo

2005

Computer Graphics Forum

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“…It has been applied to evolve weights and structure of neural networks [38][39][40], analyze human tremor [41], register 3D-to-3D biomedical image [42], play games [43], control reactive power and voltage [44,45], pattern recognition [46], etc. Generally speaking, PSO can be applied to solve most optimization problems and problems that can be converted to search or optimization problems.…”

Section: Applicationsmentioning

confidence: 99%

Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives

Das

Abraham

Konar

2008

Studies in Computational Intelligence

310

172

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Summary.Since the beginning of the nineteenth century, a significant evolution in optimization theory has been noticed. Classical linear programming and traditional non-linear optimization techniques such as Lagrange's Multiplier, Bellman's principle and Pontyagrin's principle were prevalent until this century. Unfortunately, these derivative based optimization techniques can no longer be used to determine the optima on rough non-linear surfaces. One solution to this problem has already been put forward by the evolutionary algorithms research community. Genetic algorithm (GA), enunciated by Holland, is one such popular algorithm. This chapter provides two recent algorithms for evolutionary optimization -well known as particle swarm optimization (PSO) and differential evolution (DE). The algorithms are inspired by biological and sociological motivations and can take care of optimality on rough, discontinuous and multimodal surfaces. The chapter explores several schemes for controlling the convergence behaviors of PSO and DE by a judicious selection of their parameters. Special emphasis is given on the hybridizations of PSO and DE algorithms with other soft computing tools. The article finally discusses the mutual synergy of PSO with DE leading to a more powerful global search algorithm and its practical applications.

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“…The method is focused on tailoring and calculates the geometrical parameters of the reflector facets as initial conditions. The facets are treated as singulars and are defined individually though under global conditions, thus describing freeform facets by means of quadratic Bézier surfaces that can be modified by a global optimization process (Doyle, Corcoran, and Connell 1999). Those conditions are derived from a previous segmentation and mapping process (Oliker and Newman 1993;Pohl et al 2003;Fournier, Cassarly, and Rolland 2010a).Althought the mapping proces is outside the scope of the present papers, it might be taken into account that the success of the proposed method directly depends on the choice of mapping.…”

Section: Objectivementioning

confidence: 99%

Construction Method of Tailored Facets for Use in Freeform Reflectors Design

Tomàs

Arasa

2015

LEUKOS

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A construction method to obtain sets of tailored facets to be used as the initial configuration in the design of freeform reflector surfaces is presented. The construction strategy starts from a collection of flat elementary facets and achieves the initial configuration of the reflector surface by tailoring the facets according to their Bézier surfaces description. The aim of this research is to describe a procedure capable of generating the Bézier surfaces that define elementary tailored facets; these facets could then be used as initial configurations in the design of freeform reflectors. Though beyond the scope of this article, the facets could be used on a subsequent optimization process, i.e., the geometry of the elementary facets could be modified through a global optimization process taking into account all facets, in order to further improve the entire illumination system. Ray tracing is used to calculate the facet's geometry; it applies elementary merit functions to find the parameters defining the Bézier curve that best meets specifications in each elementary facet. This method is based on a sequential 2D projection strategy that employs different strategic planes for calculations. A method to build up the facet's geometry using a Bézier surface from 2D curves is provided. This approach will successfully generate a net of control points to describe a Bézier surface compatible with any standard optical optimization tool and suitable for use with CAD and other tools that represent solids.

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Automated mirror design using an evolution strategy

Cited by 29 publications

References 15 publications

A Survey of Inverse Surface Design From Light Transport Behavior Specification

A Survey of Inverse Surface Design From Light Transport Behavior Specification

Particle Swarm Optimization and Differential Evolution Algorithms: Technical Analysis, Applications and Hybridization Perspectives

Construction Method of Tailored Facets for Use in Freeform Reflectors Design

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