Ant colony optimization in lens design

Ziyao Tang; Matthias Sonntag; Herbert Gross; Herbert Gross

doi:10.1364/AO.58.006357

Applied Optics
Vol. 58,
Issue 23,
pp. 6357-6364
(2019)
•https://doi.org/10.1364/AO.58.006357

Ant colony optimization in lens design

Ziyao Tang, Matthias Sonntag, and Herbert Gross

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Ziyao Tang, Matthias Sonntag, and Herbert Gross, "Ant colony optimization in lens design," Appl. Opt. 58, 6357-6364 (2019)

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Abstract

As the most widely used optimization algorithm in optical design, the damped least square (DLS) method is advantageous for its fast convergence and deterministic optimization path. However, results are strongly dependent on the initial system and problematic when it is stuck in a local minimum in the searching space. To overcome these disadvantages, a biology intelligence-based algorithm, ant colony optimization (ACO) is implemented and tested for optical design tasks. Additionally, the ACO method has a better performance considering glass optimization. Two ACO versions, which are proved applicable, are introduced and their feasibility is assessed based on some case studies.

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Parameter	Definition	Speed	Global	Local	Tuning Range	Ex. I
$N_{i t}$	Iteration number	+	+	0	10–1000	200
$n_{ant}$	Ant number	+	0	0	10–60	15
$q$	Bias intense parameter of better solutions	0	+	+	0.1–1	0.5
$k$	Solution archive capacity	+	−	−	10–60	30
$ς$	Convergence speed parameter	+	+	−	0.1–1	0.3
$Q_{best}$	Best solution selection probability	0	0	+	0–1	0.3
$G_{iter}$	Interval of enlarging k	−	0	−	5–20	5
$M_{a s}$	Allowed maximum k	+	0	0	10–60	50
$L_{iter}$	Local optimization interval	−	0	+	5–30	10
$L_{F}$	Allowed maximum number/solution	0	0	0	1–8	2

Parameter	Definition	Speed	Global	Local	Tuning Range	Ex. I
$N_{i t}$	Iteration number	−	+	+	10–200	10
$n_{ant}$	Ant number	+	+	+	10–60	20
$p$	Hunting site number/ant	+	−	+	1–10	2
$F$	Allowed maximum failure time/local area	−	0	0	1–10	8
$T$	Total movement/ant/iteration	+	0	0	10–60	15
$A$	Exploration ability divergence parameter	0	0	+	$10^{- 4} - 1$	0.01

Parameter	Definition	Speed	Global	Local	Tuning Range	Ex. I
$N_{i t}$	Iteration number	+	+	0	10–1000	200
$n_{ant}$	Ant number	+	0	0	10–60	15
$q$	Bias intense parameter of better solutions	0	+	+	0.1–1	0.5
$k$	Solution archive capacity	+	−	−	10–60	30
$ς$	Convergence speed parameter	+	+	−	0.1–1	0.3
$Q_{best}$	Best solution selection probability	0	0	+	0–1	0.3
$G_{iter}$	Interval of enlarging k	−	0	−	5–20	5
$M_{a s}$	Allowed maximum k	+	0	0	10–60	50
$L_{iter}$	Local optimization interval	−	0	+	5–30	10
$L_{F}$	Allowed maximum number/solution	0	0	0	1–8	2

Parameter	Definition	Speed	Global	Local	Tuning Range	Ex. I
$N_{i t}$	Iteration number	−	+	+	10–200	10
$n_{ant}$	Ant number	+	+	+	10–60	20
$p$	Hunting site number/ant	+	−	+	1–10	2
$F$	Allowed maximum failure time/local area	−	0	0	1–10	8
$T$	Total movement/ant/iteration	+	0	0	10–60	15
$A$	Exploration ability divergence parameter	0	0	+	$10^{- 4} - 1$	0.01

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Applied Optics