Understanding search behavior via search landscape analysis in design optimization of optical structures

Sacha Verweij; Shanhui Fan

doi:10.1364/JOSAB.33.002457

Journal of the Optical Society of America B
Vol. 33,
Issue 12,
pp. 2457-2471
(2016)
•https://doi.org/10.1364/JOSAB.33.002457

Understanding search behavior via search landscape analysis in design optimization of optical structures

Sacha Verweij and Shanhui Fan

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Sacha Verweij and Shanhui Fan, "Understanding search behavior via search landscape analysis in design optimization of optical structures," J. Opt. Soc. Am. B 33, 2457-2471 (2016)

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Table of Contents Category
- Optical Design and Fabrication
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: May 2, 2016
- Revised Manuscript: August 16, 2016
- Manuscript Accepted: August 22, 2016
- Published: November 10, 2016

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Abstract

Search algorithms play a crucial role in systematic design optimization of optical structures. We demonstrate how search landscape analysis sheds light on the behavior of search algorithms in this context and thereby leads to valuable insight. Specifically, we present a case study in which search landscape analysis demystifies the surprisingly good performance of a simple stochastic local search algorithm—restarted iterative best improvement—on a challenging design optimization problem—combinatorial design optimization of a multi-spatial-mode photonic crystal waveguide bend that preserves modal content. Moreover, the search landscape analysis leads to insight potentially valuable in design optimization of a broad class of optical structures.

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Equations (13)

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$d_{H}$	$d_{w s} = d_{H}$		$d_{w s} = d_{H} + 2$		$d_{w s} \geq d_{H} + 4$		+
0	0.4%	(100%)	0%	(0%)	0%	(0%)	0.4%
1	6.2%	(100%)	0%	(0%)	0%	(0%)	6.2%
2	15.5%	(98.9%)	0.2%	(1.1%)	$< .1 %$	( $< .1 %$ )	15.7%
3	21.0%	(96.9%)	0.6%	(2.9%)	$< .1 %$	(0.2%)	21.6%
4	19.8%	(94.4%)	1.1%	(5.1%)	0.1%	(0.5%)	21.0%
5	14.5%	(91.6%)	1.2%	(7.5%)	0.1%	(0.9%)	15.8%
6	8.8%	(88.8%)	1.0%	(10.0%)	0.1%	(1.3%)	9.9%
7	4.6%	(86.1%)	0.6%	(12.2%)	$< .1 %$	(1.7%)	5.3%
8	2.1%	(83.4%)	0.4%	(14.3%)	$< .1 %$	(2.3%)	2.5%
9	0.8%	(81.0%)	0.2%	(16.2%)	$< .1 %$	(2.7%)	1.0%
10	0.3%	(78.9%)	$< .1 %$	(18.1%)	$< .1 %$	(3.0%)	0.4%
11	$< .1 %$	(77.6%)	$< .1 %$	(19.1%)	$< .1 %$	(3.4%)	0.1%
12	$< .1 %$	(76.8%)	$< .1 %$	(19.5%)	$< .1 %$	(3.7%)	$< .1 %$
13	$< .1 %$	(75.7%)	$< .1 %$	(20.7%)	$< .1 %$	(3.6%)	$< .1 %$
14	$< .1 %$	(80.5%)	$< .1 %$	(17.9%)	$< .1 %$	(1.6%)	$< .1 %$
15	$< .1 %$	(83.7%)	$< .1 %$	(16.3%)	0%	(0%)	$< .1 %$
16	$< .1 %$	(89.5%)	$< .1 %$	(10.5%)	0%	(0%)	$< .1 %$
+	94.1%		5.3%		0.6%		100%

$\Pr (H_{d} = 0) \approx 0.000$	$\Pr (H_{d} = 9) \approx 0.010$
$\Pr (H_{d} = 1) \approx 0.062$	$\Pr (H_{d} = 10) \approx 0.004$
$\Pr (H_{d} = 2) \approx 0.157$	$\Pr (H_{d} = 11) \approx 0.001$
$\Pr (H_{d} = 3) \approx 0.216$	$\Pr (H_{d} = 12) \approx 0.001$
$\Pr (H_{d} = 4) \approx 0.210$	$\Pr (H_{d} = 13) \approx 0.001$
$\Pr (H_{d} = 5) \approx 0.158$	$\Pr (H_{d} = 14) \approx 0.001$
$\Pr (H_{d} = 6) \approx 0.099$	$\Pr (H_{d} = 15) \approx 0.001$
$\Pr (H_{d} = 7) \approx 0.053$	$\Pr (H_{d} = 16) \approx 0.001$
$\Pr (H_{d} = 8) \approx 0.025$	$\Pr (H_{d} \geq 17) \approx 0.000$

$d_{H}$	$d_{w s} = d_{H}$		$d_{w s} = d_{H} + 2$		$d_{w s} \geq d_{H} + 4$		+
0	0.4%	(100%)	0%	(0%)	0%	(0%)	0.4%
1	6.2%	(100%)	0%	(0%)	0%	(0%)	6.2%
2	15.5%	(98.9%)	0.2%	(1.1%)	$< .1 %$	( $< .1 %$ )	15.7%
3	21.0%	(96.9%)	0.6%	(2.9%)	$< .1 %$	(0.2%)	21.6%
4	19.8%	(94.4%)	1.1%	(5.1%)	0.1%	(0.5%)	21.0%
5	14.5%	(91.6%)	1.2%	(7.5%)	0.1%	(0.9%)	15.8%
6	8.8%	(88.8%)	1.0%	(10.0%)	0.1%	(1.3%)	9.9%
7	4.6%	(86.1%)	0.6%	(12.2%)	$< .1 %$	(1.7%)	5.3%
8	2.1%	(83.4%)	0.4%	(14.3%)	$< .1 %$	(2.3%)	2.5%
9	0.8%	(81.0%)	0.2%	(16.2%)	$< .1 %$	(2.7%)	1.0%
10	0.3%	(78.9%)	$< .1 %$	(18.1%)	$< .1 %$	(3.0%)	0.4%
11	$< .1 %$	(77.6%)	$< .1 %$	(19.1%)	$< .1 %$	(3.4%)	0.1%
12	$< .1 %$	(76.8%)	$< .1 %$	(19.5%)	$< .1 %$	(3.7%)	$< .1 %$
13	$< .1 %$	(75.7%)	$< .1 %$	(20.7%)	$< .1 %$	(3.6%)	$< .1 %$
14	$< .1 %$	(80.5%)	$< .1 %$	(17.9%)	$< .1 %$	(1.6%)	$< .1 %$
15	$< .1 %$	(83.7%)	$< .1 %$	(16.3%)	0%	(0%)	$< .1 %$
16	$< .1 %$	(89.5%)	$< .1 %$	(10.5%)	0%	(0%)	$< .1 %$
+	94.1%		5.3%		0.6%		100%

$\Pr (H_{d} = 0) \approx 0.000$	$\Pr (H_{d} = 9) \approx 0.010$
$\Pr (H_{d} = 1) \approx 0.062$	$\Pr (H_{d} = 10) \approx 0.004$
$\Pr (H_{d} = 2) \approx 0.157$	$\Pr (H_{d} = 11) \approx 0.001$
$\Pr (H_{d} = 3) \approx 0.216$	$\Pr (H_{d} = 12) \approx 0.001$
$\Pr (H_{d} = 4) \approx 0.210$	$\Pr (H_{d} = 13) \approx 0.001$
$\Pr (H_{d} = 5) \approx 0.158$	$\Pr (H_{d} = 14) \approx 0.001$
$\Pr (H_{d} = 6) \approx 0.099$	$\Pr (H_{d} = 15) \approx 0.001$
$\Pr (H_{d} = 7) \approx 0.053$	$\Pr (H_{d} = 16) \approx 0.001$
$\Pr (H_{d} = 8) \approx 0.025$	$\Pr (H_{d} \geq 17) \approx 0.000$

Abstract

Supplementary Material (1)

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Figures (18)

Tables (2)

Equations (13)

Journal of the Optical Society of America B