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Multi-Party Multi-Objective Optimization as Consensus Search: Runtime Analysis of Cross-Party Recombination

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Xiaolei Fang, Peilan Xu, Wenjian Luo

๐Ÿ’ก ๊ฐœ์š”

๋ณธ ๋…ผ๋ฌธ์€ ์ž์œจ ์˜์‚ฌ ๊ฒฐ์ • ์ฃผ์ฒด ๊ฐ„์˜ ํ•ฉ์˜๋ฅผ ์š”๊ตฌํ•˜๋Š” ๋‹ค์ž ๋‹ค๋ชฉ์  ์ตœ์ ํ™” ๋ฌธ์ œ(MPMOPs)๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•œ ์ƒˆ๋กœ์šด ์ ‘๊ทผ ๋ฐฉ์‹์ธ 'ํ•ฉ์˜ ํƒ์ƒ‰' ๊ฐœ๋…์„ ์ œ์‹œํ•˜๊ณ , ํŠนํžˆ '๊ต์ฐจ ๋‹น ์žฌ์กฐํ•ฉ' ๊ธฐ๋ฒ•์˜ ๋Ÿฐํƒ€์ž„ ๋ถ„์„์„ ์ˆ˜ํ–‰ํ•ฉ๋‹ˆ๋‹ค. ๊ต์ฐจ ๋‹น ์žฌ์กฐํ•ฉ์€ ๊ธฐ์กด์˜ ๋‹จ์ผ ๋ชฉ์  ์ตœ์ ํ™” ๋ฌธ์ œ์— ๋งž์ถฐ์ง„ ์ด๋ก ์œผ๋กœ๋Š” ์„ค๋ช…ํ•˜๊ธฐ ์–ด๋ ค์šด MPMOPs์˜ ๊ณตํ†ต ํ•ด ํƒ์ƒ‰์„ ํšจ๊ณผ์ ์œผ๋กœ ์ˆ˜ํ–‰ํ•จ์„ ์ž…์ฆํ•ฉ๋‹ˆ๋‹ค.

๐Ÿ”‘ ์‹œ์‚ฌ์  ๋ฐ ํ•œ๊ณ„

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์‹œ์‚ฌ์  1: ๋‹ค์ž ๋‹ค๋ชฉ์  ์ตœ์ ํ™” ๋ฌธ์ œ์—์„œ ๊ฐœ๋ณ„ ๋‹น์˜ ํƒ์ƒ‰ ๊ฒฐ๊ณผ๋ฌผ์„ ํšจ๊ณผ์ ์œผ๋กœ ๊ฒฐํ•ฉํ•˜๋Š” '๊ต์ฐจ ๋‹น ์žฌ์กฐํ•ฉ' ๊ธฐ๋ฒ•์ด ๊ณตํ†ต ์ตœ์  ํ•ด ํƒ์ƒ‰์— ์žˆ์–ด ๊ธฐ์กด ๋ฐฉ๋ฒ•๋ก ๋ณด๋‹ค ๋›ฐ์–ด๋‚œ ํšจ์œจ์„ฑ์„ ๋ณด์ผ ์ˆ˜ ์žˆ์Œ์„ ์ด๋ก ์ ์œผ๋กœ ์ฆ๋ช…ํ•ฉ๋‹ˆ๋‹ค.
โ€ข
์‹œ์‚ฌ์  2: ๋ฌธ์ œ์˜ ๋ณต์žก์„ฑ์„ 'ํ‰ํƒ„ํ™”'ํ•˜๋Š” ๋Œ€์‹ , ๊ฐ ๋‹น์˜ ํŠน์„ฑ๊ณผ ๊ด€๊ณ„๋ฅผ ๊ณ ๋ คํ•œ ๋ชจ๋ธ๋ง ๋ฐ ๋ถ„์„์ด MPMOPs ํ•ด๊ฒฐ์— ๋” ์ ํ•ฉํ•˜๋ฉฐ, ์ด๋ฅผ ํ†ตํ•ด ๋ณด๋‹ค ์ •ํ™•ํ•œ ๋Ÿฐํƒ€์ž„ ๋ถ„์„์ด ๊ฐ€๋Šฅํ•จ์„ ๋ณด์—ฌ์ค๋‹ˆ๋‹ค.
โ€ข
ํ•œ๊ณ„์  ๋˜๋Š” ํ–ฅํ›„ ๊ณผ์ œ: ๋ณธ ์—ฐ๊ตฌ๋Š” ๋‘ ๊ฐ€์ง€ ๋Œ€ํ‘œ์ ์ธ ๋ฒค์น˜๋งˆํฌ ๋ฌธ์ œ์— ๋Œ€ํ•œ ๋ถ„์„์— ์ง‘์ค‘๋˜์—ˆ์œผ๋ฉฐ, ์‹ค์ œ ์ ์šฉ ๊ฐ€๋Šฅํ•œ ๋‹ค์–‘ํ•œ MPMOPs ํ™˜๊ฒฝ์—์„œ์˜ ๊ต์ฐจ ๋‹น ์žฌ์กฐํ•ฉ ๊ธฐ๋ฒ•์˜ ์„ฑ๋Šฅ๊ณผ ์ผ๋ฐ˜ํ™” ๊ฐ€๋Šฅ์„ฑ์— ๋Œ€ํ•œ ์ถ”๊ฐ€์ ์ธ ์—ฐ๊ตฌ๊ฐ€ ํ•„์š”ํ•ฉ๋‹ˆ๋‹ค.
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