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๊ด€๋ฆฌ ๋ฉ”๋‰ด

๋ชฉ๋กํ•œ์ • ๋ถ„๊ธฐ (3)

์žฌ๋ƒฅ์ด๐Ÿ˜ป

0-1 Knapsack Problem - ์ตœ๊ณ  ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ (Branch and Bound)

0-1 Knapsack Problem ์ตœ๊ณ  ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ (Branch and Bound) ์„œ๋ก  ํ•œ์ • ๋ถ„๊ธฐ ์ „๋žต์˜ ๋™๊ธฐ : ๋˜์ถ”์ ์˜ ๋น„ํšจ์œจ๋˜์ถ”์ ์˜ ํƒ์ƒ‰ ๊ณผ์ •์—์„œ Valid๊ฐ€ ์ ์šฉ๋˜๋”๋ผ๋„ ์—ฌ์ „ํžˆ ์ƒ๋‹นํ•œ ๋น„์œจ์˜ ์ •์ ์„ ๋ฐฉ๋ฌธํ•˜์ง€ ์•Š์•„๋„ ๋จ์„ ๋ฐœ๊ฒฌ ๋˜์ถ”์ ์˜ ๋น„ํšจ์œจ ํ•ด๊ฒฐ์ฑ… : ๊ฐ ๋…ธ๋“œ๋ฅผ ๋ฐฉ๋ฌธํ•  ๋•Œ๋งˆ๋‹ค ํ•œ๊ณ„์น˜(bound)๋ฅผ ๊ณ„์‚ฐ ํ•œ๊ณ„์น˜(Bound) : ํ•ด๋‹น ๋…ธ๋“œ๋กœ๋ถ€ํ„ฐ ๊ฐ€์ง€๋ฅผ ๋ป—์–ด๋‚˜๊ฐ€์„œ(branch) ์–ป์„ ์ˆ˜ ์žˆ๋Š” ํ•ด๋‹ต์น˜์˜ ํ•œ๊ณ„ ๊ฐ’ 0/1 Knapsack Problem์˜ ์ตœ๊ณ  ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ(Branch and Bound) ์ „๋žต 1. ๊ทธ ๋…ธ๋“œ์˜ profit๊ณผ weight๋ฅผ ๊ณ„์‚ฐํ•œ๋‹ค. 2. ๊ทธ ๋…ธ๋“œ์˜ bound๋ฅผ ๊ณ„์‚ฐํ•œ๋‹ค. 3. ํ˜„์žฌ ๋…ธ๋“œ์˜ profit์ด maxprofit๋ณด๋‹ค ํฌ๋ฉด maxpr..

ํŒŒ์ด์ฌ 2022. 6. 15. 22:42
0-1 Knapsack Problem - ๋„ˆ๋น„ ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ (Branch and Bound)

0-1 Knapsack Problem ๋„ˆ๋น„ ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ (Branch and Bound) ์„œ๋ก  ํ•œ์ • ๋ถ„๊ธฐ ์ „๋žต์˜ ๋™๊ธฐ : ๋˜์ถ”์ ์˜ ๋น„ํšจ์œจ๋˜์ถ”์ ์˜ ํƒ์ƒ‰ ๊ณผ์ •์—์„œ Valid๊ฐ€ ์ ์šฉ๋˜๋”๋ผ๋„ ์—ฌ์ „ํžˆ ์ƒ๋‹นํ•œ ๋น„์œจ์˜ ์ •์ ์„ ๋ฐฉ๋ฌธํ•˜์ง€ ์•Š์•„๋„ ๋จ์„ ๋ฐœ๊ฒฌ ๋˜์ถ”์ ์˜ ๋น„ํšจ์œจ ํ•ด๊ฒฐ์ฑ… : ๊ฐ ๋…ธ๋“œ๋ฅผ ๋ฐฉ๋ฌธํ•  ๋•Œ๋งˆ๋‹ค ํ•œ๊ณ„์น˜(bound)๋ฅผ ๊ณ„์‚ฐ ํ•œ๊ณ„์น˜(Bound) : ํ•ด๋‹น ๋…ธ๋“œ๋กœ๋ถ€ํ„ฐ ๊ฐ€์ง€๋ฅผ ๋ป—์–ด๋‚˜๊ฐ€์„œ(branch) ์–ป์„ ์ˆ˜ ์žˆ๋Š” ํ•ด๋‹ต์น˜์˜ ํ•œ๊ณ„ ๊ฐ’ ๊ธฐ์กด ๊นŠ์ด ์šฐ์„  ๊ฒ€์ƒ‰(DFS) ๊ธฐ๋ฐ˜ ์•Œ๊ณ ๋ฆฌ์ฆ˜์€ ๋ถ„๊ธฐํ•œ์ •์˜ ํŠน์„ฑ์„ ์ œ๋Œ€๋กœ ํ™œ์šฉํ•˜๊ณ  ์žˆ์ง€ ๋ชปํ•จ. ๊ทธ๋ ‡๋‹ค๋ฉด… ๋„ˆ๋น„ ์šฐ์„  ๊ฒ€์ƒ‰(BFS)์„ ์ˆ˜์ •ํ•˜์—ฌ ๊ตฌํ˜„ 0/1 Knapsack Problem์˜ ๋„ˆ๋น„ ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ(Branch and Bound) ์ „๋žต 1. ๊ทธ ๋…ธ๋“œ์˜ p..

ํŒŒ์ด์ฌ 2022. 6. 15. 21:55
0-1 Knapsack Problem - ๊นŠ์ด ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ (Branch and Bound)

0-1 Knapsack Problem ๊นŠ์ด ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ (Branch and Bound) ์„œ๋ก  ํ•œ์ • ๋ถ„๊ธฐ ์ „๋žต์˜ ๋™๊ธฐ : ๋˜์ถ”์ ์˜ ๋น„ํšจ์œจ๋˜์ถ”์ ์˜ ํƒ์ƒ‰ ๊ณผ์ •์—์„œ Valid๊ฐ€ ์ ์šฉ๋˜๋”๋ผ๋„ ์—ฌ์ „ํžˆ ์ƒ๋‹นํ•œ ๋น„์œจ์˜ ์ •์ ์„ ๋ฐฉ๋ฌธํ•˜์ง€ ์•Š์•„๋„ ๋จ์„ ๋ฐœ๊ฒฌ ๋˜์ถ”์ ์˜ ๋น„ํšจ์œจ ํ•ด๊ฒฐ์ฑ… : ๊ฐ ๋…ธ๋“œ๋ฅผ ๋ฐฉ๋ฌธํ•  ๋•Œ๋งˆ๋‹ค ํ•œ๊ณ„์น˜(bound)๋ฅผ ๊ณ„์‚ฐ ํ•œ๊ณ„์น˜(Bound) : ํ•ด๋‹น ๋…ธ๋“œ๋กœ๋ถ€ํ„ฐ ๊ฐ€์ง€๋ฅผ ๋ป—์–ด๋‚˜๊ฐ€์„œ(branch) ์–ป์„ ์ˆ˜ ์žˆ๋Š” ํ•ด๋‹ต์น˜์˜ ํ•œ๊ณ„ ๊ฐ’ 0/1 Knapsack Problem์˜ ๊นŠ์ด ์šฐ์„  ๊ฒ€์ƒ‰์„ ์‚ฌ์šฉํ•œ ํ•œ์ •๋ถ„๊ธฐ(Branch and Bound) ์ „๋žต 1. ๊ทธ ๋…ธ๋“œ์˜ profit๊ณผ weight๋ฅผ ๊ณ„์‚ฐํ•œ๋‹ค. 2. ๊ทธ ๋…ธ๋“œ์˜ bound๋ฅผ ๊ณ„์‚ฐํ•œ๋‹ค. 3. ํ˜„์žฌ ๋…ธ๋“œ์˜ profit์ด maxprofit๋ณด๋‹ค ํฌ๋ฉด maxpr..

ํŒŒ์ด์ฌ 2022. 6. 15. 19:56