Open House, ISM in Tachikawa, 2018.6.15統計数理研究所オープンハウス（立川）、H30.6.15ポスター発

Atsushi Yoshimoto

吉本 敦

English

RISM (Repository of the Institute of Statistical Mathematics) / 統計数理研究所 学術研究リポジトリ

結果   											離散最適化による最適保護区連結ネットワークの探求	吉本　敦　　 数理・推論研究系　教授	2018年6月15日　統計数理研究所　オープンハウス		連結ネットワーク集約制約： ある特定の林分に対し、その連結の集約に対する制約 ここでは、保護区連結ネットワーク形成に応用				本研究の目的： 制約式により保護区連結ネットワークを形成し、最適保護区連結ネットワークを探求できる離散最適化モデルを構築	空間的制約： ユニットの連結を伴う制約。特に隣接に関わる制約。集約化あるいは団地化。最大伐採面積の規制。	2. Sequential Triangle Connection (STC)	1. Spatial component for unit aggregation (MFC) 	Optimal habitat connection	s topqr3/33/32/3 3/32/22/21/40/2L1L3L4L5L2L6L7L8L9LiiL1L3L4L5L2L6L7L8L9Lii yij=1 if an arc is connected between i -th and j -th nodes0 otherwise⎧⎨⎪⎪⎩⎪⎪wi,j:  flow from i - to j -th nodeyij+yji≤1, ∀i, j ∈NBiyi0+ yijj∈NBi∑ = 1, ∀iwij≤L ⋅yij, ∀i, j ∈NBiwi0+ wijj∈NBi∑ = wjij∈NBi∑ +Li, ∀ii=1m∑wi0 =i=1m∑Liwi0≤Lup⋅yi0, ∀i{yij}∈ {0,1},{wij}≥ 0, ∀i, j ∈ (NBi∪{0})123456 789101112131415161718192021222320~50haw3,0 = 32.5w4,0 = 48.9w11,0 = 46.9w14,0 = 46.550ha Aggregation	123456 789101112131415161718192021222320~50haw3,0 = 32.5w4,0 = 48.9w11,0 = 46.9w14,0 = 46.5123456 789101112131415161718192021222320~50haw3,0 = 32.5w4,0 = 48.9w11,0 = 46.9w14,0 = 46.5yijB(n) =1 if n-th process connects a boundary between i - and j -th nodes 0 otherwise⎧⎨⎪⎪⎩⎪⎪uijk(n) =1 if the triangle by nodes (i, j,k) is created at the n-th process0 otherwise⎧⎨⎪⎪⎩⎪⎪yijB(1) = yij+yji, ∀i, j ∈NBi2 ⋅uijk(n)+ 3 ⋅ uijk(l )l=1n−1∑ ≤ {yijB(l )+yikB(l )+yjkB(l )}l=1n∑ ≤ 2 ⋅uijk(n)+ 3 ⋅ uijk(l )l=1n−1∑ +1, ∀i, j ∈MBi,k ∈ (MBi ∩MBj ),n = 1,…,N3 ⋅uijk(n) ≤ {yijB(l )+yikB(l )+yjkB(l )}l=1n+1∑ , ∀i, j ∈MBi,k ∈ (MBi ∩MBj ),n = 1,…,NyijB(n+1) ≤ uijk(n)k∈(MBi∩MBj )∑ , ∀i, j ∈MBi,n = 1,…,NyijB(n)n=1N∑ ≤1, ∀i, j ∈MBi{yijB(n)},{uijk(n)}∈ {0,1}3. Temporal & Integrated component	Table 1: Example of treatments 1    Period   Treatment No. Decision Variable Coefficient 1 2 3 4 5 6 7 8 9 10 1 ,1ix  ,1ic  X 0 0 0 0 0 0 0 0 0 2 ,2ix  ,2ic  X 0 0 0 0 0 X 0 0 0 3 ,3ix  ,3ic  X 0 0 0 0 0 0 X 0 0 4 ,4ix  ,4ic  X 0 0 0 0 0 0 0 X 0 5 ,5ix  ,5ic  X 0 0 0 0 0 0 0 0 X 6 ,6ix  ,6ic  0 X 0 0 0 0 0 0 0 0 7 ,7ix  ,7ic  0 X 0 0 0 0 0 X 0 0 8 ,8ix  ,8ic  0 X 0 0 0 0 0 0 X 0 9 ,9ix  ,9ic  0 X 0 0 0 0 0 0 0 X 10 ,10ix  ,10ic  0 0 X 0 0 0 0 0 0 0 11 ,11ix  ,11ic  0 0 X 0 0 0 0 0 X 0 12 ,12ix  ,12ic  0 0 X 0 0 0 0 0 0 X 13 ,13ix  ,13ic  0 0 0 X 0 0 0 0 0 0 14 ,14ix  ,14ic  0 0 0 X 0 0 0 0 0 X 15 ,15ix  ,15ic  0 0 0 0 X 0 0 0 0 0 16 ,16ix  ,16ic  0 0 0 0 0 X 0 0 0 0 17 ,17ix  ,17ic  0 0 0 0 0 0 X 0 0 0 18 ,18ix  ,18ic  0 0 0 0 0 0 0 X 0 0 19 ,19ix  ,19ic  0 0 0 0 0 0 0 0 X 0 Treatment 20 ,20ix  ,20ic  0 0 0 0 0 0 0 0 0 X Note: X denotes harvesting while 0 denotes no harvesting xikk=0K∑ = 1, ∀i(1−α) ⋅v0≤ vikt ⋅xikk=1K∑i=1m∑ ≤ (1+α) ⋅v0, ∀taklv ⋅xik+alkv ⋅xjl≤1, ∀i, j ∈NBi,k,l(≠ k){xij}∈ {0,1} aklv =1  if k -th and l -th treatments have any concurrent harvest0  otherwise⎧⎨⎪⎪⎩⎪⎪4. Habitat connection	Linking with Harvest Scheduling Aggregation => Spatial Harvesting => Temporal	2 ⋅zijk ≤ xik+ xjk≤ 2 ⋅zijk +1, ∀i, j ∈NBi,kyijB(n)n=1N∑ = zijkk=1m∑ , ∀i, j ∈NBi{xij},{yijB(n)},{zijk }∈ {0,1}Arc connection	 yij+yji≤1, ∀i, j ∈NBiyi0+ yijj∈NBi∑ = 1, ∀iCorridor flow constraints	Two habitats connection	Five habitats connection	Three habitats connection	        Maximum flow networkForest Map Flow NetworkSuper nodeUnit in-flowUnit in-flowUnit in-flowOut-flow wijc ≤Nc ⋅yij, ∀i, j ∈NBiwi0c ≤Nc ⋅yi0, ∀i ∈ ScNc: the number of habitats wi0c + wijcj∈NBi∑ = wjicj∈NBi∑ +1, ∀i ∈ Scwijcj∈NBi∑ = wjicj∈NBi∑ , ∀i ∉ ScNo connection,   no flowFlow balance,   no leakage wi0ci∈Sc∑ = Ncyi0i∈Sc∑ = 1One connection   to super nodeMF-Model	I	for	Corridor+ Maximum Flow Constraints+ Sequential Triangle ConnectionTemporal SchedulingSpatial ConnectionSpatial ContinuityBridge + Linkage ConstraintsModel I+ Corridor Flow ConstraintsHabitat Connection31123552431324141131311354442555223444322533321 55511455522235452445443154325113554 414352525331 period2 period3 period4 period5 periodPreserved311245524313142411312113554442545222444322532255511555222354434544354325213554314251525331123553132413321135444425552123443225332555115555222254443431542421314533143552533Five habitats	 Z = max{xij }cij⋅xijj=1K∑i=1m∑st.xikk=0K∑ = 1, ∀im(1−α)v0≤ vijp ⋅xijj=1K∑i=1m∑ ≤ (1+α)v0, p = 1,!,TMax NPV Land Account Constraints Harvest Flow Constraints Model	I1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162636465666768697071727374757677787980818283848586878889 90919293949596979899100

離散最適化による最適保護区連結ネットワークの探求

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離散最適化による最適保護区連結ネットワークの探求

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離散最適化による最適保護区連結ネットワークの探求

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