2009年研究生数模D题110警车配置及巡逻方案

234ACEBDiAiNcp5cpvp[]visitedi[]patrolei[]polulationi[]strengthiss∆d6itMetropolisMetropolisiA{1ℜ,}N1{,,}|1,,,1,,{}miijCcccNccforijmℜ==≤≤≠=0{1,[],,}NCm=NA[]LENA11max({,,})()immcinccLENA==∪1{,,}mCcc=icic'ic''1{,,}imCccc=ic'ic''1{,,}imCccc='()()nnCnC∆=−71,0exp(/),0nPnbTn∆⎧=⎨∆∆≤⎩0n∆0n∆≤exp(bT/)nbT∆89cpcp[]visitedi101,[]0,ivisitedii⎧=⎨⎩vp1visited[]NivipN==∑[]polulationi[]patrolei[][][]patrolistrengthipopulationi=([]0.8[]1strengthistrengthj.5=1121[][]/[]([])NNiiNsistrengthipatrolipopulationisNNstrengthis===⎧⎪⎪==⎪⎨⎪⎪∆=−⎪⎩∑∑∑1100ciiicpsOpsαβ=−iO,αβciips0c0psiOiO1234.538176.252237-5.414()1.925100.9555()4.656100.9314()0.0050190.008231()4.176109.167fxxfxxfxxfxx−−⎧=−×+⎪=−×+⎪⎨=+⎪⎪=×+⎩13(,)aij(,)rij(),(,)ijrij{}2211,NNnniiiiFAAAσ×==−∀⊆ℜ∑11NiiAAN==∑2,,1nijFijA==∑a10lim[log()log()]dNεεε→=()Nεε14123456789102.52.42.52.42.64.66.13.92.33.3111213141516171819202.53.82.75.85.16.64.75.23.35.5212223242526272829303.44.23.03.24.54.23.74.04.02.4()1/Nεε=2()(1/)Nεε=3()(1/)Nεε=1500ciiicpsOpsαβ=−0cicppβ16171()1()min,1,,.0.9..1,1,2,3.01,1,,.NiijijiNiikktinxxyforiNyNstxfortxorforiN===⎧≥=⎪⎪⎪≥⎪⎨⎪≥=⎪⎪==⎪⎩∑∑∑∑ixiiyinN()jiit()kt[1]1995[2]1999[3]MATLAB7200518