甌北網(wǎng)站制作報價山西seo優(yōu)化公司
一、優(yōu)化模型介紹
在所研究的區(qū)塊鏈網(wǎng)絡(luò)中，優(yōu)化的變量為：挖礦決策（即 m）和資源分配（即 p 和 f），目標(biāo)函數(shù)是使所有礦工的總利潤最大化。問題可以表述為：
max ? m , p , f F miner? = ∑ i ∈ N ′ F i miner? s.t.? C 1 : m i ∈ { 0 , 1 } , ? i ∈ N C 2 : p min ? ≤ p i ≤ p max ? , ? i ∈ N ′ C 3 : f min ? ≤ f i ≤ f max ? , ? i ∈ N ′ C 4 : ∑ i ∈ N ′ f i ≤ f total? C 5 : F M S P ≥ 0 C 6 : T i t + T i m + T i o ≤ T i max ? , ? i ∈ N ′ \begin{aligned} \max _{\mathbf{m}, \mathbf{p}, \mathbf{f}} & F^{\text {miner }}=\sum_{i \in \mathcal{N}^{\prime}} F_{i}^{\text {miner }} \\ \text { s.t. } & C 1: m_{i} \in\{0,1\}, \forall i \in \mathcal{N} \\ & C 2: p^{\min } \leq p_{i} \leq p^{\max }, \forall i \in \mathcal{N}^{\prime} \\ & C 3: f^{\min } \leq f_{i} \leq f^{\max }, \forall i \in \mathcal{N}^{\prime} \\ & C 4: \sum_{i \in \mathcal{N}^{\prime}} f_{i} \leq f^{\text {total }} \\ & C 5: F^{M S P} \geq 0 \\ & C 6: T_{i}^{t}+T_{i}^{m}+T_{i}^{o} \leq T_{i}^{\max }, \forall i \in \mathcal{N}^{\prime} \end{aligned} m,p,fmax??s.t.??Fminer?=i∈N′∑?Fiminer??C1:mi?∈{0,1},?i∈NC2:pmin≤pi?≤pmax,?i∈N′C3:fmin≤fi?≤fmax,?i∈N′C4:i∈N′∑?fi?≤ftotal?C5:FMSP≥0C6:Tit?+Tim?+Tio?≤Timax?,?i∈N′?
其中：
C1表示每個礦工可以決定是否參與挖礦；
C2 指定分配給每個參與礦機的最小和最大傳輸功率；
C3 表示分配給每個參與礦工的最小和最大計算資源；
C4表示分配給參與礦機的總計算資源不能超過MEC服務(wù)器的總?cè)萘?
C5保證MSP的利潤不小于0;
C6 規(guī)定卸載、挖掘和傳播步驟的總時間不能超過最長時間約束。
在所研究的區(qū)塊鏈網(wǎng)絡(luò)中，我們假設(shè) IoTD 是同質(zhì)的，并且每個 IoTD 都具有相同的傳輸功率范圍和相同的計算資源范圍。
上式中：
F i m i n e r = ( w + α D i ) P i m ( 1 ? P i o ) ? c 1 E i t ? c 2 f i , ? i ∈ N ′ R i = B log ? 2 ( 1 + p i H i σ 2 + ∑ j ∈ N ′ \ i m j p j H j ) , ? i ∈ N ′ T i t = D i R i , ? i ∈ N ′ T i m = D i X i f i , ? i ∈ N ′ E i m = k 1 f i 3 T i m , ? i ∈ N ′ P i m = k 2 T i m , ? i ∈ N ′ F M S P = ∑ i ∈ N ′ ( c 2 f i ? c 3 E i m ) ? c 3 E 0 P i o = 1 ? e ? λ ( T i o + T i s ) = 1 ? e ? λ ( z D i + T i t ) , ? i ∈ N ′ F_i^{miner}=(w+\alpha D_i)P_i^m(1-P_i^o)-c_1E_i^t-c_2f_i,\forall i\in\mathcal{N'}\\R_{i}=B \log _{2}\left(1+\frac{p_{i} H_{i}}{\sigma^{2}+\sum_{j \in \mathcal{N}^{\prime} \backslash i} m_{j} p_{j} H_{j}}\right), \forall i \in \mathcal{N}^{\prime}\\T_{i}^{t}=\frac{D_{i}}{R_{i}},\forall i\in\mathcal{N}^{\prime}\\T_{i}^{m}=\frac{D_{i}X_{i}}{f_{i}},\forall i\in\mathcal{N}'\\E_i^m=k_1f_i^3T_i^m,\forall i\in\mathcal{N}'\\P_i^m=\frac{k_2}{T_i^m},\forall i\in\mathcal{N}^{\prime}\\F^{MSP}=\sum_{i\in\mathcal{N}^{\prime}}\left(c_2f_i-c_3E_i^m\right)-c_3E_0\\\begin{aligned} P_{i}^{o}& =1-e^{-\lambda(T_{i}^{o}+T_{i}^{s})} \\ &=1-e^{-\lambda(zD_{i}+T_{i}^{t})},\forall i\in\mathcal{N}^{\prime} \end{aligned} Fiminer?=(w+αDi?)Pim?(1?Pio?)?c1?Eit??c2?fi?,?i∈N′Ri?=Blog2?(1+σ2+∑j∈N′\i?mj?pj?Hj?pi?Hi??),?i∈N′Tit?=Ri?Di??,?i∈N′Tim?=fi?Di?Xi??,?i∈N′Eim?=k1?fi3?Tim?,?i∈N′Pim?=Tim?k2??,?i∈N′FMSP=i∈N′∑?(c2?fi??c3?Eim?)?c3?E0?Pio??=1?e?λ(Tio?+Tis?)=1?e?λ(zDi?+Tit?),?i∈N′?
二、差分進化算法求解
2.1部分代碼
close all
clear
clc
dbstop if all error
NP = 100;%礦工數(shù)量
para = parametersetting(NP);
para.MaxFEs =5000;%最大迭代次數(shù)
Result=Compute(NP,para);
figure(1)
plot(Result.FitCurve,'r-','linewidth',2)
xlabel('FEs')
ylabel('Token')
figure(2)
plot(Result.ConCurve,'g-','linewidth',2)
xlabel('FEs')
ylabel('Con')2.2部分結(jié)果
當(dāng)?shù)V工數(shù)量為100時：所有礦工的利潤隨迭代次數(shù)的變化如下圖所示
算法得到的資源分配：
1.99763301712028 0.222528597636855
1.98480090600989 0.232003797981878
1.99810737020089 0.516878075461127
1.99450954175327 0.121004799048830
1.98894335292950 0.457573161395314
1.98141441375851 0.764801153373885
1.99123792611056 0.0618336115864624
1.99957268156257 0.121004799048830
1.99869990696838 0.0545812896345451
1.99958167059988 0.555322442727203
1.99842776886770 0.0425674932800246
1.99782546212753 0.556999423219330
1.99781790486039 0.196587806899822
1.99507786088204 0.115226131066544
1.99052235611421 0.245674972808444
1.99670598640193 0.0505531222716088
1.99482731112569 0.570493296084591
1.99736278961552 0.483094177861634
1.98894335292950 0.262561711571175
1.98784689496156 0.0324778719744346
1.98851683245790 0.171964220456218
1.98796386190418 0.110054645825889
1.98418972990049 0.0724358226961023
1.99516235341290 0.0341179120870288
1.99873738363101 0.489382783726158
1.99697974388302 0.0173712437086769
1.98964833679332 0.0320026913839283
1.99751719786278 0.147890074497164
1.99751719786278 0.434936315273999
1.99748331769841 0.232003797981878
1.99960825876476 0.483665232586750
1.99763301712028 0.631745087572258
1.99703599779628 0.358292746434059
1.99528222092061 0.514944354258863
1.99655084169003 0.753834027257007
1.99842776886770 0.940560567187612
1.99836116767571 0.221230559879615
1.99981576341436 0.184249732087410
1.99836116767571 0.0324778719744346
1.99654201611710 0.335915952413277
1.99237903891650 0.155001423906853
1.99760611708088 0.375017552592607
1.99978704361437 0.561786832194378
1.98578574172372 0.0236239899979008
1.99866761178096 0.0324778719744346
1.99763301712028 0.472369465588862
1.99721838438050 0.700915679954801
1.99428564716577 0.157199586550231
1.99655135483398 0.105209390328771
1.94788362094720 0.0258755419701254
1.99449453062393 0.132251896484895
1.99700992290778 0.0898397719008559
1.99965518095321 0.596537124037070
1.99278786910748 0.0256042543513514
1.99957848431148 0.894961847587823
1.99175299365895 0.0890674637434230
1.99750797157559 0.607592532504797
1.99748331769841 0.0724358226961023
1.99260527116064 0.631745087572258
1.99928439965780 0.127930497832236
1.99817708666189 0.104282160660561
1.99421206141539 0.803656147079701
1.98359960108601 0.118868109287597
1.99899700099444 0.518357001275729
1.99528222092061 0.0324778719744346
1.99877098644022 0.665529673319171
1.99763301712028 0.334090268607101
1.99860560539076 0.0866379799536027
1.99979684848517 0.377299990245342
1.99855631180132 0.389679849807951
1.99731236573268 0.434936315273999
1.99696360320736 0.570493296084591
1.99993018378939 0.391296247028955
1.99965327995029 0.287460195344814
1.99979684848517 0.450997212108626
1.99751719786278 0.287460195344814
1.99763301712028 0.155001423906853
1.99783983352391 0.103569288167448
1.99654201611710 0.127930497832236
1.98747116264687 0.0330088002325308
1.99655135483398 0.0797018166113099
1.99108222250111 0.0866379799536027
1.99718273730151 0.662248213795699
1.99869990696838 0.191058236556442
1.99652919147221 0.215505887700011
1.99459957647011 0.140056664895674
1.99806054285466 0.120547231379614
1.98593862830166 0.0916486389328984
1.97931641143295 0.462734428071515
1.99855631180132 0.101120011114003
1.99421206141539 0.258443908859530
1.99781790486039 0.543516910843497
1.99720522726900 0.0737173931186571
1.98303440848516 0.152622777636722
1.99900862513681 0.674526132004626
1.99866761178096 0.358292746434059
1.99783983352391 0.491305146804456
1.99960825876476 0.122579254402338
1.96710953562570 0.0513811784835662
1.99842776886770 0.0112006869294710