a time-driven cloudlet placement strategy for workow
TRANSCRIPT
A Time-Driven Cloudlet Placement Strategy forWorkow Applications in Wireless MetropolitanArea NetworksJianshan zhang
Fuzhou University https://orcid.org/0000-0002-3006-1328Ming Li
Fuzhou UniversityXianghan Zheng ( [email protected] )
Fuzhou UniversityChing-Hsien Hsu
Asia University
Research Article
Keywords: mobile edge computing, wireless metropolitan area network, workow application, cloudletplacement, computation ooading
Posted Date: July 19th, 2021
DOI: https://doi.org/10.21203/rs.3.rs-693704/v1
License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
❩♥ t
♠r♥ ♦t P♠♥t trt② ♦r❲♦r♦ ♣♣t♦♥s ♥ ❲rss tr♦♣♦t♥r t♦rs♥s♥ ❩♥ ♥ ❳♥♥ ❩♥ ♥ ♥s♥ s
strt
❲t t r♣ ♦♣♠♥t ♦ ♠♦ t♥♦♦② ♠♦ ♣♣t♦♥s ♥rs♥ rqr♠♥ts ♦r♦♠♣tt♦♥ rs♦rs ♥ ♠♦ s ♥ ♥♦ ♦♥r ♠t ts rqr♠♥ts ♦ ♦♠♣t♥ s ♠r ♥ ts ♦♥t①t ♥ s r♦t ♥♥♦t♦♥ ♥t♦ t ♦r♥ ♠♦ ♦ trt♦♥ ♦♦♠♣t♥ ② ♣r♦s♦♥♥ srr ♣♠♥t t ♦♠♣t♥ ♣♦r ♦ t ♦ ♥tr s strt t♦t ♦ t ♥t♦r ♥♥t ♦♠♣tt♦♥ rs♦rs ♦ srrs ♦♠♣♥st ♦r t ♦♠♦ s ♥ s♦rt♥ t ♦♠♠♥t♦♥ ② t♥ srrs ♥ srs ♦♥sttt♥ s♣ ♦r♠s♦ srrs ♦ts ♥ ② st t♥ ♠ ♥ ♥str② ♥ r♥t ②rs ♦r①st♥ sts ♠♥② ♦s ♦♥ ♦♠♣tt♦♥ ♦♦♥ ♦r ♥r ♦♠♣t♥ tss ♥r ①♦t ♣♠♥t ♣♦st♦♥s ② ♥♦r t ♠♣t ♦♥ ♦♠♣tt♦♥ ♦♦♥ rsts r♦♠ ♦t♣♠♥t ♣♦st♦♥s ♥ t ♣♥♥s ♠♦♥ ♠♦ ♣♣t♦♥ ♦♠♣♦♥♥ts ♥ ts ♣♣r st② t♦t ♣♠♥t ♣r♦♠ s ♦♥ ❲♦r♦ ♣♣t♦♥s ❲s ♥ ❲rss tr♦♣♦t♥ r t♦rs❲s ❲ s ♦t ♣♠♥t strt② s ♦♥ Prt sr♠ ♦♣t♠③t♦♥ ♦rt♠ s♥♥t ♦rt♠ ♦♣rt♦rs t t ♥♦♥ rr② ♣t♥ ♠♦ P ♥s t ♦t t♦ ♣ ♥ ♣♣r♦♣rt ♣♦st♦♥s s♠t♦♥ rsts s♦ tt t ♣r♦♣♦s strt② ♥ ♦t♥ ♥r♦♣t♠ ♦ts ♣♠♥t s♠ ♥ ♦♠♣r t ♦tr ss ♦rt♠s ts ♦rt♠ ♥r t ①t♦♥ t♠ ♦ ❲s ②
②♦rs ♠♦ ♦♠♣t♥ rss ♠tr♦♣♦t♥ r ♥t♦r ♦r♦ ♣♣t♦♥ ♦t♣♠♥t ♦♠♣tt♦♥ ♦♦♥
♥tr♦t♦♥❲t t ♠r♥ ♦ ♠♦r ♥ ♠♦ rr ♥ ♥ ♥rt♦♥ ♦ ♠♦ ♦♠♠♥t♦♥ t♥♦♦② tt ♥trts rss ♦♠♠♥t♦♥ ♥ ♠♦r♥ ♥tr♥t t♥♦♦s ♠♥② ②s♥st ♥ ♦♠♣tt♦♥♥t♥s ♠♦ ♣♣t♦♥s s s ♦ r♦♥t♦♥ ♣♣t♦♥s ♦♥♥♠s sts ♥ ♠♥t rt② ♣♣t♦♥sr ♣rs♥t ♦♥ ♠♦ s s ♣♣t♦♥s♣♦s ♥ ♥s t♦ ♠♦ s t♦ ♠♦ rrrt t♥♦♦s ♠ rt♣r♦rss t♦ t rstrt♦♥s ♦ ♠♦ s ♥s③ t ttr② ♥ t ss♣t♦♥ t ♣t♥ t ♣t② ♦ ♠t ♦♠♣tt♦♥ rs♦rs ♥ ♦♠♣tt♦♥♥t♥s ♣♣t♦♥ rqr♠♥ts s r② ♥rs♥ ❬❪ ♦ ♦ ♦♠♣t
♦rrs♣♦♥♥ ①♥♥③♥③♥♦ ♦ t♠ts ♥ ♦♠♣tr ♥ ③♦ ❯♥rst②
③♦ ♥
st ♦ t♦r ♥♦r♠t♦♥ s t t ♥ ♦ t rt
♥ ♦♠♣t♥ ♣r♠ ♥trts ♦♦♠♣t♥ ♥ ♠♦ ♦♠♣t♥ t♦ ♥♥ t ♦♠♣tt♦♥ ♣r♦r♠♥ ♦ ♠♦ s ❬❪ ② ♦♦♥ ♣♦rt♦♥ ♦r ♦ t ♦♠♣♦♥♥ts ♦ ♠♦ ♣♣t♦♥s t♦ ♦ srr t ♣r♦r♠♥ ♦ ♠♦ ♣♣t♦♥s ♥ rt② ♠♣r♦ ❬❪ ♦r ♠♦r♥ ♠♦ ♣♣t♦♥s ♥r② rqr♠♥ts ♦r ♥st♥t♥t② trt♦♥ ♥tr♦ s s② r♠♦t② ♦t ♥ st♥t r♦♠ tsrs ♦r ♠♦st ♠♦r♥ ♠♦ ♣♣t♦♥s ♦♦♥t♦ t ♥tr ♦ ♠② ♥♦t ♦♣t♠ s♦t♦♥♦ ♦r♦♠ ts s♥ts ♠♦ ♦♠♣t♥ s ♥ ♥t s♦t♦♥ tt ♥ ttrs♦ t ♣r♦♠ ♦ ♥s♥t rs♦rs ♦ ♠♦s s ♥ ♦♠♣t♥ ♣r♠ ♣r♦♣♦s tr s r♦t ♥♥♦t♦♥ t♦ t ♦r♥ ♠♦ ♦ trt♦♥ ♦ ♦♠♣t♥ ❲♥ srrs r ♣ t t ♦ t ♥t♦r t ♦♠♣t♥ ♣♦r ♦ t ♥tr ♦ s strt t♦ t
❩♥ t P ♦
♥t♦r ♥ t r ♦♠♣tt♦♥ rs♦rs ♦t srrs ♦♠♣♥st ♦r t ♦ ♠♦ s ♥ ♣rtr ♦♥sttt♥ s♣ ♦r♠ ♦ srr ♦ts ♥ ② st ② ♠♥ ♥str② ♥ r♥t ②rs ♣r♦♠ ♦ ♦t♣♠♥t s t ② t♦ t ♥t t③t♦♥ ♦ rs♦rs ♥ t ♥t♦r ❬❪ ♦t s ♦♠♣♦s♦ ♦♠♣tr strs t ♠♥② ♦♠♣tt♦♥ ♥st♦r rs♦rs t rss t ♥ ss ♣♦♥t P♥ t ♥t♦r t♦ ♣r♦ ♦♠♣t♥ srs ♦r♠♦ s ♦ ♣♣t♦♥s ♥ ♥tr t ♥t♦r tr♦ t P ♥ t♠t② ♦♦ t♦t ♦ts ♥ t ♥t♦r ♦r ♣r♦ss♥ ♦♠♣rt tt ♦r t trt♦♥ ♥tr ♦ t s♣tst♥ t♥ ♦ts ♥ ♠♦ s s ♦sr ♥rss t ♥t♦r ♦♥♥t♦♥ stt② ♥s♣ t♥ t♠ r♥ t t♠ ♦st ♦♠♦ s ①♣♥ ♦♥ ♦t♥♥ t♦♥ ♦♠♣tt♦♥ rs♦rs①st♥ rsr ♦r s ♠♥② ♦s ♦♥ t
♣r♦♠ ♦ ♦♠♣tt♦♥ ♦♦♥ ♦ ♥r tss ♥r ♦♥t♦♥s ♦ ① ♦t ♣♠♥t ♣♦st♦♥s❬❪ ♥ s sts ♦t ♣♠♥t ♣♦st♦♥sr rt② ♥ s ♣rt ♦ t ♥t♦r ♥r♦♥♠♥t ♥♦r♥ t ♠♣t ♦♥ ♦♠♣tt♦♥ ♦♦♥rsts r♦♠ ♦t ♣♠♥t ♣♦st♦♥s ♥ t t♣♥♥ ♠♦♥ ♠♦ ♣♣t♦♥ ♦♠♣♦♥♥ts ♥t t ♦t ♣♠♥t ♣♦st♦♥ ♥ t ♥t♦rs rt t♦ t ①t♦♥ t♠ ♦ ♦♠♣t♥ tss♦♦ r♦♠ ♠♦ s ♥ t rs♦r t③t♦♥ ♦ ♦ts s♣② ♥ rs rss♠tr♦♣♦t♥ r ♥t♦rs ❲s t t♦s♥s♦ Ps ❲ ♣r♦s ♥t♦r srs ♦r ♠♦ srs ♥ rs ♠tr♦♣♦t♥ rs s ♥t♦rs r s② ♣ ♥rstrtr ♥ ♦♣rt② t ♦ ♦r♥♠♥t ❬❪ r♥s t ♦♦♥ ♥ts t ♠tr♦♣♦t♥ r ♦r ② t❲ s ♣♦♣t♦♥ ♥st② ♥ ♦ts♥ ♣r♦ ♦♠♣t♥ srs ♦r ♠♦r ♠♦ s t♦ ♠♣r♦ t t③t♦♥ ♦ ♦ts ♥ ♦ t r s ♦ ❲s sr ♣r♦rs ♥t ♥t ♦ ♦♥♦♠s ♦ s t♦ r t s♣r ♦ ♦ts ♠♥ ♦t srs ♠♦r s② ♣t ② t ♣ ♦r t ♦rrt ♣♠♥t ♦ ♦ts ♥ ❲s s ♠♦r ♥♥ t♦♥ t ♦rrt ♦t ♣♠♥t ♣♦st♦♥s ② ♠♣♦rt♥t t♦ ♠♣r♦ t sr ①♣r♥ ♦♠♦ ♣♣t♦♥s r t♦ ♣r♦♣r② ♣ ♦ts rst ♥ ♦♠♣tt♦♥ ♦♦♥ tt ♥♥♦t t② r t ①t♦♥ t♠ ♦ ♠♦ ♣♣t♦♥s ♥t② t t sr ①♣r♥♦ ♠♦ ♣♣t♦♥s s ♣♣r ♦ss ♦♥ s♦♥t K(≥ 1) ♦ts ♣♠♥t ♣r♦♠ ♥ rs❲s ♥ ② ♦♥srs t ♠♣t ♦ t tr♥s♠ss♦♥ t♠ ♥ ①t♦♥ t♠ ♦ stss ♥
♥ ♦r♦ ♣♣t♦♥s ❲s ♦t s t♦ ♥ ♦t ♣♠♥t s♠ tt ♠♥♠③s t ①t♦♥ t♠ ♦ ❲s ♠♥ ♦♥trt♦♥s ♦ ts♣♣r r s ♦♦s• ❲ ♣r♦♣♦s ♥ strt ♠♦ ♦ ♦t ♣♠♥t s②st♠ ♥ t ❲ ♥ ts s②st♠ ♠♦♠♦ ♣♣t♦♥s r ❲s t ♦♠♣① ♥tr♥ ♣♥♥s ❲t t ♦t ♦ ♠♥♠③♥t ①t♦♥ t♠ ♦ ❲s t ♠t♠t ♥②ss ♥ ♠♦♥ ♦ tK ♦t ♣♠♥t ♣r♦♠ ♥ ❲ s ♣r♦r♠
• ♣rt ♥♦♥ ♥ ♦t♦♥ ♣t ♠♦♣r♦sss ♥ t trt♦♥ ♣rt sr♠ ♦♣t♠③t♦♥ P ♦rt♠ r ♠♣r♦ ♥t ♦t ♣♠♥t strt② s ♦♥ P ♦rt♠ s♥ ♥t ♦rt♠ ♦♣rt♦rst t ♥♦♥ rr② ♣t♥ ♠♦ Ps ♣r♦♣♦s ② ♥tr♦♥ t ♣t ♦♣rt♦r♦ t ♥ t ♥♦♥ rr② ♣t ♠♦♥ t ♣rt ♣t ♣r♦ss ts strt② s♦st ♣r♦♠s ♦ s② ♥ ♥t♦ ♦ ♦♣t♠♥ r♥♥t ♦♣rt♦♥s r♥ t ♣rt ♣t ♣r♦ss tt r ♥♦♥tr ♥ t trt♦♥ P ♦rt♠
• ♦ r② t t♥ss ♥ s♣r♦rt② ♦ t♣r♦♣♦s strt② ♦♥t s♥t s♠t♦♥ ①♣r♠♥ts ①♣r♠♥t rsts s♦tt t ♣r♦♣♦s strt② ♥♦t ♦♥② ♦t♥s ♥r♦♣t♠ ♦t ♣♠♥t s♠ ♥ t②♣ ❲s t s♦ ♠♥t♥s ①♥t ♣r♦r♠♥ ♥ t ❲ ♥s s ♣♣r♦ s♦ s ♠♦r ♥t ♥ t ♥st sr ss ♦rt♠s
rst ♦ t ♣♣r s ♦r♥③ s ♦♦s ♥ t♦♥ sss ♦rs rt t♦ ts ♣♣r ♥ t♦♥ sr t s②st♠ ♠♦s ♥ ♥ t♣r♦♠ t♦ st ♥ t♦♥ ♥tr♦ t♦t ♣♠♥t strt② s ♦♥ P ♥ t♦♥ ♣rs♥t ♦r ①♣r♠♥t st♣ t♦♥♥ ♥②ss ♦ t rsts ♥② t♦♥ ♦♥st ♣♣r
t ❲♦r❯s♥ r♠♦t srrs t♦ ①♣♥ t ♦♠♣tt♦♥ rs♦rs ♦ ♠♦ s s ♥♦ ♥ ♠♣♦rt♥trsr rt♦♥ ♦ s ♠♣♠♥t ♦♠♣tt♦♥ ♦♦♥ ② ♥♣st♥ ♦♠♣t♥ tss♥ rt ♠♥ ♥ t♥ ♦♦♥ t♠ t♦ r♠♦t srrs ♦r ①t♦♥ ❬❪ ①st♥ ts ♦♦♥r♠♦rs ♥ ♦rt♠s ♠♥② ♦s ♦♥ ♦♦♥♦♠♣t♥ tss t♦ t ♦ srr ❬ ❪ ♦r ♦♥ t♦ sr ♥ts ♦ ♦ts t② r♣ ♦ srs ♥ ♦♠ t ♥♦♦♥ st♥t♦♥s ♥ ♠♥② s♥r♦s ❬ ❪ ♦♠♣r t ♦ srr s r ② r♦♠ t
❩♥ t P ♦
sr ♦t t rt♥ ♦♠♣tt♦♥ rs♦rs♣ ♦♥ t P ♥ t ♥t♦r s s♠r s♣tst♥ r♦♠ t sr ♠♥s tt t tr♥s♠ss♦♥ ② ♥♦ ♥ t ♣r♦ss ♦ ts ♦♦♥t♦ t ♦t s rt② r tr② t②♠♣r♦♥ t sr ①♣r♥ ♦ ②s♥st ♣♣t♦♥s ♦r ①♠♣ t s♥ ♦ t s ❬❪s②st♠ ♥ s♣♣♦rt ♥trt ♠♦ ♣♣t♦♥s ②♦♦♥ s♦♠ ♦♠♣♦♥♥ts ♦ t ♣♣t♦♥ t♦ t♦t ♥st ♦ t ♥tr ♦ t rs tt tr♥s♠ss♦♥ t♠ ♥ t ①t♦♥ t♠ ♦ ♦♠♣t♥ tss ♥ ♥s t ♣♣t♦♥ t♦ ♠t tstr♥♥t rqr♠♥ts ♦ rs♣♦♥s t♠ ② ♦♥sr♥ t qt② ♦ sr ♦ rqr♠♥ts ♦ ♠♦srs ♥ ♠♥ t♦ ♠①♠③ t r♥ ♦ sr♣r♦rs ♦♥ t ❬❪ ♣r♦♣♦s ♥r ♣r♦r♠♠♥ s♦t♦♥ t♦ t ts ♦♦♥ ♣r♦♠ ♦♦s ♦♠♣t♥ tss t♦ t ♣♣r♦♣rt ♦t♥ t ❬❪ ② ♦♥sr t ts ♣♥♥②♥ t ♥ ♦r r r♦r② tr ♦♦♥ sr t ts ♦♦♥ ♣r♦♠ ♥ ♦t s②st♠ s t ♠♥♠③t♦♥ ♦ ①t♦♥ ♦st ♥r t♦♥str♥t ♦ ts ♦♠♣t♦♥ ♥ ♥ ♣r♦♣♦s r♦st ♦♠♣tt♦♥ ♦♦♥ strt② tr r♦r② rtrsts ♥ t ❬❪ ♣r♦♣♦s ♥ ♥♥♦t r♠♦r tt ss strts♦♥♠♥ ♠♥♥r ♥ t② s ♦♦♣rt ♦ ♥♥ ♠♦♥ ♠t♣ s s ♦♥r♥♦r♠♥t r♥♥ ♥ ♥str ♦ ♥r♦♥♠♥ts♠r② ♥ t ❬❪ ♣r♦♣♦s ♥♦ ♠♦r ♦♦♥ ♠♦ ♥ ♥ ♥r♦♥♠♥t ♦♥srs t ①t♦♥ ♥② ♦ ♦♦♥ ts♣r♦ss♥ t♠ ♦♥str♥ts ♥ ♥r② ♥② ♥s♦s t ♥tr♥ ♦♦♥ s♥ ♣r♦♠ ♥♦ r tr♦♥♦s rs♦r ♦t♦♥ ♣r♦♠♥ ♦tst♦ rsr ♦♥ s♥ ♦ts s ♦♠♣t
t♦♥ ♦♦♥ st♥t♦♥s s ♦♠ ♣♦♣rrsr t♦♣ t ♦rrt ♦t ♣♠♥t ♣♦st♦♥ ♥ t ♥t♦r s ♥ ♥♦r ♦♠ ①st♥ sts ss♠ tt ♦ts r s ♥ s♠♥t♦r ♥r♦♥♠♥ts s s ♠♣ss ♦♠♣♥s♥ t♦r② ♣rs ❬❪ ♥ s ♥t♦r ♥r♦♥♠♥t rrss ♦ r ♦ts r ♣ t s♣t st♥ t♥ t♠ ♥ ♠♦ s s ①tr♠② ♠t ♠s t ♠♣t ♦ ♦t♣♠♥t ♣♦st♦♥ ♦♥ t s ♦ ♦ts ♥♦r ♥ ❲ s ♦♠♣♦s ♦ t♥s ♦t♦s♥s ♦ Ps t ♣♠♥t ♦ ♦ts ♦♠s①tr♠② ♠♣♦rt♥t ♥ ♦♠♣① ♦ ♠♥♠③ t①t♦♥ t♠ ♦ ♠♦ ♣♣t♦♥s t s ♠♣rt t♦ st② t ♦t ♣♠♥t ♣♦st♦♥ ♥ t❲ r rt sts ①st ♦♥ t ♣♠♥t♦ ♦ts ♥ rs ♥t♦rs t ❬❪ ♣r♦♣♦s ♠tsr ❲ ♦t ♣♠♥t ♠♦
s ♦♥ q♥ t♦r② ♠♦ s ♠♦ ♦♥srst ♣♠♥t ♦ ♦ts ♥ ♥s② ♣♦♣t rs♦ ❲ t ♠♦ srs ♥ ♦ts ♠♦srs t♦ ♥ t ♦ ♦ ♦ts tr t♦t ♣♠♥t s ♦♠♣t tr② ♠♥♠③♥t rs♣♦♥s t♠ ♦ t s②st♠ t ❬❪ stt ♣♠♥t ♦ ♦ts ♥ rs♦r ♦t♦♥ ♥ rs ❲ t♦rs ♣rs♥t ♠t♠t ♠♦ ♦ r ss ② t♥ ♠♦srs ♥ ♦ts ♥ ♣ K ♦ts ♥ ♠♣♦rt♥t♣♦st♦♥s ♦ ❲s ♠♥ t♦ ♠♥♠③ t ♥♠r♦ ♦ts ❳ t ❬❪ s♦ st t ♣r♦♠ ♦♦t ♣♠♥t ♥ rs ♥t♦rs ♣r♦♣♦s ♦t ♣♠♥t ♠♦ tt ♠♥♠③s t r ss t♠ t♥ ♠♦ srs ♥ ♦ts♥ t♥ r t t♦ ♥ ♥tr ♥r ♣r♦r♠♠♥P ♣r♦♠ t♦ ♦t♥ ♥ ①t s♦t♦♥ ♦♥sr♥ t ♣♦♦r st② ♦ P t t♦rs ♣r♦♣♦s rst ♦rt♠ ♦r ♦t ♣♠♥t st ♦rt ♣r♦♣♦s ♥t♦r ♥ s♥ ♥ ♣♣r♦①♠t ♦rt♠ tt r♥ts t ♣♣r♦①♠t rt♦ ♦r s♣ s♥r♦s r t ♦t ♣ts r q♥ t ❬❪ ♦♥sr ♣♥ ♦ts ♦♥ rss Ps ♥ t ♥t♦r ♥ ♦♦♥ t ♦♠♣t♥tss ♦ ♠♦ srs ♦♥ t Ps t♦ ♦ts ♦r ①t♦♥ t♦ ♠♥♠③ ♦♠♠♥t♦♥ ②s ♥ t♦♠♣t♥ tss ♦ ♠♦ srs rr t t Ps ②♥♠② t t♦rs rst ♦♥strt sr s♥♣s♦ts s ♦♥ st♦r t t r♥t t♠ ♥trs ♥ ♥ ♣♣r♦①♠t ♦rt♠ s r ♦r s♥♣s♦t t♦ tt t st♦♥ ♦ s♦♠ Pss ♥t ♣♦st♦♥s ♦ ♦ts ♥ t ❬❪♣r♦♣♦s r♥t♠ ♠♦s ♣♣r♦ t♦ ♦ ♣♣t♦♥ ♦♣♠♥t ♠ t rst tt♠♣tt♦ ♠♥ r♦s ♦ s s ♦♥ r♥t♠ s♦tr rttr ❩ t ❬❪ ♣r♦♣♦s ♠♦ ♣♦♣t♦♥ r ♦♣t♠③t♦♥ ♦rt♠ t♦ s♦ t ♦♥t ♣r♦♠ ♦ ♦t ♣♠♥t ♥ ts ♦♦♥ ♦t s t♦ ♠♥♠③sr ♥r② ♦♥s♠♣t♦♥ ts rs♣♦♥s ② ♥ t♥♠r ♦ ♦ts ♣ ♦ t ❬❪ st t♣♠♥t ♦ srrs ♥ t ♥tr♥t ♦ ❱s♦♥sr t tr♥s♠ss♦♥ ② ♦r♦ ♥♥r② ♦♥s♠♣t♦♥ ♣♠♥t ♦st ♥t♦r rt② ♥ t ♥♠r ♦ srrs ♦♥strt ♠t♦t srr ♣♠♥t ♦♣t♠③t♦♥ ♣r♦♠ ♥ ♣r♦♣♦s ♠t♦t ♦t♦♥r② ♦rt♠ t♦ s♦ t ♦ ♣r♦♠s t♦ t♠t♦s ♣r♦♣♦s ♥ t ♦ rt rsr ♦r♥ s♦ t ♣r♦♠ ♦ ♦t ♣♠♥t t♦ rt♥ ①t♥t t ♣r♦♣♦s ♠t♦s r ♥st ♦rs♥r♦s r t ♦♠♣t♥ tss ♦♠♣① ♣♥♥s
❩♥ t P ♦
②st♠ ♦ ♥ Pr♦♠♦r♠t♦♥
♥ ts st♦♥ rst sr t ❲ ♥ ❲s②st♠ ♠♦s ❲ t♥ ♥ t ② t♠ ♣♦♥ts ♥t ①t♦♥ ♣r♦ss ♦ ❲s ♥② ♥ t♣r♦♠ ♣rs② ♦r s ♦ rr♥ st t ②♥♦tt♦♥s ♦ ♦r s②st♠ ♠♦ ♥
②st♠ ♦ ❲ ♦
s s♦♥ ♥ ♦♥sr ❲ ♦♠♣♦s ♦sr Ps Ps r ♦♥♥t tr♦ r♥t♦r t♦ ♦r♠ ♦♥♥tt② r♣ strtr t sss♠ tt P ♥ t ❲ r ❲♥ t ♦♥sr t♠ s♦t ♥ ts ❲s r ♦♥t②①t ② sr ♦ts ♣ ♦♥ t Ps ♦t ♣♠♥t s♠ ♥ t ♦♦♥ strt② ♦ ❲s t t ①t♦♥ t♠ ♦ ❲s ❲ ♥ r♣rs♥t ② r♣ G = (V,E)♥ ♥♦ ♥ V = v1, v2, ..., vn r♣rs♥ts ♥ P♥ t ❲ E s t st ♦ s t♥ Ps♥ (vi, vj) ∈ E r♣rs♥ts t ♥t ttr♥s♠ss♦♥ ② t♥ vi ♥ vj ♥ ♣rtr♥ t♦ Ps r ♥♦t rt② ♦♥♥t t ♥t ttr♥s♠ss♦♥ ② s ♦t♥ ② ♥ t ♥t ttr♥s♠ss♦♥ ② ♦ s ♥ t s♦rtst ♣t❬❪
t♥ t♠ ❲ ♥ ♠tr① D ∈ Rn×n rDi,j ∈ D r♣rs♥ts t ♥t t tr♥s♠ss♦♥ ②t♥ vi ♥ vj
❲ ♦
♥ ❲ t ❲ r ② P ♦♥ssts ♦ sr stss ♥ tr s t ♣♥♥② t♥t♠ st ♦ ❲s r ② Ps s ♥♦t sG
❲ = G❲1 ,G❲
2 , ...,G❲n ♥ ❲ ♥ r♣
rs♥t ② rt ② r♣ G❲i = (Li,Ei)
s s♦♥ ♥ Li = l1i , l2i , ..., l
si r♣rs♥ts s
stss ♥ ♥ G❲i ♥ t ♦♠♣tt♦♥ r
qr♠♥t ♦ lji s r♣rs♥t ② θji Ei = ej,ki , ∀j, k ∈
1, ..., s ♥ts t t ♣♥♥ t♥ s
tss ♥ ♥ G❲i ♥ e
j,ki > 0 tr s t
♣♥♥② rt♦♥s♣ t♥ lji ♥ lki ♥ ♥
ej,ki = 0 tr s ♥♦ t ♣♥♥② rt♦♥s♣
t♥ lji ♥ lki
♦t P♠♥t ♥ ts ♦♥
❲ s st C = c1, c2, ..., cK t♦ r♣rs♥t K
♦ts t♦ ♣ ♥ ❲ r t ♦♠♣t♥ ♣♦r ♦ ♦t ci s r♣rs♥t ② ηi K ♦t ♣♠♥t s♠ ♥ t ❲ ♥
❬❪♥ ♥ P ♥t♦r t♦♣♦♦② t s♦rtst ♣tt♥ Ps ♥ ♦t♥ ② t str ♦rt♠
♥ s ω = ωi,j , ∀i ∈ 1, ...,K, j ∈ 1, ..., n❲♥ ♦t ci s ♣ t P vj ωi,j = 1 ♦trs ωi,j = 0
s ♦r ♦r ♦ss ♦♥ ♦t ♣♠♥t ♥ ❲ t ♦s ♥♦t ♦♥sr t ♠♣t ♦ tsts ♦♦♥ strt② ♦♥ t ❲ ①t♦♥ rsts ❲♥ t ♦t ♣♠♥t ♣♦st♦♥s r tr♠♥ t ♦ ❲ ♥t♦ sr rs ♦♥ r ♥ r r② ♦♦♥ ♦rt♠ s♠r t♦ tt ♥ ❬❪ s s t♦ ♦♦ tstss tt s t ❲s r ② r r♦♥t② ①t ② t ♦ts ♣ ♥ t r ①t♦♥ ♦rr ♦ t stss ♥ ♥ ts♠ ❲ s tr♠♥ ② t rtrst trrs ♦ t r♣ ❬❪ ❲♥ t ♦ r② ♦♦♥ ♦rt♠ ♦♦s t stss t strt②♦ ♠♥♠③♥ t t♦t t♠ ♦st ♦ ts ①t♦♥♥♠② t s♠ ♦ ①t♦♥ t♠ ♥ tr♥s♠ss♦♥t♠ s ♦♣t ♦r♥ t♦ t ①t♦♥ ♦t♦♥♦ stss ♣rrs♦r stss t s ♦♦t♦ t ♣♣r♦♣rt ♦t ♥ t ♦ sts♦♦♥ strt② s t♠t② ♦t♥ s
♥♦t s M =⋃|G❲|
i=1(lji , ck)|l
ji ∈ Li, ck ∈ C
❲ ①t♦♥ t♠
♥ t ♦t ♣♠♥t s♠ ω ♥ sts♦♦♥ strt② M t ♦♦♥ ② t♠ ♣♦♥tsr ♥
strt ①t♦♥ t♠ ♦ t sts strt t♠ ♦ sts l
ji ♦♥ ♦t ck s tr♠♥
② t ①t♦♥ ♥ t♠ ♥ t ♣♥♥t ttr♥s♠ss♦♥ t♠ ♦ ts ♣rss♦r stss t sq♥t s
tstart(lji , ck) =
maxep,j
i>0,∀ep,j
i
tend(lpi , cw) + ttrs(l
pi , l
ji , cw, ck),
∀(lji , ck), (lpi , cw) ∈ M
r tend(lpi , cw) ♥ ttrs(l
pi , l
ji , cw, ck) r t ①
t♦♥ ♥ t♠ ♦ sts lpi ♥ t ♣♥♥t t
tr♥s♠ss♦♥ t♠ t♥ stss lpi ♥ lji rs♣
t② r t♦♥ qt♦♥s ♥ ♥ q ♥ q rs♣t②
①t♦♥ t♠ ♦ t sts ①t♦♥ t♠ ♦ sts l
ji s tr♠♥ ② ts ♦♠♣
tt♦♥ rqr♠♥ts ♥ t ♦♠♣t♥ ♣♦r ♦ t♦t ①t♥ t sts t s q♥t s
texe(lji , ck) =
θji
ηk, ∀(lji , ck) ∈ M
❩♥ t P ♦
♣♥♥t t tr♥s♠ss♦♥ t♠
t♥ t stss ♣♥♥t t tr♥s♠ss♦♥ t♠ t♥ stss lpi ♥ l
ji s tr♠♥ ②
t s③ ♦ t ♣♥♥t t t♥ t t♦ stss ♥ t ♥t t tr♥s♠ss♦♥ ② t♥t Ps t ♦ts ♣ t s q♥t s
ttrs(lpi , l
ji , cw, ck) = e
p,ji dw′,k′ ,
∀(lji , ck), (lpi , cw) ∈ M , ωw,w′ , ωk,k′ = 1
①t♦♥ ♥ t♠ ♦ t sts ①t♦♥ ♥ t♠ ♦ sts l
ji ♦♥ ♦t ck s
tr♠♥ ② t strt ①t♦♥ t♠ ♦ sts lji ♥
ts ①t♦♥ t♠ ♦♥ ♦t ck t s q♥t s
tend(lji , ck) = tstart(l
ji , ck) + texe(l
ji , ck),
∀(lji , ck) ∈ M
①t♦♥ ♥ t♠ ♦ t ❲ ①t♦♥ ♥ t♠ ♦ ❲ G
❲i s t ♠①♠♠ ♦ t
①t♦♥ ♥ t♠ ♦ ts stss t s q♥t s
tend(G❲i ) = max
lj
i∈Li
tend(lji , ck), ∀(l
ji , ck) ∈ M
①t♦♥ ♥ t♠ ♦ ❲s ♥t♠ ♦ ❲s ♥ t ❲ s t ♠①♠♠ ♦ t①t♦♥ ♥ t♠ ♦ t ❲s t s q♥t s
tend(G❲) = max
G❲i
∈G❲tend(G
❲i )
Pr♦♠ ♦r♠t♦♥
K ♦t ♣♠♥t s ♦♥ t ❲ ♣r♦♠ P❲P ♥ ❲ s ♥ s ♦♦s♥ ♥ ♥tr K > 1 ♥ s②st♠ ♠♦ ♣r♠trs (G,D,G❲) t ♣r♦♠ s t♦ ♥ ω s ttt ①t♦♥ t♠ ♦ ❲s ♥ q s ♠♥♠③
minω
tend(G❲)
st
n∑
j=1
ωi,j = 1, ∀i ∈ 1, ...,K
K∑
i=1
ωi,j ≤ 1, ∀j ∈ 1, ..., n
♦♥str♥t ♥ts tt ♦t t♦ ♣s ♦♥② ♦♥ ♣♠♥t ♣♦st♦♥ ♥ ♦♥str♥t ♥ts tt P s t ♠♦st ♦♥ ♦t t♦ ♣
♦t P♠♥t trt② s ♦♥P
♥ ts st♦♥ rst ♥tr♦ t trt♦♥ P♦rt♠ ♥ t♥ ♥tr♦ t ♦t ♣♠♥tstrt② s ♦♥ P ♥ t
rt♦♥ P P ♦rt♠ s st♦st ♦♣t♠③t♦♥ t♥q s ♦♥ ♣♦♣t♦♥ ♥ s ♣r♦♣♦s ② rrt ♥ ♥♥② ♥ ❬❪ ♥ ♥tr ♥♠s tt♦♥ t♦ t s♠ ♣♦♣t♦♥ ♦♦♣rt t ♦tr ♥ rt♥ ② ♠♠r ♦ t ♣♦♣t♦♥♥s ts ♦r ② r♥♥ ts ♦♥ ♥ ♦trs①♣r♥s P ♦rt♠ s♦s t ♦♣t♠③t♦♥ ♣r♦♠ ② ♠tt♥ t str♥ ♦r ♦♥♠s ♥ t P ♦rt♠ ♣rt r♣rs♥ts ♥t s♦t♦♥ ♦ t ♦♣t♠③t♦♥ ♣r♦♠ ♥ ♣rts ♥ ♠♦s ♥ t ♦ s♦t♦♥ s♣ ♥ t♣r♦ss ♦ sr t ♣rt ♠♦ t rt♥s♣ s t ② tr t♦rs t stt♦♥♦ t ♣rt ts t st ♣♦st♦♥ ♦ t ♣rtts ♥ t st♦r st ♣♦st♦♥ ♦ t ♣rt♥ t ♦ ♣rt sr♠ t♦ t trt♦♥P ♦rt♠ s t ♥ts ♦ ♦♦ r♦st♥ss♥ s② ♦♥r♥ t s♦ s ts ♦ ♦♣♥ ♣r♠tr ♦♥r♥ ♥ ♦♠♥ tr♣♣ ♥ ♦ ♦♣t♠♠ ♥ ts ♣♣r ② ♥tr♦♥ tr♦ss♦r ♦♣rt♦r ♥ ♠tt♦♥ ♦♣rt♦r ♦ t ♥t♦ t trt♦♥ P ♦rt♠ t P ♦t♣♠♥t ♦rt♠ s ♣r♦♣♦s t♦ ♦♠♣♥st ♦r tts ♦ t trt♦♥ P ♦rt♠ ♦♣t♠③ ts♦♣t♠③t♦♥ t② ♥ ttr s♦ t K ♦t♣♠♥t ♣r♦♠ ♥ ❲s
P Pr♦♠ ♥♦♥
♦ s♦ t P❲P ♥ ❲s s t ♦t♣♦st♦♥ sq♥ ♥♦♥ strt② t♦ ♥♦ t ♣rts ♣rt ♥ t ♣rt sr♠ ♦♠♣♦s♦ Ω ♣rts r♣rs♥ts ♣♠♥t s♠ ♦ K
♦ts ♥ ❲ stt ♦ t it ♣rt ♥t tt trt♦♥ s s ♦♦s
P ti = (pti,1, p
ti,2, ..., p
ti,K)
r pti,j ∈ 1, 2, ..., n r♣rs♥ts t ♣♠♥t ♣♦st♦♥ ♦ t jt ♦t ♠♣♣ ② ♣rt i ♥ ttt trt♦♥
t♥ss ♥t♦♥
♦ t ♦t ♣♠♥t s♠ ♦rrs♣♦♥♥ t♦ ♣rt t♥ss ♥t♦♥ s ♥tr♦r ♣r♣♦s s t♦ ♦t♥ ♦t ♣♠♥t s♠tt ♥ ♠♥♠③ t ①t♦♥ t♠ ♦ ❲s ♥
❩♥ t P ♦
❲ r♦r t ♣rt t s♠r ①t♦♥ t♠ ♦rrs♣♦♥♥ t♦ t ♠♣♣ ♦t ♣♠♥t s♠ ♥ s♠♣② rr s ttr ♣rt t♥ss ♥t♦♥ ♦ ♣rt P t
i ♥ ♥s
fitness(P ti ) = T ime(P t
i )
r T ime(P ti ) r♣rs♥ts t ①t♦♥ t♠ ♦ ❲s
t ② q ♥ t ♣♠♥t s♠♦rrs♣♦♥♥ t♦ P t
i s ♦♣t ♣rt t s♠r t♥ss ♦♦s② ♦rrs♣♦♥s t♦ t ♦t♣♠♥t s♠ t s♦rtr ①t♦♥ t♠ ♦r❲s
❯♣t trt②
♥ ♦r ♣r♦s ♦r ❬❪ t ♣t strt② ♦ ttrt♦♥ P ♦rt♠ s ♥tr♦ ♥ t P ♥s tr ♦r ♣rts ♥rt ♣rs♦♥♦♥t♦♥ ♥ s♦ ♦♥t♦♥ ♥ t trt ♣r♦ss♦ t ♦rt♠ t ♣t ♦ ♣rt s t② ts ♣rs♦♥ ♦♣t♠ ♣♦st♦♥ ♥ t rr♥t ♦♦♣t♠ ♣♦st♦♥ ♦ ♦ t t♥♥② ♦ t trt♦♥ P ♦rt♠ t♦ ♥t♦ t ♦ ♦♣t♠♠♣r♠tr② ♥ t♦ ♥♥ t sr t② ♦ t♦rt♠ ♥tr♦ t r♦ss♦r ♦♣rt♦r ♥ t♣rs♦♥ ♦♥t ♥ s♦ ♦♥t ♦♠♥s ♥t ♠tt♦♥ ♦♣rt♦r ♥ t ♥rt ♣rt t♦ ♦♠♣♥st ♦r t ts ♦ t trt♦♥ P ♦rt♠ ♣t strt② ♦ ♣rt i ♥ t (t + 1)t trt♦♥ s s ♦♦s
P t+1
i =
SC(PC(IT (P ti , w
t+1, µ), pBestti, ct+1
1 ), gBestt, ct+1
2 )
r PC(x, y, z) ♥ SC(x, y, z) r t ♣rs♦♥ ♦♥t♦♥ ♣t ♦♣rt♦♥ ♥ t s♦ ♦♥t♦♥ ♣t ♦♣rt♦♥ rs♣t② ♥ IT (x, y) s t ♥rt♣t ♦♣rt♦♥ r♦ss♦r ♦♣rt♦r ♦ t s ♥tr♦ ♥t♦
t ♣rs♦♥ ♦♥t ♣t ♦♣rt♦♥ ♥ s♦ ♦♥t ♣t ♦♣rt♦♥ rsts ♦ t ♣rs♦♥♦♥t♦♥ ♣t ♦♣rt♦♥ ♥ s♦ ♦♥t♦♥ ♣t ♦♣rt♦♥ r q♥t s
PC(At+1
i , pBestti, ct+1
1 ) =
CO(At+1
i , pBestti) , r1 ≤ ct+1
1
At+1
i , r1 > ct+1
1
SC(Bt+1
i , gBestt, ct+1
2 ) =
CO(Bt+1
i , gBestt) , r2 ≤ ct+1
2
Bt+1
i , r2 > ct+1
2
rs♣t② r r1 ♥ r2 r r♥♦♠ ♥♠rs r♦♠ t♦ ♥ CO(x, y) r♣rs♥ts t r♦ss♦r ♦♣rt♦r♦ r♦ss♦r ♦♣rt♦r r♥♦♠② sts ♥ ♥♦ s♠♥t ♦ ♣rt x t♦ ♣t ♥ r♣st t t ♦rrs♣♦♥♥ ♥♦ s♠♥t ♦ ♣rty r♦ss♦r ♦♣rt♦r ♥ t ♣rs♦♥ ♦r s♦♦♥t ♣t ♦♣rt♦♥ s s♦♥ ♥ ♠tt♦♥ ♦♣rt♦r ♦ t s ♥tr♦ ♥t♦
t ♥rt ♣t ♦♣rt♦♥ rst ♦ t ♥rt♣t ♦♣rt♦♥ s s ♦♦s
IT (P ti , w
t+1, µ) =
MU(P ti , µ) , r3 ≤ wt+1
P ti , r3 > wt+1
r r3 s r♥♦♠ ♥♠r r♦♠ t♦ ♥ MU(x)r♣rs♥ts t ♠tt♦♥ ♦♣rt♦r ♦ t ♠tt♦♥ ♦♣rt♦r r♥♦♠② sts µ ♥♦♥s ♦ ♣rt x t♦ ♣t ♥ t♥ r♥♦♠② ♥s ts ♦ ts ♥♦♥s ♠tt♦♥ ♦♣rt♦r ♥t ♥rt ♣t ♦♣rt♦♥ s s♦♥ ♥ ❲♥µ = 2 t ♥♦ ind1 ♥ ind2 r st tts t ♣♠♥t ♣♦st♦♥s ♦ t ♦rrs♣♦♥♥ t♦♦ts ♥ rt♦♥ ♣t♥ ♠♦
♥ ♦r ♣r♦s ♦r ❬❪ s t trt♦♥♣t♥ ♠♦ t♦ ♣t t ♥♦♥s ♦ t ♣rt trt♦♥ ♣t♥ ♠♦ s s ♦♦s ♥t③t♦♥ ♥♦♠② ♥♦ ♥♦♥ ts
♦ t ♣rt ♥ ♥sr tt t ♥♦♥s r ♥♦tq r♦ss♦r t ♣rts ♥♦♥ ♦t♥ ②
t r♦ss♦r ♦♣rt♦r ♦♥ts t t ♦r♥ ♥♦♥ tt s t ♦s ♥♦t ♠t t ♦♥str♥t tt♥ P ♣s ♦♥② ♦t t ♥s t♦ st t♥♦♥ ♦r♥ t♦ rt♥ rs s s t ♠♦stq♥t r♣♠♥t ♠t♦ t♦ ♥sr tt r②t♦ ♥♦♥s r ♥♦t q s s♦♥ ♥ tr♦ss ♥ ♦♥t t t ♦r♥ ♥♦♥ ♥♥ t♦ st t♦ ♦ ♦♥t tt♦♥ ♠r② t ♣rts ♥♦♥ ♦
t♥ ② t ♠tt♦♥ ♦♣rt♦r ♦♥ts t t♦r♥ ♥♦♥ t ♠tt ♥♦♥ ♥s t♦ st t♦ ♥sr tt t t♦ ♥♦♥s r ♥♦tq s s♦♥ ♥ ♥ t ♦r♥ ♥♦♥♥s t♦ ♥ t ♥ ♥♦♥ ♦♥ts t t♦r♥ ♥♦♥ ♥ ♦ t st♠♥t s♠s s t♦♥ t♦ ♥ t ♠tt ♥♦♥tr t ♠tt♦♥ ♦♣rt♦r ♥ r♦ss♦r ♦♣rt♦r
r ①t ♥ t trt♦♥ ♣t♥ ♠♦ t ♥♦♥s ♥ t s♠ ♣rt ♠② ♦♥t ♥ ♥ ♥t♦♥ st♠♥t ♣r♦ss rst ♥ t♦♥ ①t♦♥ t♠ r♥ t ①t♦♥ ♣r♦ss♦ t ♦rt♠ ♥♦♥ rr② ♣t♥ ♠♦
❩♥ t P ♦
♥ P s t ♥♦♥ rr② ♣t♥♠♦ t♦ ♦ ♣♦ss ♥♦♥ ♦♥ts t♦ ♦ t①tr t♠ s ② t st♠♥t ♣r♦ss ❲ t ♥♦♥ rr② ♦r ♣rt ♥ ♣t t ♥t ♦♦♥ ② ♥t③t♦♥ ❲♥ t ♣rts r ♥t③
t ♥♦♥s r r♠♦ r♦♠ t ♥♦♥ rr②♦♥ ② ♦♥ s♦ tt t② ♦ ♥♦t ♦♥t r♦ss♦r ♥ t ♣r♦ss ♦ ①t♥ t r♦ss♦r
♦♣rt♦r rst t r♣ ♥♦♥s ♦ t ♣rt t♦ tr ♦♥ ♥♦♥ rr② ♥ t♥ t ♥♦♥s ♦t♥ ② t r♦ss ♦♥ ② ♦♥ ♥♦♥ ①sts ♥ t ♥♦♥ rr② t t r♦♠t ♥♦♥ rr② ♥♦♥ ♦s ♥♦t ①st ♥ t♥♦♥ rr② t ♦sst ♥♦♥ s st r♦♠t ♥♦♥ rr② t♦ r♣ t ♦ t Ps tr♠♥ ② ts s♣ s♣t ♦t♦♥ s♦ t♦t♦♥ ♦ t ss ♣♦♥t ♥ t ♥t♦r r♣rs♥t② t ♦sst s t ♦sst s♦ t ♦ ♦♣rt♦♥ ♥ rt♥ t ♦r♥ ♣rt ♣♠♥t s♠t♦ t rtst ①t♥t tt♦♥ ❲♥ t ♠tt♦♥ ♦♣rt♦r ♥s t♦
①t ♥ ♥♦♥ s r♥♦♠② st r♦♠ t♥♦♥ rr② t♦ r♣ t ♦r♥ ♥♦♥ ♥t♥ t ♦r♥ ♥♦♥ s t♦ t ♥♦♥rr② ♥♦♥ rr② ♣t ♠♦ ♥ ♥sr tt
t ♥♦♥s ♥ t ♣rts ♦ ♥♦t ♦♥t ♥ t② s♦rt♥ t ①t♦♥ t♠ ♦ t r♦ss♦r♦♣rt♦r ♥ t ♠tt♦♥ ♦♣rt♦r
♣ r♦♠ Prtt♦♦t P♠♥t
♠
♠♣♣♥ ♦rt♠ ♦ t ♣rtt♦♦t♣♠♥t s♠ s s♦♥ ♥
♣♣♥ ♣rt t♦ ♦t♣♠♥t s♠
♥♣t Pt P ti
t♣t ♦t ♣♠♥t s♠ ω ♥ ♦r ωi,j ∈ ω ♦ ωi,j = 0 ♥
♦r pti,j ∈ P ti ♦
ωj,pti,j
= 1
♥ rtr♥ ω
♥
♥♣t ♦ s ♣rt P ti ♥
t ♦t♣t s ♦t ♣♠♥t s♠ ω rst♦t ♣♠♥t s♠ ω s ♥t③♥s s♦♥ t ♣♠♥t ♣♦st♦♥ ♦ ♦t s tr♠♥ ♦r♥ t♦ ♥♦♥ ♦ t ♣rt
♥s ♥ st ♦t ♣♠♥t s♠ ω s♦t♣t ♥
Pr♠tr tt♥s
♥rt t t♦r w tr♠♥s t ♦♥r♥ ♥ sr t② ♦ P s♦ ts stt♥ s r②♠♣♦rt♥t ♦r♥ t♦ q ♥ w s s♠ t♣r♦t② ♦ ♣rt ♠tt♦♥ s s♠ ♥ t rr♥t stt ♦ t ♣rt s rt ♥♥ ♦♥ t♣t ♦ t ♥①t stt s♦ P s str♦♥ ♦sr t② ♥ ♦♥trst ♥ w s r t ♣r♦t② ♦ ♣rt ♠tt♦♥ s r ♥ t rr♥tstt ♦ ♣rt s tt ♥♥ ♦♥ t ♥①t stt♣t s♦ P s str♦♥ ♦ sr t② ♥t r② st ♦ ♦rt♠ ♠♣♠♥tt♦♥ ♦r ♠♣ss s ♦♥ ♥ ♠♦r tt♥t♦♥ t♦ t ♦ srt② s t sr ♣♥s ♦r ♦s s ♦♥ ♦♥♥trt♥ ♠♦r tt♥t♦♥ ♦♥ t ♦ sr t② ♥♦♥s♦♥ w s♦ ♦ t t ♦t♦♥ ♦ ♣♦♣t♦♥ ♣rts ♥ P ♥ ♥rt t t♦rst♠♥t strt② s s s st ♣t② ♦r♥ t♦ t ♥ts ♥ s♥ts♦ t rr♥t ♣♦♣t♦♥ ♦ ♣rts ♥ t tt trt♦♥ t ♦ t ♥rt t t♦r s s ♦♦s
wt =
wmax − (wmax − wmin)× exp
(
d(P t−1)
d(P t−1)− 1.01n
)
r wmax ♥ wmin r t ♠①♠♠ ♥ ♠♥♠♠s ♦ t ♥rt t t♦r rs♣t② ♥d(P t−1) s t ♥♠r ♦ ts ♥♦ r♥t② t♥ ♣rt P t−1 ♥ t ♦ st ♣rt
♥ t♦♥ t ♣rs♦♥ ♦♥t t♦r cmax1 ♥
t s♦ ♦♥t t♦r cmax2 r st ② t ♥r②
♥rs♥ strt② ♥ t ♥r② rs♥ strt② ♥ t trt ♣r♦ss ❬❪ rs♣t② ② rq♥t s
ct1 = cmin1 + t×
cmax1 − cmin
1
tmax
ct2 = cmax2 − t×
cmax2 − cmin
2
tmax
r r cmax1 ♥ cmax
2 r t ♠①♠♠ s♦ t ♣rs♦♥ ♦♥t t♦r ♥ s♦ ♦♥tt♦r rs♣t② cmin
1 ♥ cmin2 r t ♠♥♠♠
s ♦ t ♣rs♦♥ ♦♥t t♦r ♥ s♦ ♦♥t t♦r rs♣t② ♥ tmax s t ♠①♠♠♥♠r ♦ trt♦♥s ♦ t ♦rt♠
❩♥ t P ♦
♦rt♠ ♦
♠♥ st♣s ♦ P r s ♦♦st♣ ♣r♠trs ♦ P r ♥t③ ♥
t♥ t ♥t ♣♦♣t♦♥ s ♥rtt♣ ♦r♥ t♦ t ♠♣♣♥ t♥ ♦ts
♥ Ps t t♥ss ♦ ♣rt s t ♦r♥ t♦ q ♣rs♦♥ st stt ♦ ♣rt s ♥t③ ② ts ♥t stt ♥ t ♣rt t t st t♥ss ♥ t ♥t ♣rt sr♠s st s t ♦ st ♣rtt♣ ♣rts r ♣t ♦♥ ② ♦♥
♦r♥ t♦ q ♥ t t♥ss ♦ t ♣rts st tr ♣t♥t♣ t t♥ss ♦ t ♣t ♣rt s ss
t♥ tt ♦ ts ♣rs♦♥ st t s st s ts ♣rs♦♥st trs ♦ t♦ t♣ t♣ t t♥ss ♦ t ♣t ♣rt s ss
t♥ tt ♦ t ♦ st ♣rt t s st s t♦ st ♣rtt♣ ❱r② tt t st♦♣ ♦♥t♦♥ s ♠t t
st♦♣ ♦♥t♦♥ s ♥♦t sts rtr♥ t♦ t♣ ♦trs t ♦rt♠ tr♠♥t
Pr♦r♠♥ t♦♥♥ ts st♦♥ t♦ r② t t♥ss ♦ t ♣r♦♣♦s ♣♠♥t strt② s ♦♥ P ♥ s♦♥P❲P ♥ ❲s t ①♣r♠♥t t♦♥ srr ♦t ♥ t s♠t♦♥ ♥r♦♥♠♥t ♥ ♣rtr t ♦♦♥ rsr qst♦♥s s r r② s♠t♦♥ ①♣r♠♥ts• ♥ P ♦t♥ ♥r♦♣t♠ ♦t♣♠♥t s♠ ♥ t②♣ ❲s
• ❲t s t ♠♣t ♦ ♥s ♥ t❲ ♦♥ t ♣r♦r♠♥ ♦ P
• ♥ t②♣ ❲s ♦♠♣r t srss ♦rt♠s ♦s P ♣r♦r♠♥♥ts ♥ s♦♥ P❲P
♦r t ①♣r♠♥t rsts s♦ tt P♥ ♦t♥ ♥r♦♣t♠ ♦t ♣♠♥t s♠♥ t②♣ ❲s ♦r t ♥ s♥ r♦♠ t①♣r♠♥t rsts tt rrss ♦ ♦ ❲s♥ t ♣r♦r♠♥ ♦ P s ♥♦t t♥ ♥r♦♣t♠ ♦t ♣♠♥t s♠ ♥ ♦t♥ ♦r t ①♣r♠♥t rsts s♦tt P s s♣r♦r t♦ ♦tr ♦rt♠s ♥ t②♣❲s
①♣r♠♥t tt♥s s♠t♦♥ ①♣r♠♥ts ♥ ts st♦♥ r rr♦t ♦♥ P q♣♣ t ♥ P❯ ♥ ♦ ♦♣rt♥ s②st♠ rs♦♥ s ❲♥♦s P ♥ ss ♦rt♠s r♠♣♠♥t ♥ P②t♦♥ r♥t ♣r♠trs♦ P rr t♦ ❬❪ ♥ r st s tmax = 1000
Ω = 100 wmax = 0.9 wmax = 0.4 cmax1 = 0.9
cmin1 = 0.2 cmax
2 = 0.9 cmin2 = 0.4 ♥ µ = 0.1K
❲ st t r♦♥s r♦♠ t tst ♦ t ♥ ♦♠ s stt♦♥ ❬❪ t♦ s♠t t ❲s♦r♥ t♦ rt♥ ♦♥t ♥ tt s♣♥ r♥t ❲s ♥ r♥t ♥♠rs ♥ ♦♥♥t♦♥ t♦♣♦♦s ♦r Ps ♥t t tr♥s♠ss♦♥② ♦ ♥ t ❲ s ♥rt r♥♦♠② r♦♠ ♠s t♦ ♠s ❬❪ r♥ t ♣r♦ss♦ sts ♦♦♥ t ❲ s ♥t♦ ×rs
ss ♦rt♠s♦ r② t ♥ts ♦ P ♥tr♦ t♦♦♥ ss ♦rt♠s ♥ t s♠t♦♥ ①♣r♠♥ts• ♣t♠ ♣♠♥t ♦rt♠ P s ♦rt♠ trrss ♣♦ss ♦t ♣♠♥ts♠s ♥ sts t ♣♠♥t s♠ tt ♠♥♠♠ ①t♦♥ t♠ ♦ ❲s s t ♦♣t♠ ♦t ♣♠♥t s♠
• P s trt♦♥ P ♦rt♠ s ts♠ ♥♦♥ ♥ ♣r♠tr stt♥s s P
• ♦r♥ t♦ t ♣t strt② ♦ tss t t rt♥t♦♥ strt② ♥r② t♦r♥♠♥t st♦♥ ♦♣rt♦r t♦♣♦♥t r♦ss♦r ♦♣rt♦r ♥ ①♥ ♠tt♦♥ ♦♣rt♦r t♦ ♣tt r♦♠♦s♦♠ ♥ ts t ♥ t s♦t♦♥s t ♦♣t♠ s♦t♦♥
• ♥♦♠ ♦t ♣♠♥t ♦rt♠ s ♦rt♠ r♥♦♠② sts K r♦♠ Ps♦ t ❲ ♥ r♥♦♠② ♣s K t♦♣ ♦ts ♦♥ ts Ps rst s ♥r ♦ r♣tt♦♥s
P ♥ ♦t♥ ♥r♦♣t♠ ♦t♣♠♥t s♠ ♥ t②♣ ❲s
♦r♥ t♦ t ♠♥strt s♦♥s ♦ ♥ st r♦♥s t s♣♥s ♦ ♥ ♣♦♥ts♥ tt ♥ ♦♥t rs♣t② r♦♠ ♥♣❳ ♥♥ ♥ P♦♥ s t②♣ ❲s strt♦♥ ♥ t♦♣♦♦② ♦ Ps ♥ t ❲ rs♠t ② t t ♦ t ♦♠ s stt♦♥♥ ❬❪ t s ss♠ tt t ♥♠r ♦ t♦♣♦ts K ♥ t ❲ s tr♠♥ ② t ♥♠r ♦ Ps n tt s K = κ · n, κ ∈ (0, 1) ♦r♥ t♦ t ♣♦♣t♦♥ ♥st② ♦ t ♦ ♠♥strt s♦♥s t κ s ♦ t st r♦♥s r♦♠ ♥♣ ❳ ♥♥ ♥ P♦♥ rst t♦ ♥ rs♣t② ♥ t♦ r♦♥s t ❲s r ② Ps r r♥♦♠②♥rt r♦♠ r♦s ♥t♦r rttrs ♥♠②①t ❱s ♦♠tr② r♦♣ ♥t♦r ❱t♦♦t ♥ rs ♥t♦r st ❬❪ ♥ t♦♥ t ♦ rq♥② ♦ t P❯ q♣♣ t
❩♥ t P ♦
t t♦♣ ♦ts ♥ t s♠ ❲ stss ♥♦r♠ strt♦♥ ♦ ③ t♦ ③② r♥♥♥ P ♥ P ♥ r♥t t②♣
❲s ♥ ♦t♥ t ♦ ♦t ♣♠♥t rsts r s♦♥ ♥ t♦t ♦t ♣♠♥t s♠ ♦t♥ ② P ♥ t②♣ ❲ s ♥♦t q♥t t♦ t ♦♣t♠ ♦t ♣♠♥t s♠ tr r ♦♥② ♦t ♣♠♥t ♣♦st♦♥s tt r ♦② ♦tr♦t ♣♠♥t ♣♦st♦♥s r t s♠ ♥ t♦r ♣♠♥t s♠ s ♦s② t♥ t ①t♦♥ t♠ ♦ t ❲s ♦r
rs♣♦♥♥ t♦ t ♦t ♣♠♥t s♠ s♦♥♥ t st♦r♠ s♦♥ ♥ ♥ ♦t♥ rsts s♦ tt ♥ ♦r r♥t t②♣❲s ♥♣ ❳ ♥♥ ♥ P♦♥♥ t ①t♦♥ t♠s ♦ t ❲s ♦rrs♣♦♥♥ t♦t ♦t ♣♠♥t s♠ ♦t♥ ② P r ♥ rr t♥ t♦s♦rrs♣♦♥♥ t♦ t ♦♣t♠ ♣♠♥t s♠ rs♣t② ♦♠♥ ♥sts ♦ ♥ ♥t tt t♦ t ♦t ♣♠♥t s♠s♦t♥ ② P ♥ t ❲s s♦♠t rr♦♠ t ♦♣t♠ ♣♠♥t s♠s t r♥ sr② s♠ P ♥ ♦t♥ t ♣♣r♦①♠t ♦♣t♠ s♦t♦♥ ♦ P❲P ♥ t②♣ ❲s t♦tr s st rt♥ ♣ t♥ t ♦♣t♠ ♣♠♥t s♠ ♥ t ♣♠♥t s♠ ♦t♥ ②P t s ♥s t♦ ♦t♥ t ♦♣t♠ ♣♠♥t s♠ ② rt ♦r ♥ t ♥t♦r s♥rss s♦ P s rt♥ ♣rtt②
♥s ♥ t ❲ ♠♦st ♥♦♠♣t ♦♥ t ♣r♦r♠♥ ♦ P
r♦♠ st♦♥ ♥♦ tt P ♥ r②♦s② ♣♣r♦ t ♦♣t♠ ♦t ♣♠♥t s♠♥ t②♣ ❲s ♦r t ❲ ♥♥♦t ① t s ♦t t♠♣♦r ♥ s♣t ①t sss t ♠♣t ♦ ❲ ♥s ♦♥ P ♣r♦r♠♥
♠♣t ♦ ♥s ♥ P t♦♣♦♦② ♦♥ t
♣r♦r♠♥ ♦ P
❲ s t r♦♥s st r♦♠ r♥t ♠♥strt s♦♥s ♦ ♥ s sr ♥ st♦♥ t♦ s♠t ♥s ♥ P t♦♣♦♦② ♥ ts ♣rt ts ss♠ tt t ♥♠r ♦ t♦♣ ♦ts♥ r♦♥ ♥ t ♦ rq♥② ♦ t P❯q♣♣ t t t♦♣ ♦ts r t s♠♥ ♦tr stt♥s r t s♠ s t♦s ♥ st♦♥ ♥ t♦♥ t ❲s r ② Ps r s♠t ② ♦♦t t strtr ♦ s s♦♥♥ ❬❪s s♦♥ ♥ ♥ ♦r ❲s t r♥t
P t♦♣♦♦s t♦ t ♥♠r ♦ t♦♣
♦ts ♥ tr P❯ ♦ rq♥② r t s♠t ①t♦♥ t♠s ♦ t ♥t ♥♠r ♥ t②♣♦ ❲s r r♥t s s s t P t♦♣♦♦② t t ♣♠♥t ♣♦st♦♥s ♦ ♦ts rst♥ ♥ r♥t sts ♦♦♥ s♠s ♥ ttr♥s♠ss♦♥ t♠s r♦♠ t ①♣r♠♥t rsts t♥ ♦♥ tt ♥ ♦r ❲s t r♥t P t♦♣♦♦s ♥♣ ❳ ♥♥ ♥P♦♥ t ①t♦♥s t♠ ♦ t ❲s ♦rrs♣♦♥♥ t♦ t ♦t ♣♠♥t s♠ ♦t♥ ②P r ♥ rr t♥t♦s ♦rrs♣♦♥♥ t♦ t ♦♣t♠ ♣♠♥t s♠rs♣t② t♦ tr s ♣ t♥ t♠ t♥ ♠♦st ♥♦r ♥ t ss ♦ ts rsts ♥ ♦♥ tt t ♥s ♥ t P t♦♣♦♦② tt ♠♣t ♦♥ t ♣r♦r♠♥ ♦ P ♥P ♥ st ♦t♥ ♥r♦♣t♠ ♦t ♣♠♥t s♠
♠♣t ♦ t ♥s ♥ t t♦♣
♦t P❯ ♦ rq♥② ♦♥ t
♣r♦r♠♥ ♦ P
♥ st♦♥ ss♠ tt t P❯ ♦ rq♥② ♦ t♦♣ ♦ts ♠ts t ♥♦r♠strt♦♥ t♥ rt♥ r♥ ♥ ts ♣rt s♠t t ♥s ♥ t P❯ ♦ rq♥② ♦t t♦♣ ♦ts ② ♥♥ t ♠①♠♠♥ ♠♥♠♠ s ♦ t ♥♦r♠ strt♦♥ ♥t♦♥ t rst t②♣ ❲ ♥♣ ♦st♦♥ s ♦♣t ❲s r ② Psr s♠t ② ♠♣♠♥t♥ ♦♦t rsts s♦♥ ♥ ♥t tt t ①
t♦♥ t♠ ♦ t ❲s s ♥t② ♦rrt tt P❯ ♦ rq♥② ♦ t♦♣ ♦tss s s t P❯ ♦ rq♥② tr♠♥st ①t♦♥ t♠ ♦ stss rtr t P❯♦ rq♥② s t s♠r t ①t♦♥ t♠ ♦stss ①t♦♥ t♠ ♦ stss r② tr♠♥s t ①t♦♥ t♠ ♦ ❲s ♥ t♦♥ t①♣r♠♥t rsts ♥t tt t ①t♦♥ t♠♦ t ❲s ♦rrs♣♦♥♥ t♦ t ♦ ♣♠♥ts♠ ♦t♥ ② P s ♥ rr t♥ t ♦♣t♠ ♣♠♥t s♠ ♥rt ♦r t♦♣ ♦t P❯ ♦ rq♥srs♣t② t♦ tr s ♣ t♥ t s t ♥ ♠♦st ♥♦r r♦♠ ts rsts ♥ ♦♥ tt t P❯ ♦ rq♥② ♥s♦ t t♦♣ ♦ts tt ♠♣t ♦♥ t♣r♦r♠♥ ♦ P ♥ P ♥ st s t♦♦t♥ t ♥r♦♣t♠ ♦t ♣♠♥t s♠
♠♣t ♦ t ♥s ♥ ❲s ♦♥ t
♣r♦r♠♥ ♦ P
♥ st♦♥ ss♠ tt t ❲s r♥♦♠②st r♦♠ ♦r t②♣ tss ♥ ts ♣rt s♠t
❩♥ t P ♦
t ♥s ♥ ❲s ② ♥♥ t t②♣ ♦ ❲s♥ t♦♥ t r♥t stt♥s ♦ t rst t②♣❲ ♦ st♦♥ r ♦♣t ♥ ❲sr q♥ts s♦♥ ♥ ♥ t t②♣s ♦ ❲s r
r♥t t ①t♦♥ t♠s ♦ t ❲s r r♥ts s s r♥t t②♣s ♦ ❲s r♥t ♦♠♣tt♦♥ rqr♠♥ts ♥ t tr♥s♠ss♦♥ rts s♦ t ①t♦♥ t♠ s r♥t r♦♠t ①♣r♠♥t rsts ♥ t ❲ t②♣s r①t ❱t ♦♦t ♥ st t ①t♦♥ t♠s ♦ t ❲s ♦rrs♣♦♥♥ t♦ t ♦t♣♠♥t s♠ ♦t♥ ② P r ♥ rr rs♣t② t♥t♦s ♦rrs♣♦♥♥ t♦ t ♦♣t♠ ♣♠♥t s♠t♦ tr s ♣ t♥ t s t ♥ ♠♦st ♥♦r r♦♠ ts rsts ♥ ♦♥tt t ♥s ♥ t ❲s tt ♠♣t ♦♥ t♣r♦r♠♥ ♦ P ♥ P ♥ st ♦t♥ ♥r♦♣t♠ ♦t ♣♠♥t s♠♥ s♠♠r② ♥ ♦♥ tt ♥s ♥ t
❲s ♠♦st ♥♦ ♠♣t ♦♥ t ♣r♦r♠♥♦ P ♥ P ♥ st ♦t♥ ♥r♦♣t♠♦t ♣♠♥t s♠
P s rtr ♣r♦r♠♥ ♥tst♥ sr ss ♦rt♠s ♥ t②♣ ❲s♦
♥② s ①♣r♠♥ts t♦ tst t ♣r♦r♠♥♥ts ♦ t ♣r♦♣♦s P ♦r sr ss♦rt♠s ♥ s♦♥ P❲P ♥ t②♣ ❲ss s♦♥ ♥ ♥ t ♦r t②♣ ❲s sss ♥ st♦♥ P r t ①t♦♥t♠ ♦ ❲s ② ♥ ♦♥ r ♦♠♣r t t♦s ♦ t P ♥ rs♣t② P ♣t② sts t sr ♣t② ♦r♥ t♦ t rr♥t stt♦♥ ♥ trt②♣ts r♦♠ ♦ ♣rs♣t ♥ t ♦r r♥t❲s P ♣r♦r♠s ttr t♥ sr ss♦rt♠s ♦ t♦ t P ♦rt♠ s rt♥ sr t② t s② s ♥t♦ ♦ ♦♣t♠♠s♦ ts ♣r♦r♠♥ s ♠t ♣r♦r♠s ♦♥② ♣rt sr r♥ trt♦♥ s♦ ts ♣r♦r♠♥ s ♣♦♦r ♥ ♥ rt ♦♥② t r ♦ ♣♠♥t s♠s ♥ s♠♠r② t ♥ ♦♥ tt P s rtr ♣r♦r♠♥ ♥t t♥ ♦ sr ss ♦rt♠s ♥ s♦♥P❲P ♥ ❲s
♦♥s♦♥♦r ♠♦ srs s♥ s♦t♦♥s t♦ t ♣r♦♠ ♦♥s♥t rs♦rs tr♦ r♠♦t srrs ♦tt♥♦♦② s ss♥t ♦r t ♣r♦♠ ♦♦t ♣♠♥t s ♥ r② ♥♦r ♦ s♦
t ♣r♦♠ ♦ ♦t ♣♠♥t ts ♣♣r ♣r♦♣♦s t♠r♥ ♦t ♣♠♥t strt② s♦♥ P ♠s t♦ r t ①t♦♥ t♠♦ ❲s ♥ ❲s ❲ st ♣ rs♦♥ s♠t♦♥ ♥r♦♥♠♥t ♥ ♦♥t ♦♠♣t s♠t♦♥ ①♣r♠♥t s ♦♥ ts ♣♣r♦ rstss♦ tt ♦♠♣r t t ①st♥ s♦t♦♥s ♦r♣r♦♣♦s strt② s ttr ♣r♦r♠♥ ♥ s ①tr♦r♥r② ♦s t♦ t ♦♣t♠ ♣♠♥t s♠♥ t tr ♦♥sr t ♠♣t ♦ ♥r♦♥
♠♥t tt♦♥s ♥t♦r ②s ♥ttt♦♥s ♥ ♦t rs ♦♥ ♦t ♣♠♥t ♥ ♠♣r♦ ①st♥ strts t♦ ♣t t♦ t②♥♠ ♥r♦♥♠♥t ♥ t♦♥ ② ♦♥sr t rtrsts ♦ t stss ♥ ♥t ❲ ♥ t ♣♠♥t ♦st ♦ t ♦t ♥ r♥t ♣♦st♦♥s ♥ s♥ ♠♦r s♥t ♥ ♦♠♣t s②st♠ ♦st ♠♦
♥♦♠♥ts
❲ t♥ tt♣ssr♦♠ ♦r ts ♥st ssst♥
r♥ t ♣r♣rt♦♥ ♦ ts ♠♥sr♣t
♥♥
s ♦r s ♣rt② s♣♣♦rt ② t ②r sr ♥
♦♣♠♥t Pr♦r♠ ♦ ♥♦♥ Pr♦♥ ♥r r♥t
♦
♦♠♣t♥ ♥trsts
t♦rs r tt t② ♥♦ ♦♠♣t♥ ♥trsts
t♦rs ♦♥trt♦♥s
♥s♥ ❩♥ ♥ ♥ rt t ♦r♥ ♠♥sr♣t ♥
s♥ t ①♣r♠♥ts ❳♥♥ ❩♥ ♣r♦ s ♥
sst♦♥s ♥s♥ s ♣r♦ rt r ♥ ♣ t♦ rt
t ♠♥sr♣t t♦rs r ♥ ♣♣r♦ t ♥ ♠♥sr♣t
t♦rs ♥♦r♠t♦♥
♥s♥ ❩♥ r s r ♥ trs ♥♥r♥ r♦♠
♥ ♦r♠ ❯♥rst② ♥ ♥ s rr♥t② ♦r♥ t♦r
t P r t t ♦ ♦ t♠ts ♥ ♦♠♣tr ♥
③♦ ❯♥rst② s s♦ ♥ ♣rt ♦ t ♥ ② ♦rt♦r②
♦ t♦r ♦♠♣t♥ ♥ ♥t♥t ♥♦r♠t♦♥ Pr♦ss♥ t ③♦
❯♥rst② s♥ ♣t♠r s rr♥t rsr ♥trsts ♥
♦♠♣t♥ ♦♠♣tt♦♥ ♥t♥ ♥ ♦ ♦♠♣t♥
♥ r t r ♥ ♦♠♣tr s♥ ♥ t♥♦♦②
r♦♠ ③♦ ❯♥rst② ♥ ♥ ♥ r s rr♥t②
♦r♥ t♦r t r ♥ ♦♠♣tr t♥♦♦② ♥ t ♦
♦ t♠ts ♥ ♦♠♣tr ♥ ③♦ ❯♥rst② s s♦
♥ ♣rt ♦ t ♥ ② ♦rt♦r② ♦ t♦r ♦♠♣t♥ ♥
♥t♥t ♥♦r♠t♦♥ Pr♦ss♥ ③♦ ❯♥rst② s♥ ♣t♠r
s rr♥t rsr ♥trsts ♥ s②st♠ s♦tr
♦♠♣t♥
❳♥♥ ❩♥ s rr♥t② Pr♦ss♦r t t ♦ ♦
t♠ts ♥ ♦♠♣tr ♥s ③♦ ❯♥rst② ♥
r t r ♥ strt s②st♠ ♥ t P r ♥
♥♦r♠t♦♥ ♦♠♠♥t♦♥ t♥♦♦② r♦♠ t ❯♥rst② ♦ r
♦r② ♥ ♥ rs♣t② s rr♥t rsr ♥trsts
♥ ♥ ♥rt♦♥ ♥t♦r t s♣ ♦s ♦♥ ♦ ♦♠♣t♥
srs ♥ ♣♣t♦♥s ♥ t ♣r♦ss♥ ♥ srt②
♥s♥ s s rr♥t② r Pr♦ss♦r ♥ t ♥ ♦ t
♦ ♦ ♥♦r♠t♦♥ ♥ tr ♥♥r♥ s ❯♥rst②
♥ ♥ Pr♦ss♦r t t ♣rt♠♥t ♦ ♦♠♣tr ♥ ♥
♥♦r♠t♦♥ ♥♥r♥ t♦♥ ♥ ♥ ❯♥rst② s rsr
♥trsts ♥ ♣r♦r♠♥ ♦♠♣t♥ ♦ ♦♠♣t♥ ♣r
♥ strt s②st♠s t ♥②ts ♥ qt♦s♣rs
♦♠♣t♥ ♥ ♥t♥
❩♥ t P ♦
t♦r ts
♦ ♦ t♠ts ♥ ♦♠♣tr ♥ ③♦ ❯♥rst②
③♦ ♥ ♥ Pr♦♥ ② ♦rt♦r② ♦ t♦r
♦♠♣t♥ ♥ ♥t♥t ♥♦r♠t♦♥ Pr♦ss♥ ③♦ ♥♣rt♠♥t ♦ ♦♠♣tr ♥ ♥ ♥♦r♠t♦♥ ♥♥r♥ s
❯♥rst② ♥ ♥
r♥s
P ♥ ♥ ❨ r♥
rs♦r♣♦♦r ♠♦ s t ♣♦r ♦s rttrs
♥s ♥ ♣♣t♦♥s ❲rss ♦♠♠♥t♦♥s
♥ ❳♥ ❲ ♦ ♦ ♦♠♣t♥ sr
♠♦s sr♥tr ♣♣r♦ ♥t♦r
rr ❨ ♦t ♠ ②②♦
♥ tr ♦ ♠♦ ♦ ♦♠♣t♥ ♥trt♥
♦ts ♥ ♠♦ ♦♠♣t♥ ♥ ♥tr♥t♦♥ ♦♥r♥
♦♥ ♦♠♠♥t♦♥s
❳ ❩ ♥ ❲ ❳ ❲ ♦ ♥t ♦rt♠s ♦r
♣tt ♦t ♣♠♥ts r♥st♦♥s ♦♥ Pr ♥
strt ②st♠s
❳ ❩ ♥ ❲ ❳ ❲ ♦ ♣tt ♦t
♣♠♥ts ♥ rss ♠tr♦♣♦t♥ r ♥t♦rs ♥ t
♦♥r♥ ♦♥ ♦ ♦♠♣tr t♦rs
♦ ♥ ❲ ♣t♠ ♦t ♣♠♥t ♥ sr t♦
♦t ♦t♦♥ ♥ rss ♠tr♦♣♦t♥ r ♥t♦rs
r♥st♦♥s ♦♥ ♦ ♦♠♣t♥
♥ ♦ ♦ ❳ ❳♦ ♦st ♦♠♣tt♦♥
♦♦♥ ♥ rs♦r s♥ ♥ ♦ts ♠♦ ♦
♦♠♣t♥ r♥st♦♥s ♦♥ ♦ ♦♠♣t♥
♥ ♠ ♥ts P Ptt ♦♥♦
st ①t♦♥ t♥ ♠♦ ♥ ♦ ♥ ①t
♦♥r♥ ♦♥ ♦♠♣tr ②st♠s
r♦ sr♠♥♥ ♦ ❲♦♠♥ r♦
♥r P ❯ ♠♥ s♠rt♣♦♥s st ♦♥r
t ♦ ♦♦ ♥ t ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦
②st♠s ♣♣t♦♥s ♥ rs
♦st ♥s P ♦rtr ❩♥ ❳ ♥r
②♥♠ rs♦r ♦t♦♥ ♥ ♣r ①t♦♥ ♥ t ♦ ♦r
♠♦ ♦ ♦♦♥ ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥
♦♠♣tr ♦♠♠♥t♦♥s
♦♠♠tt t st♥r ♦r ♦ ♥ ♠tr♦♣♦t♥
r ♥t♦rs r ♥ rttr ♥ í♥
❨♦r❨❯ ♥sttt ♦ tr ♥ tr♦♥s ♥♥rs
♥
P P tr ❲ ❨ t②♥r②♥♥
st♥t♠ ♣r♦s♦♥♥ ♦r ②r ♦r♥ ♥ t ♥♥
♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦ ②st♠s ♣♣t♦♥s ♥
rs
❩♥ ❨ ♦ ❳ ♦ ♦♦ ♦r ♥♦t t♦ ♦♦ ♥
♥t ♦ ♣rtt♦♥ ♦rt♠ ♦r ♠♦ ♦ ♦♠♣t♥ ♥
st ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦ t♦r♥
❯
❩♥ ❨ ♥ ❳ ❩♥ ❲ ❨♥
t♦r♥ ♥r♦ ♦ ♦r ♦♥♠♥ ♦♠♣tt♦♥
♦♦♥ ♥ ♥♥ P ♦♥r♥ ♦♥
tr♥t Pr♦r♠♠♥ ②st♠s ♥s ♥
♣♣t♦♥s P
t ♠♠rt P P ❲tr
♦♥♥ ss ♥♥ ♥trt ♣r♣t♦♥ ♣♣t♦♥s
♦♥ ♠♦ s ♥ t ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦
②st♠s ♣♣t♦♥s ♥ rs
♦♥ ②t♦ ❲♥ P ♣t♠ ♠ss♦♥ ♦♥tr♦
♣♦② ♦r ♠♦ ♦ ♦♠♣t♥ ♦ts♣♦t t ♦t ♥
❲rss ♦♠♠♥t♦♥s ♥ t♦r♥ ♦♥r♥ ❲
♥ ❳ ♥ ❩ ♥ ❳♦♥ ♥
r♥♦r♠♥t r♥♥ ♠♣♦r ♦♥tr♦ s②st♠ ♦r
♥str ♥tr♥t ♦ t♥s r♥st♦♥s ♦♥ ♥str
♥♦r♠ts ♦
♥ ♦r ♥♦ ♠♦t②r ♦♦♥
♠♥♠♥t s♠ ♥ sst♥ ♠tss ♦♠♣t♥
r♥st♦♥s ♦♥ st♥ ♦♠♣t♥
♦❯
❩♥ ❨ ②t♦ ❲♥ P ♦♥ ♥ ♠♦ ♦t
s②st♠s t ♥tr♠tt♥t ♦♥♥tt② r♥st♦♥s ♦♥
♦ ♦♠♣t♥
❩♦ ♦ ❩♦♥ ❩ ②♥♠
♥r②r ♦ts ♠♦ ♦ ♦♠♣t♥ ♠♦ ♦r
r♥ ♦♠♣t♥ ♦r♥ ♦ t♦r ♥ ♦♠♣tr ♣♣t♦♥s
r ♦② ♣♦r ♥ t♥② r
♦t st♦♥ strt② ♦r ♠t♦t ♥r♦♥♠♥t
r♥st♦♥s ♦♥ ♦ ♦♠♣t♥
♦ ♥ ❲ ♣t♠ ♦t ♣♠♥t ♥ sr t♦
♦t ♦t♦♥ ♥ rss ♠tr♦♣♦t♥ r ♥t♦rs
r♥st♦♥s ♦♥ ♦ ♦♠♣t♥
❲ ♥ ♦t ② ♦♥ ♦♣t♠ ♦t
♣♦②♠♥t ♥ sr ss♦t♦♥ ♥ ❲s ♥ t
♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ str ♦ ♥ r ♦♠♣t♥
♥ ❲ ♥ ❳ ♦t ♣♠♥t ♥
♠♥♠♠② r♦t♥ ♥ ♦t ♦♠♣t♥ ♥ ♥tr♥t♦♥
♦♥r♥ ♦♥ t ♦♠♣t♥ ♥ ♦♠♠♥t♦♥s
♥ ❳ ♦ ❲ ♥ t ♥t♠ ♠♦ s
♣♣r♦ t♦ ♦ ♣♣t♦♥ ♦♣♠♥t r♦♥trs ♦ ♦♠♣tr
♥
❩ ❳ ❩♦ t♦t ♦♣t♠③ ♦t ♣♦②♠♥t
♥ ts ♦♦♥ ♦r ♠♦ ♦♠♣t♥ ♥tr♥t ♦
♥s ♦r♥ ♦
♦ ♥ ❩♦ ♥ ❩♥ ❩ ❨♥ ❨ ❨♥ P
rs ♠♥②♦t ♣♦②♠♥t ♦♣t♠③t♦♥ ♦
srrs r♥st♦♥s ♦♥ ♥t♥t r♥s♣♦rtt♦♥ ②st♠s
♥ ❩ ♥ ❳ ❩♥ ❳ ♥ ♦♠♣tt♦♥
♦♦♥ ♥ ts s♥ ♦r s ♣♣t♦♥s ♥
♦ ♦♠♣t♥ ss
♥♥② rrt Prt sr♠ ♦♣t♠③t♦♥ ♥
♥tr♥t♦♥ ♦♥r♥ ♦♥ r t♦rs
♦ ❲ ♥ ♥ ♥ ❨ ♥ ♦str♥
s♥ ♦r ♥s ♦r♦ r♦ss ♠t♣ ♦s
r♥st♦♥s ♦♥ t♦r ♥ r ♥♠♥t
❨ rrt ♠♦ ♣rt sr♠ ♦♣t♠③r ♥
♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦t♦♥r② ♦♠♣tt♦♥ Pr♦♥s
P
❲♥ ❩♦ ❨ ♥ ❳ s ♦s ♣rt♦♥
♦r sr r♦♠♠♥t♦♥s ♥ ♠♦ ♦♠♣t♥ ♦r♥ ♦
Pr ♥ strt ♦♠♣t♥
❳ ❩ ♥ ❲ ❳ ❲ ♦ ♥t ♦rt♠s ♦r
♣tt ♦t ♣♠♥ts r♥st♦♥s ♦♥ Pr ♥
strt ②st♠s
♥ ♥r ❱ ②r ♣ ♥r ♥t♦r ♦r
♦♥♥ r♥♥ ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♥s ♥ Pttr♥
♦♥t♦♥ P
❩♥ t tt♣st♦♠♠s❩tst
s
rs
❩♥ t P ♦
Access Point (AP)Access Point (AP)
Cloudlet
Placement
WA
Offloading
Workflow Application (WA)
WMAN Cloudlet Placement & WA Offloading Results
CloudletCloudlet Wired Connection
r ♦t ♣♠♥t ♥ ❲ ♦♦♥ ♥ ❲
1
il
2
il
1,2
ie
W
iG
r r♠ ♦ t ❲
pBest
(gBest)
0 1 5 4
2 3 6 7
0 3 6 4
crossover
ind1
ind1
ind2
ind2
new particle
old particle
r r♦ss♦r ♦♣rt♦r ♥ t ♣rs♦♥ ♦♥t ♣t♦♣rt♦♥ ♥ t s♦ ♦♥t ♣t ♦♣rt♦♥
♠♠r② ♦ ② ♥♦tt♦♥s
♦tt♦♥ sr♣t♦♥G = (V,E) ❲vi ∈ V ♥ P ♥ ❲Di,j ∈ D ♥t t tr♥s♠ss♦♥ ② t♥
vi ♥ vjG❲ = G❲
1, ...,G❲n st ♦ ❲s r ② Ps
G❲i = (Li,Ei) ❲Li = l1i , ..., l
si stss ♥ ♥ G❲i
Ei = ej,ki t ♣♥♥ t♥ stss ♥ ♥ G❲i
θji ♦♠♣tt♦♥ rqr♠♥t ♦ l
ji
C = c1, ..., cK ♦ts t♦ ♣ ♥ ❲ηi ♦♠♣t♥ ♣♦r ♦ ♦t ciω = ωi,j ♦t ♣♠♥t s♠
M =⋃|G❲|
i=1(lji , ck) ♦ sts ♦♦♥ strt②
tstart(lji , ck) strt t♠ ♦ sts l
ji ♦♥ ♦t ck
texe(lji , ck) ①t♦♥ t♠ ♦ sts l
ji
ttrs(lpi , l
ji , cw, ck) ♣♥♥t t tr♥s♠ss♦♥ t♠
t♥ stss lpi ♥ l
ji
tend(lpi , l
ji , cw, ck) ①t♦♥ ♥ t♠ ♦ sts l
ji ♦♥
♦t cktend(G
❲
i ) ①t♦♥ ♥ t♠ ♦ ❲ G❲itend(G
❲) ♥ t♠ ♦ ❲s ♥ t ❲
old particle 0 1 5 4
0 2 5 3
mutation
new particle
ind1ind1 ind2ind2
ind1ind1 ind2ind2
r tt♦♥ ♦♣rt♦r ♥ t ♥rt ♣t ♦♣rt♦♥
❩♥ t P ♦
Old particle 1
5 2 4 3 6Old particle 2
Crossover particle
Cloudlets 1 2 3 4 5
0 2 4 4 20 2 4 4 2
New particle
0 1 5 4 20 1 5 4 2
0 2 4 3 10 2 4 3 1
r rt♦♥ r♦ss♦r ♦♣rt♦r
Old particle
0 1 1 4 2Mutant particle
New particle
Cloudlets 1 2 3 4 5
0 3 1 4 20 3 1 4 2
0 1 5 4 20 1 5 4 2
r rt♦♥ ♠tt♦♥ ♦♣rt♦r
❩♥ t P ♦
OPT PGEL
♥♣
OPT PGEL
❳
OPT PGEL
♥♥
OPT PGEL
P♦♥
r ♦♠♣rs♦♥ ♦ ♦ ♦t ♣♠♥t rsts ♥ t②♣ ❲s
Huangpu Xuhui Minhang Pudong0
1000
2000
3000
4000
t end(GW)(ms)
OPT PGEL
Administrative divisions
r ♦♠♣rs♦♥ ♦ ①t♦♥ t♠s ♦ ❲s ♥ t②♣❲s
❩♥ t P ♦
Huangpu Xuhui Minhang Pudong0
700
1400
2100
2800
3500
t end(GW)(ms)
OPT PGEL
Administrative divisions
Ps t♦♣♦♦② ♥s
[1, 2] [1.5, 2.5] [2, 3] [2.5, 3.5]0
400
800
1200
1600
2000
CPU clock frequency
t end(GW)(ms)
OPT PGEL
P❯ ♦ rq♥② ♥s
AlexNet VGGNet GoogleNet ResNet0
1100
2200
3300
4400
5500
WA type
t end(GW)(ms)
OPT PGEL
❲ ♥s
r ♠♣t ♦ ❲ ♥s ♦♥ t ♣r♦r♠♥ ♦ P
PGEL
PSO
GA
RAN
0 900 1800 2700 3600tend(GW) (ms)
♥♣
PGEL
PSO
GA
RAN
0 525 1050 1575 2100tend(GW) (ms)
❳
PGEL
PSO
GA
RAN
0 875 1750 2625 3500tend(GW) (ms)
♥♥
PGEL
PSO
GA
RAN
0 1125 2250 3375 4500tend(GW) (ms)
P♦♥
r ♦♠♣rs♦♥ ♦ ♦t ♣♠♥t