1/54 博士予備審査 2005.10.19 Makoto Watanabe Department of Computational Intelligence and Systems Science 03D35183 A Schedule Optimization based on Genetic Algorithm

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博士予備審査 2005.10.19

Makoto WatanabeMakoto Watanabe

Department of Computational Intelligence Department of Computational Intelligence and Systems Scienceand Systems Science

03D3518303D35183

A Schedule Optimization based on A Schedule Optimization based on Genetic Algorithm with Fuzzy Logic and Genetic Algorithm with Fuzzy Logic and

its Application to Various Scheduling Problemsits Application to Various Scheduling Problems

Hirota LabHirota Lab

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ContentsContents

Chap. 3Chap. 3.. Application to Generalized Restaurant Application to Generalized Restaurant Work Scheduling ProblemWork Scheduling Problem

Chap. 2. Chap. 2. Restaurant Work Scheduling Based on Restaurant Work Scheduling Based on Genetic Algorithm with Fuzzy LogicGenetic Algorithm with Fuzzy Logic

Chap.1. Chap.1. IntroductionIntroduction

Chap. 5. Chap. 5. ConclusionsConclusions

Chap. 4Chap. 4 Efficient Computation for Work Scheduling Efficient Computation for Work Scheduling Problem Based on Alpha-Level Fuzzy Sets Problem Based on Alpha-Level Fuzzy Sets

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Background (1)Background (1)

Family RestaurantFamily Restaurant

Attendance SheetAttendance Sheet(Work Schedule)(Work Schedule)

AutomaticAutomatic

Needs 5 hoursNeeds 5 hours(per week)(per week)

ManualManual

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WaiterWaiter

CookCook

DeliveryDelivery

Background (2)Background (2)

Member nameMember name

Total work timeTotal work time Work timeWork time

Rest timeRest time

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D – day shift (7:00-15:30)

E – evening shift (15:00-23:30)

N – night shift (23:00-7:30)

SUN MON TUE WED THU FRI SATRN1 D D D D DRN2 D D D D DRN3 E E E E ERN4 E E E N NRN5 D D D D D DRN6 D D D D D DRN7 E D D D E ERN8 N N N N N

Nurse Schedule Problem <NSP>Nurse Schedule Problem <NSP>

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NSP softwareNSP software

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SUNRN1 DRN2RN3RN4 ERN5 DRN6 DRN7 ERN8 N

Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 8Member2 0Member3 0Member4 8Member5 0Member6 0Member7 6Member8 0Member9 0Member10 6Member11 8Member12 0Member13 4Member14 0Member15 5

ＮＳＰＮＳＰ Restaurant WSRestaurant WS

Not applicable

NSP and Restaurant WSPNSP and Restaurant WSP

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ContentsContents

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Purpose (1)Purpose (1)

NameName Optimized Working ScheduleOptimized Working Schedule

1010/54/54

Large search spaceLarge search space

DifficultiesDifficulties

Evaluation of satisfaction Evaluation of satisfaction

daytime member24 15 7 25202 2

Complicated constrains Complicated constrains

1111/54/54

Fuzzy DivisionFuzzy Division

Proposed Algorithm (1)Proposed Algorithm (1)


time member24 15 3602 2

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Weekly WS problemWeekly WS problem

Whole solution Whole solution spacespace

Daily solution spaceDaily solution space

Weekly solution Weekly solution spacespace

fuzzy division


Daily WS problemDaily WS problem

WEDWED

FRIFRI

THUTHU

SATSAT

TUETUE

MONMON

SUNSUN

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Large search spaceLarge search space

Evaluation of satisfaction Evaluation of satisfaction Complicated constrains Complicated constrains


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Member’s requirementsMember’s requirements

Time

Conventional AlgorithmConventional Algorithm

Total Time/day

Total Time/day

Time

SystemSystemInputInput

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Proposed AlgorithmProposed Algorithm

Total Time/day

Time

SystemSystemInputInput

FuzzyFuzzy

Member’s requirementsMember’s requirements

Time

Total Time/day

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BeforeBefore


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AfterAfter


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SystemSystem

Overview of systemOverview of system

Daily Work Schedule ProblemDaily Work Schedule Problem

Weekly Work Schedule ProblemWeekly Work Schedule Problem

Fuzzy Membership Fuzzy Membership FunctionFunction

Condition Member Request

Constrains

Constrains

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Crossover

Selection

Evaluation fuzzy logic

Genetic Algorithm

End conditions

END

Initialize

YesNo

Mutation

Start


ChromosomesChromosomes

・・・・・

・・・・・・

・

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Experimental Conditions (1)Experimental Conditions (1)

• DataData– Data of real chain reData of real chain re

staurants in Japanstaurants in Japan

• Data conditions Data conditions – 24-hours operation24-hours operation– 15 members15 members

• Machine conditionsMachine conditions– Athlon XP 1900+Athlon XP 1900+– C++ LanguageC++ Language

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• MethodMethod– Random Search– Genetic Algorithm– Proposed Method

• Genetic AlgorithmGenetic Algorithm

　　 Crossover - Crossover - Two point crossoverTwo point crossover

　　 Selection - Minimal Generation GapSelection - Minimal Generation Gap

population size generation

Daily WS problem 1000 25000

Weekly WS problem 100 500

population sizepopulation size generationgeneration

Daily WS problemDaily WS problem 10001000 2500025000

Weekly WS problemWeekly WS problem 100100 1500015000

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ＳＡＴＳＡＴ

ＳＵＮＳＵＮMONMON

Random SearchRandom Search

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 9 W W W W W W W W WMember2 14 W W W W W W W W W W W W W WMember3 13 W W W W W W W W W W W W WMember4 10 W W W W W W W W W WMember5 13 W W W W W W W W W W W W WMember6 15 W W W W W W W W W W W W W W WMember7 7 W W W W W W WMember8 13 W W W W W W W W W W W W WMember9 10 W W W W W W W W W WMember10 15 W W W W W W W W W W W W W W WMember11 12 W W W W W W W W W W W WMember12 11 W W W W W W W W W W WMember13 10 W W W W W W W W W WMember14 10 W W W W W W W W W WMember15 12 W W W W W W W W W W W W

Required Member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 10 W W W W W W W W W WMember2 9 W W W W W W W W WMember3 9 W W W W W W W W WMember4 11 W W W W W W W W W W WMember5 10 W W W W W W W W W WMember6 14 W W W W W W W W W W W W W WMember7 11 W W W W W W W W W W WMember8 11 W W W W W W W W W W WMember9 9 W W W W W W W W WMember10 12 W W W W W W W W W W W WMember11 15 W W W W W W W W W W W W W W WMember12 6 W W W W W WMember13 7 W W W W W W WMember14 10 W W W W W W W W W WMember15 9 W W W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 13 W W W W W W W W W W W W WMember2 11 W W W W W W W W W W WMember3 10 W W W W W W W W W WMember4 13 W W W W W W W W W W W W WMember5 13 W W W W W W W W W W W W WMember6 11 W W W W W W W W W W WMember7 4 W W W WMember8 8 W W W W W W W WMember9 11 W W W W W W W W W W WMember10 12 W W W W W W W W W W W WMember11 6 W W W W W WMember12 13 W W W W W W W W W W W W WMember13 11 W W W W W W W W W W WMember14 10 W W W W W W W W W WMember15 11 W W W W W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 10 W W W W W W W W W WMember2 11 W W W W W W W W W W WMember3 8 W W W W W W W WMember4 12 W W W W W W W W W W W WMember5 12 W W W W W W W W W W W WMember6 10 W W W W W W W W W WMember7 9 W W W W W W W W WMember8 12 W W W W W W W W W W W WMember9 10 W W W W W W W W W WMember10 16 W W W W W W W W W W W W W W W WMember11 8 W W W W W W W WMember12 15 W W W W W W W W W W W W W W WMember13 5 W W W W WMember14 7 W W W W W W WMember15 9 W W W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Experimental Results (1)Experimental Results (1)

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 10 W W W W W W W W W WMember2 11 W W W W W W W W W W WMember3 11 W W W W W W W W W W WMember4 14 W W W W W W W W W W W W W WMember5 14 W W W W W W W W W W W W W WMember6 7 W W W W W W WMember7 10 W W W W W W W W W WMember8 13 W W W W W W W W W W W W WMember9 9 W W W W W W W W WMember10 13 W W W W W W W W W W W W WMember11 11 W W W W W W W W W W WMember12 13 W W W W W W W W W W W W WMember13 11 W W W W W W W W W W WMember14 13 W W W W W W W W W W W W WMember15 12 W W W W W W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 12 W W W W W W W W W W W WMember2 10 W W W W W W W W W WMember3 9 W W W W W W W W WMember4 10 W W W W W W W W W WMember5 12 W W W W W W W W W W W WMember6 10 W W W W W W W W W WMember7 9 W W W W W W W W WMember8 12 W W W W W W W W W W W WMember9 7 W W W W W W WMember10 9 W W W W W W W W WMember11 8 W W W W W W W WMember12 7 W W W W W W WMember13 12 W W W W W W W W W W W WMember14 9 W W W W W W W W WMember15 12 W W W W W W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 3 2 2 2 2 1 1 1

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 11 W W W W W W W W W W WMember2 12 W W W W W W W W W W W WMember3 9 W W W W W W W W WMember4 4 W W W WMember5 11 W W W W W W W W W W WMember6 11 W W W W W W W W W W WMember7 14 W W W W W W W W W W W W W WMember8 10 W W W W W W W W W WMember9 10 W W W W W W W W W WMember10 12 W W W W W W W W W W W WMember11 11 W W W W W W W W W W WMember12 14 W W W W W W W W W W W W W WMember13 12 W W W W W W W W W W W WMember14 11 W W W W W W W W W W WMember15 7 W W W W W W W

Required Member 1 1 1 2 2 3 4 3 2 2 1 1 2 4 4 3 3 2 2 2 2 1 1 1

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ＳＡＴＳＡＴ


Genetic AlgorithmGenetic Algorithm

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 W W WMember2 7 W W W W W W WMember3 4 W W W WMember4 7 W W W W W W WMember5 3 W W WMember6 4 W W W WMember7 6 W W W W W WMember8 0Member9 5 W W W W WMember10 2 W WMember11 6 W W W W W WMember12 1 WMember13 6 W W W W W WMember14 9 W W W W W W W W WMember15 4 W W W W

Required Member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 2 W WMember2 5 W W W W WMember3 5 W W W W WMember4 2 W WMember5 3 W W WMember6 3 W W WMember7 1 WMember8 4 W W W WMember9 3 W W WMember10 8 W W W W W W W WMember11 4 W W W WMember12 2 W WMember13 6 W W W W W WMember14 7 W W W W W W WMember15 2 W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 4 W W W WMember2 2 W WMember3 5 W W W W WMember4 2 W WMember5 1 WMember6 1 WMember7 11 W W W W W W W W W W WMember8 2 W WMember9 0Member10 0Member11 5 W W W W WMember12 3 W W WMember13 3 W W WMember14 6 W W W W W WMember15 3 W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 0Member2 1 WMember3 4 W W W WMember4 1 WMember5 1 WMember6 2 W WMember7 3 W W WMember8 1 WMember9 3 W W WMember10 1 WMember11 3 W W WMember12 2 W WMember13 6 W W W W W WMember14 10 W W W W W W W W W WMember15 5 W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 1 WMember2 1 WMember3 7 W W W W W W WMember4 1 WMember5 3 W W WMember6 3 W W WMember7 5 W W W W WMember8 4 W W W WMember9 2 W WMember10 3 W W WMember11 2 W WMember12 1 WMember13 3 W W WMember14 4 W W W WMember15 2 W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 0Member2 5 W W W W WMember3 4 W W W WMember4 3 W W WMember5 1 WMember6 1 WMember7 2 W WMember8 5 W W W W WMember9 5 W W W W WMember10 3 W W WMember11 3 W W WMember12 6 W W W W W WMember13 0Member14 6 W W W W W WMember15 7 W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 3 2 2 2 2 1 1 1

Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 8 W W W W W W W WMember2 6 W W W W W WMember3 3 W W WMember4 2 W WMember5 6 W W W W W WMember6 8 W W W W W W W WMember7 6 W W W W W WMember8 1 WMember9 0Member10 1 WMember11 2 W WMember12 1 WMember13 5 W W W W WMember14 7 W W W W W W WMember15 9 W W W W W W W W W

Required Member 1 1 1 2 2 3 4 3 2 2 1 1 2 4 4 3 3 2 2 2 2 1 1 1


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Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Member1 0Member2 3 W W WMember3 0Member4 7 W W W W W W WMember5 4 W W W WMember6 0Member7 4 W W W WMember8 0Member9 0Member10 2 W WMember11 4 W W W WMember12 4 W W W WMember13 4 WMember14 0Member15 8 W

Required members 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3Available member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3

Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3Member1 3 W W WMember2 0Member3 0Member4 7 W W W W W W WMember5 4 W W W WMember6 0Member7 4 W W W WMember8 4 W W W WMember9 4 W W W WMember10 2 W WMember11 0Member12 0Member13 4 W W W WMember14 0Member15 8 W W W W W W

Required members 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1Available member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1

Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Member1 0Member2 3 W W WMember3 0Member4 7 W W W W W W WMember5 4 W W W WMember6 0Member7 4 W W W WMember8 4 W W W WMember9 4 W W W WMember10 0Member11 4 W W W WMember12 3 WMember13 3Member14 8 W WMember15 0

Required members 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 3Available member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 3

Name Total Working time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 W W WMember2 7 W W W W W W WMember3 0Member4 0Member5 0Member6 5 W W W W WMember7 0Member8 4 W W W WMember9 7 W W W W W W WMember10 5 W W W W WMember11 5 W W W W WMember12 3 W W WMember13 7 W W W W W WMember14 6 W W W W WMember15 0

Required members1 1 1 2 2 3 4 3 2 2 1 1 2 4 4 3 3 2 2 2 2 1 1 1Available member1 1 1 2 2 3 4 3 2 2 1 1 2 4 4 3 3 2 2 2 2 1 1 1

Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 W W WMember2 3 W W WMember3 0Member4 0Member5 0Member6 3 W W WMember7 0Member8 5 W W W WMember9 5 W W W W WMember10 8 W W W W W W W WMember11 7 W W W W W W WMember12 5 W W W W WMember13 7 W W W W W W WMember14 0Member15 7 W W W W W W W

Required members 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1Available member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 W W WMember2 0Member3 0Member4 7 W W W W W W WMember5 4 W W W WMember6 0Member7 4 W W W WMember8 4 W W W WMember9 0Member10 0Member11 4 W W W WMember12 6 W W W W W WMember13 0Member14 8 W W W W W W W WMember15 0


Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22Member1 0Member2 3 W W WMember3 0Member4 7 W W W W W W WMember5 4 W W W WMember6 0Member7 4 W W W WMember8 0Member9 4 W W W WMember10 2 W WMember11 4 W W W WMember12 0Member13 0Member14 8 W WMember15 4 W W

Required members 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2Available member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2

Proposed AlgorithmProposed AlgorithmExperimental Results (3)Experimental Results (3)

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MondayMonday

Experimental Comparison (1)Experimental Comparison (1)

Proposed methodProposed method

Random searchRandom search





Name Total Working Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 2 W WMember2 5 W W W W WMember3 5 W W W W WMember4 2 W WMember5 3 W W WMember6 3 W W WMember7 1 WMember8 4 W W W WMember9 3 W W WMember10 8 W W W W W W W WMember11 4 W W W WMember12 2 W WMember13 6 W W W W W WMember14 7 W W W W W W WMember15 2 W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Working Time6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 10 W W W W W W W W W WMember2 9 W W W W W W W W WMember3 9 W W W W W W W W WMember4 11 W W W W W W W W W W WMember5 10 W W W W W W W W W WMember6 14 W W W W W W W W W W W W W WMember7 11 W W W W W W W W W W WMember8 11 W W W W W W W W W W WMember9 9 W W W W W W W W WMember10 12 W W W W W W W W W W W WMember11 15 W W W W W W W W W W W W W W WMember12 6 W W W W W WMember13 7 W W W W W W WMember14 10 W W W W W W W W W WMember15 9 W W W W W W W W W

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

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MONMON

Computation Time : 6minComputation Time : 6min


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Value Time Solution

Proposed Method -0.135 6min ○

Genetic Algorithm -19077 20min Ｘ

Random Search -103438 2days Ｘ



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1.1. I was very surprised that the proposed system can I was very surprised that the proposed system can produce the schedule, produce the schedule, only 6 minutesonly 6 minutes..

2.2. I think, in the I think, in the real worldreal world, we can use the schedule , we can use the schedule which was generated by the proposed system as a which was generated by the proposed system as a prototype.prototype.

3.3. The proposed system should be improved by The proposed system should be improved by considering considering various tasksvarious tasks for members in for members in real real restaurantrestaurant..

CommentsComments

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ContentsContents




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Purpose (2)Purpose (2)

3131/54/54

Name Total Working time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 W W WMember2 3 W W WMember3 0Member4 0Member5 0Member6 3 W W WMember7 0Member8 5 W W W WMember9 5 W W W W WMember10 8 W W W W W W W WMember11 7 W W W W W W WMember12 5 W W W W WMember13 7 W W W W W W WMember14 0Member15 7 W W W W W W W


ExamplesExamples

Manager Manager

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SystemSystem


sub-worktime member 224 15 16 57602 2

Member Skill Sub Work

Fuzzy Membership FunctionFuzzy Membership FunctionFuzzy LogicFuzzy Logic

Member SkillMember Skill

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0

0.5

1

1 2 3 4

( )mO k

: sub-workk

mO

DCBA

k

( ) ( )×L

L max ( )m

m m

mTT n

G t G t

L n

T

( ) ( ) • ( )m m m

T

G t P t R t

1rT

yes

No

1 1ˆ s.t ( ) ( )max

r

S S mr rt T m M

t G t G t

yesNo

( ) 0N t

, 11, ( ) 1

s jmT N t

1r

1k

( )

1 ( )1 ( )

,..., M1

{ ,..., } arg max ( ) ( ).N ts

s q qN ts

pl

N t m s m pm m

qj

B

m m G t O j

J

Start

End

1 11, ( ) 1, \{ }

s j k jkm s S S DW t m

M M

Working skill membership functionWorking skill membership function

3434/54/54

• DataData– Data of real chain restaData of real chain resta

urants in Japanurants in Japan

• Data conditions Data conditions – 24-hours operation24-hours operation– 15 members15 members– 4 sub-works4 sub-works



3535/54/54


• MethodMethod– Random Search– Genetic Algorithm– Proposed Method

• Genetic AlgorithmGenetic Algorithm　　 Crossover - Crossover - Two point crossoverTwo point crossover

　　 Selection - Minimal Generation GapSelection - Minimal Generation Gap

population sizepopulation size generationgeneration

Daily WS problemDaily WS problem 10001000 2500025000

Weekly WS problemWeekly WS problem 10001000 1500015000

Genetic AlgorithmGenetic Algorithm 10001000 80000008000000

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Random SearchRandom SearchExperimental Results (1)Experimental Results (1)

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 12 D B C B BC D CD A D ACD D B

Member2 7 AC C B D B A B

Member3 10 A B A C D C D B AC B

Member4 10 B AD CD B A A AB AC A AB

Member5 10 B D D A D BD A C B A

Member6 7 B BD CD C D AC B

Member7 12 A D D C A AD C C C A D C

Member8 11 AD C B C D A D C D BC D

Member9 8 C C D D C D B B

Member10 11 D A BCD C D B D B B B C

Member11 10 BC BC AC A A B BC B D D

Member12 11 C B A AC C D B C A A B

Member13 11 A B A AD B C AD B C AB BD

Member14 13 AD C A D A A B A D A B C B

Member15 15 D C B B BD D A A B B B BC C AB B

Required Member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 9 C B BC A B CD A B B

Member2 13 BC B AB A C B AB C C D B AB AC

Member3 9 B B D A A C CD AC B

Member4 7 B C D C A C A

Member5 11 D D B BD AC D CD B B B D

Member6 11 C C A A C A D D A B C

Member7 8 C A D CD C A AB B

Member8 9 C B D B C C B D A

Member9 10 B BC BD A D A D D B A

Member10 4 D C CD C

Member11 10 D AD AB BD A A CD A A D

Member12 10 B AB A A AD CD B D B CD

Member13 9 D BD A BD B C B C A

Member14 9 B BC B AD AB D A B D

Member15 8 D B AB A B C B D

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 12 A B D BC D A AB B A D A B

Member2 10 A B A C BCD B D B D B

Member3 8 D B B A B AD C BC

Member4 9 D B C D A C AB BD B

Member5 8 D A BD B A A A AD

Member6 10 A B B D D A ABD AD ABD D

Member7 13 AB C D D CD D D C A D D B B

Member8 12 D A CD D C D B D D A A AC

Member9 12 B A B A B D C D C BC B C

Member10 12 D A A D A AD BD C D B A B

Member11 7 C B B C B D B

Member12 5 A D A AD D

Member13 8 B C C AC CD A A B

Member14 6 BCD A C B BC C

Member15 11 A B B A D A B B D B A

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 8 D ACD AC D CD C D A

Member2 11 B C D C C CD BD D AD A B

Member3 10 ACD AC A B A C A CD AC A

Member4 7 C BC C A A D B

Member5 10 D D B AC CD C A D A D

Member6 7 A AB D B A C AB

Member7 8 BC A B B C AC B C

Member8 10 D B D A B C D B D B

Member9 9 A BD C A C D B D D

Member10 11 BD AC D A B AD C AB C A D

Member11 11 C C D CD C BD B A B A D

Member12 8 B D D B A D D B

Member13 10 CD D D C D D D A D C

Member14 8 BD D C B B C C A

Member15 9 D B D C D D C B D

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1 Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 11 AD BC A BC D A B AC C C D

Member2 9 D B B C D C A D D

Member3 10 B A B A AB B D C C C

Member4 9 B B A AB D C D D C

Member5 5 C C C D ACD

Member6 10 A A C C D C D D C D

Member7 7 C C D AC BC A D

Member8 11 B A C B B C B A B B CD

Member9 13 A D AB B D AD BD B A C AC B B

Member10 8 B A C C C B CD B

Member11 4 AC A C D

Member12 8 A CD AB A B B ACD AC

Member13 9 BC BD B A C D D AD A

Member14 6 A D CD AD C A

Member15 14 C C D B D B A A C AB A A C A

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 10 A B AC A B BC AB C D A

Member2 10 A D B C C C CD C C C

Member3 7 D C A A CD D B

Member4 11 A A D C A A B CD B D B

Member5 10 AD AC C B A C A D A C

Member6 8 D B ACD C D B AD C

Member7 9 B B B B B B D D AC

Member8 10 B C D C C AD D A A BD

Member9 13 A D A D AD AC A D B A B AC B

Member10 10 C B A B B A D B B B

Member11 7 C C D B A D B

Member12 8 B C A CD B C D B

Member13 15 D D A BC A CD C C D AD C D A CD A

Member14 7 A B CD AD C CD BC

Member15 13 D B C C C D AD A C A C D BD

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 3 2 2 2 2 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 8 AB A AD B B A B B

Member2 10 A D A C B C BC D B C

Member3 8 B B C C D D A C

Member4 8 A B C D BC B C A

Member5 12 C D A A D D A C D A A D

Member6 8 C B D C A B B C

Member7 12 B B BC C D D CD D C C D C

Member8 7 C C C B BC B D

Member9 8 BCD BC B BCD D D C CD

Member10 7 D C C C CD D A

Member11 6 C C AD A D A

Member12 9 B D D AB C D AB D D

Member13 5 C CD D A D

Member14 13 A AC B AD A A D C B C B AC C

Member15 13 D B C B A BC AB A C BC B B B

Required Member 1 1 1 2 2 3 4 3 2 2 1 1 2 4 4 3 3 2 2 2 2 1 1 1

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ＴＵＥＴＵＥ

ＷＥＤＷＥＤ

ＴＨＵＴＨＵ

ＦＲＩＦＲＩ

ＳＡＴＳＡＴ

ＳＵＮＳＵＮＭＯＮ

Genetic AlgorithmGenetic AlgorithmExperimental Results (2)Experimental Results (2)

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 11 AB B AB B BD AB D D C C AB

Member2 11 D C A A AC BC B BC A D C

Member3 8 AB AC AD C C D B C

Member4 7 AB B C C B BC D

Member5 11 C A BC B C A D A B D B

Member6 9 D D A B D A B C A

Member7 8 C B A A D A A AB

Member8 15 D A B D D A D C A BD A C D C A

Member9 11 B C C B C A C A CD D B

Member10 11 D C D B B CD B D D A B

Member11 11 C D A AC BC B D D D B AD

Member12 11 C C B A C D ABC C B B BD

Member13 13 A ABD A AC CD A AD C D ABC AD C C

Member14 10 D C B D BC AB BCD AD D C

Member15 8 D CD A A B BC C D

Required Member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 8 C B BD D D AB D AC

Member2 11 D B AD C D A A BD D D B

Member3 7 B A C C B D BC

Member4 11 B B BCD C B C CD A D A C

Member5 12 C AC C C A CD B A C C A A

Member6 8 A A C C A A B D

Member7 15 D B CD B AB AD A A A A B D B B D

Member8 10 A D BD D AB B B B C B

Member9 11 A D D D B C B B C C A

Member10 5 C B C C D

Member11 13 C A BD A A A C ABC B A B D AD

Member12 6 B D D B B A

Member13 6 B A C A CD A

Member14 7 A B C CD D D C

Member15 7 B C CD AD AD B BC

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 7 D A A BD A C C

Member2 11 C C BD A B B C AC D B BC

Member3 7 D A B C AB B C

Member4 10 A D A D B A D ACD B B

Member5 6 AC B A BC D C

Member6 7 D B B C ABC C B

Member7 4 C CD BD B

Member8 9 A C C A D D D A D

Member9 9 BC D D B A A C BD C

Member10 13 BC A A B B BC A C D B B C AD

Member11 10 C BC A C A AB A B A AC

Member12 7 D D D BC D A A

Member13 7 AB B D A A D B

Member14 10 C D AC C C B A AD C B

Member15 10 D C D A BD B B C D D

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 9 D D A D B C B BD D

Member2 11 A B D A AB A CD C AD A B

Member3 7 C AC A B C D C

Member4 11 D D D CD B C B B B A D

Member5 8 AC C D B D D BD B

Member6 9 D A C D C C B D C

Member7 7 A BD BCD A AD C A

Member8 9 B B A B D AD A C C

Member9 11 B C C C A C B AC A A A

Member10 11 D B BD D BC B CD B D D A

Member11 10 D AC B D AC A D C B C

Member12 5 AB D C B D

Member13 10 BD BD D C A AD A C BD A

Member14 9 D C C AC D AB C C A

Member15 10 A B B B D B B A A B

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 9 C B A C B CD CD C D

Member2 10 C B C BD C B B D A B

Member3 7 D D C B BCD ABC AB

Member4 8 B C C B C BD D A

Member5 6 D D B A C C

Member6 11 A A B D C D BD B C C BC

Member7 10 C D B B D C AC C B A

Member8 9 B A D A C B D C B

Member9 8 AC C A C B B D D

Member10 13 D D BC C AD D D AD B A D C D

Member11 8 D D A B CD D ABD B

Member12 8 A D C C A D AC C

Member13 11 C B AB A A AB A A B B A

Member14 10 C B AD A B A C AD B D

Member15 7 A A A C D A A

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 12 A AC AC D A D D B C B D A

Member2 12 D A A D C A AD BC BC D A B

Member3 10 A B D C B C D A A A

Member4 7 C B D C B C D

Member5 6 AC AB D AD C C

Member6 10 B A BC AC D D C CD D A

Member7 6 C CD B C C AB

Member8 14 C B D D ABD D D C AC B A D A B

Member9 9 C C C D AB BC B D C

Member10 13 C B A C D A ABD A D C B C B

Member11 7 B D AD D C C AD

Member12 9 A BC BD A C AD C B A

Member13 11 A B BC AB A B BC AD ACD B BD

Member14 9 B B A B BD BD AB B CD

Member15 10 D CD B C B C D A D C

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 3 2 2 2 2 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 10 C A D B D B A C A A

Member2 14 AD A D C A D D BC C AC A CD C B

Member3 10 B B A B AC C A AD A C

Member4 5 C B C D B

Member5 8 C B B B D B B C

Member6 13 C AC C C B B B B B AB C BC D

Member7 11 D C AD C C BD B B D B C

Member8 9 B D D C B C C C B

Member9 12 D A C B D C B ABD A B D C

Member10 13 B C D A AC A B B AD A C AD A

Member11 8 B D D C BD D B B

Member12 6 C B A A A C

Member13 13 C AD D B B BC D C D BD ABC B ACD

Member14 9 A C A B C D D A B

Member15 11 D B D ACD AB A D A A D D

Required Member 1 1 1 2 2 3 4 3 2 2 1 1 2 4 4 3 3 2 2 2 2 1 1 1

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ＴＵＥ

ＷＥＤ

ＴＨＵ

ＦＲＩ

ＳＡＴ

ＳＵＮMONName Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5

Member1 3 BD BD A

Member2 3 ABCD ABCD ABCD

Member3 0Member4 0Member5 0Member6 5 A CD A A C

Member7 0Member8 4 C C B BC

Member9 7 AC C R C C B BCD BCD

Member10 8 D D D A R BCD CD D D

Member11 3 B B B

Member12 4 B B B CD

Member13 7 A A R A B B B B

Member14 0Member15 8 A D CD CD CD R BCD BCD BCD

Requird Member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 ABCD ABCD ABCD

Member2 0Member3 0Member4 5 ABCD CD CD B B

Member5 5 AB AB A A AB

Member6 5 CD CD CD ABCD ABCD

Member7 0Member8 0Member9 4 ABCD AB CD CD

Member10 0Member11 5 CD A A AC AC

Member12 5 B B B R BC ABCD

Member13 0Member14 0Member15 8 D BD AD R ABCD ABCD ABCD ABCD ABCD

Requird Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 0Member2 3 ABCD ABCD ABCD

Member3 0Member4 7 ABCD BCD BCD B B R ABCD ABCD

Member5 5 A A A A AB

Member6 3 CD CD CD

Member7 0Member8 0Member9 0

Member10 4 ABCD CD CD CD

Member11 4 A A C BC

Member12 6 AB B B B R BC BC

Member13 0Member14 0Member15 8 AD AD AD R ABCD ABCD ABCD ABCD ABCD

Requird Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1


Member3 0Member4 7 ABCD BCD BCD B B R ABCD ABCD

Member5 5 A A A A AB

Member6 3 CD CD CD

Member7 0Member8 4 AB B B AB

Member9 5 ABCD CD CD CD CD

Member10 2 A A

Member11 0Member12 0Member13 4 A AB AB ABCD

Member14 7 CD CD R ABCD ABCD ABCD ABCD ABCD

Member15 0Requird Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 2 CD D

Member2 7 ABCD ABCD ABCD CD R C C BC

Member3 0Member4 0Member5 0Member6 5 A A CD CD CD

Member7 0Member8 4 C C B AB

Member9 0Member10 8 D D AB AB R ABCD CD D D

Member11 4 AB AB AB B

Member12 5 AB B B CD CD

Member13 8 A A A R AB AB AB AB AB

Member14 7 A CD CD CD CD R ABCD ABCD



Member3 0Member4 7 ABCD CD CD B B R ABCD ABCD


Member6 3 CD CD CD

Member7 0Member8 4 BCD B A B

Member9 4 CD CD C AC

Member10 1 A

Member11 0Member12 7 CD B R BD B BC BC BC

Member13 2 AD AB

Member14 8 A D AD AD R CD ABCD ABCD ABCD



Member2 0Member3 0Member4 7 ABCD CD CD B B R ABCD ABCD


Member6 3 CD CD CD

Member7 0Member8 2 B B

Member9 4 CD CD CD BC

Member10 4 ABCD AB A A


Member14 0Member15 8 D CD CD R ABCD ABCD ABCD ABCD ABCD

Requird Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1


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MondayMonday

Experimental ComparisonExperimental Comparison (1) (1)

Proposed methodProposed method

Random searchRandom search











Requird Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 8 C B BD D D AB D AC

Member2 11 D B AD C D A A BD D D B

Member3 7 B A C C B D BC

Member4 11 B B BCD C B C CD A D A C

Member5 12 C AC C C A CD B A C C A A

Member6 8 A A C C A A B D

Member7 15 D B CD B AB AD A A A A B D B B D

Member8 10 A D BD D AB B B B C B

Member9 11 A D D D B C B B C C A

Member10 5 C B C C D

Member11 13 C A BD A A A C ABC B A B D AD

Member12 6 B D D B B A

Member13 6 B A C A CD A

Member14 7 A B C CD D D C

Member15 7 B C CD AD AD B BC

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 9 C B BC A B CD A B B

Member2 13 BC B AB A C B AB C C D B AB AC

Member3 9 B B D A A C CD AC B

Member4 7 B C D C A C A

Member5 11 D D B BD AC D CD B B B D

Member6 11 C C A A C A D D A B C

Member7 8 C A D CD C A AB B

Member8 9 C B D B C C B D A

Member9 10 B BC BD A D A D D B A

Member10 4 D C CD C

Member11 10 D AD AB BD A A CD A A D

Member12 10 B AB A A AD CD B D B CD

Member13 9 D BD A BD B C B C A

Member14 9 B BC B AD AB D A B D

Member15 8 D B AB A B C B D

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

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R: rest timeR: rest time

A,B,C,D: sub-worksA,B,C,D: sub-works









Requird Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

MONMON

Computation Time : 11minComputation Time : 11min


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Value Time Solution

Proposed Method -0.214 11min ○

Genetic Algorithm -33167 120min Ｘ

Random Search -80863.3 1days Ｘ



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1.1. I was very surprised that the proposed system I was very surprised that the proposed system can produce the schedule, can produce the schedule, only 11 minutesonly 11 minutes..

2.2. I think, in the I think, in the real worldreal world, we can use the , we can use the schedule which was generated by the proposed schedule which was generated by the proposed system as a prototype.system as a prototype.

CommentsComments

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User interfaceUser interface

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ContentsContents




Chap. 4Chap. 4 Efficient Computation for Work Scheduling Efficient Computation for Work Scheduling Problem Based on Alpha-Level Fuzzy Sets Problem Based on Alpha-Level Fuzzy Sets

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Alpha-Level Fuzzy Sets (1) Alpha-Level Fuzzy Sets (1)

0

1

α1

α2

α3

AA ・]1,0[

11 A・

A

Membership valueMembership value

t

4646/54/54

Time

Alpha-Level Alpha-Level Fuzzy SetsFuzzy Sets

Alpha-Level Fuzzy Sets (2)Alpha-Level Fuzzy Sets (2)

Total Time/day

Time

Total Time/day

・・・

・・・・・

・・・・

・・・・・

・・・・

・・・ChromosomesChromosomes ChromosomesChromosomes

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Initialize

Crossover

Selection

Generated Schedules

Yes

No

Mutation

End conditionsEnd conditions

Start

END

( ) ( )×L, L max ( )m

m m mTT n

G t G t L n

T , ( ) ( ) • ( )m m mT G t P t R t

1jT

yesNo

1 1ˆ s.t ( ) ( )max

J

S S mj jt T m M

t G t G t

1 1

ˆ̂ s.t ( )maxsk k

S k

s m m S jm

m G G t

M

111 ( ) 1, \{ }

s k kkkm s S S DW t m

M M

yes

No( ) 0N t

11, ( ) 1

s kmT N t

1j

1k

Start

END


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・・・・・・


TimeTimeTimeTime

Algebra product

TimeTime

M

15M

15 24 360time

productproduct

15 24 360time

GaussianGaussian

chromosome

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・・・・・・


TimeTimeTimeTime

Algebra product

TimeTime

Mchromosome

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(24 )A G M { : ( ( ) 0) ( ( ) 0)}

{ : , , ( ( ) ( )) ( ( ) ( ))} / 2

x T A x B x

x T y T x y A x A y B x B y

24 24G M

FormulateFormulate

G: derivation of Gaussian functionM: product of membership function

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• DataData– Data of real chain restaData of real chain resta

urants in Japanurants in Japan

• Data conditions Data conditions – 24-hours operation24-hours operation– 15 members15 members– 4 sub-works



• Alpha-LevelAlpha-Level

1212

5252/54/54

Time

Alpha-LevelAlpha-Level 9m40s

ConventionalConventional 11m06s

14% down14% down

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 AD AD AD


Member3 0Member4 0Member5 0Member6 3 B A A

Member7 0Member8 4 C C B AB

Member9 5 C C C C CD

Member10 8 D D A AD R ABCD CD D D

Member11 7 BC B R B B B BC ABCD

Member12 4 B B CD CD

Member13 8 AB A A A R AB AB AB ABCD

Member14 0Member15 6 CD CD CD R ABCD ABCD ABCD

Required Member 1 1 1 2 3 3 4 4 3 2 1 1 2 4 4 3 3 2 2 2 1 1 1 1

W1Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5


Member2 0Member3 0Member4 7 ABCD BC BC B B R ABCD ABCD

Member5 5 AD AD A A AB

Member6 3 CD CD CD

Member7 0Member8 5 ABCD AB A A AB

Member9 3 CD CD CD

Member10 0Member11 0Member12 6 CD B B R BC BC ABCD

Member13 0Member14 8 AD AD R ABCD ABCD ABCD ABCD ABCD

Member15 0Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1


Member3 0Member4 5 ABCD BC BC B B AB

Member5 4 AD AD A A

Member6 4 CD CD CD ABCD

Member7 1Member8 0Member9 4 ABCD R CD CD CD CD

Member10 2 A R A

Member11 4 ABCD AB B A B

Member12 4 B R AB AB ABCD

Member13 0Member14 0Member15 7 CD CD R ABCD ABCD ABCD ABCD ABCD

Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1


Member3 0Member4 7 ABCD BC BC B B R ABCD ABCD

Member5 5 AD AD A A AB

Member6 3 CD CD CD

Member7 0Member8 4 ABCD AB B B BC

Member9 3 CD CD CD

Member10 2 A A



Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1


Member2 0Member3 0Member4 7 ABCD BC BC B B R ABCD ABCD

Member5 5 AD AD A A A

Member6 3 CD CD CD

Member7 0Member8 4 ABCD AB B B BC

Member9 3 CD CD CD

Member10 2 A A



Required Member 1 1 1 1 2 2 3 3 2 1 1 1 2 3 3 3 2 2 1 1 1 1 1 1

Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 1 ABCD

Member2 2 ABCD ABCD

Member3 0Member4 7 ABCD BC BC B B R ABCD ABCD

Member5 5 AD AD A A A

Member6 3 CD CD CD

Member7 0Member8 0Member9 0

Member10 5 ABCD AD D D D

Member11 4 A A A A

Member12 6 BC BC BC R BC BC BC

Member13 3 A AB AB

Member14 8 BC D AD R CD CD ABCD ABCD ABCD


Name Total Time 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3 4 5Member1 3 AD AD AD

Member2 8 ABCD ABCD ABCD BC R C C BC BC

Member3 0Member4 0Member5 0Member6 4 A A AD AC

Member7 0Member8 3 CD CD C

Member9 0Member10 8 B B D D R BD ABCD ABCD AB

Member11 1 B

Member12 6 CD B B R BC BC BC

Member13 7 A A AB A R AD AB AB

Member14 8 D D AD R CD CD ABCD ABCD ABCD


Experimental ResultsExperimental Results

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ContentsContents




Chap. 4.Chap. 4. Efficient Computation for Work Scheduling Efficient Computation for Work Scheduling Problem Based on Alpha-Level Fuzzy Sets Problem Based on Alpha-Level Fuzzy Sets

Chap. 5. Chap. 5. ConclusionsConclusions

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Chap. 2.Chap. 2.

• A quasi-optimization algorithm for generating WS is proposedA quasi-optimization algorithm for generating WS is proposed

Chap. 3.Chap. 3.

• A quasi-optimization algorithm for generating WS included sub-work A quasi-optimization algorithm for generating WS included sub-work is proposedis proposed

• A weekly schedule is produced in 11 minutesA weekly schedule is produced in 11 minutes

• Satisfactorily evaluated by expertSatisfactorily evaluated by expert

Chap. 4.Chap. 4.

• shortening of calculate timeshortening of calculate time

ConclusionsConclusions

Documents

1/54 博士予備審査 2005.10.19 Makoto Watanabe Department of Computational Intelligence and Systems Science 03D35183 A Schedule Optimization based on Genetic Algorithm