dr. keshav dahal 13 nov 2002 scheduling and optimisation using ga-based hybrid methods
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Dr. Keshav Dahalwww.mosaic.brad.ac.uk
13 Nov 2002
Scheduling and optimisation
using GA-based hybrid
methods
OverviewOverview• Scheduling and optimisation problems• Solution techniques• Case studies• Future research• Summary
Problem introductionProblem introduction
• Optimisation problem – optimise functions fi(x)
– subject to constraints gk(x)>0
• Scheduling– determine what happens when and where– decide future activities from possible
alternatives in order to meet objectives– allocate resources to tasks over time– is interrelated optimisation problem
Real-World problemsReal-World problems• are vital to solve from technical, operational
and financial points• are generally NP-hard, discrete, multi-model,
uncertain and multi-objective• should consider contingency analysis • are intractable using the traditional
approaches
• selection of an appropriate method is difficult
Modelling & solution Modelling & solution processprocess
Real systems (optimisation
problems)
Model
(Eq’s, Var’s, Param’s)
ModelResults
Approximations
Results
c.f. Reality
Numerical equations/Simulation
Solution techniques
Interpretation
Modelling
SolutionTechniques
(Solution and Analysis)
Modelling & optimisation Modelling & optimisation techniquestechniques
• Mathematical programming: – linear programming, Lagrangian relaxation,
dynamic programming, branch and bound
• Problem specific: – knowledge based systems, conventional
heuristic methods
• Metaheuristic and AI algorithms: – GA, simulated annealing, tabu search, ant
colony, hyperheuristic, fuzzy logic, neural
networks, game theory
Case 1: Generator maintenance Case 1: Generator maintenance schedulingscheduling
~ ~ ~
Pmin<Poutput<Pmax
Problem
MinimiseM&O costs
Maximise
reliability
Objectives
Gen
erat
ors
Time
Maintenance program
Solution
Time
Dem
and
Time
Rese
rve
Constraints
SelectionCrossoverMutation
Population of solutions
SA probabilistic replacement
Evaluation(Fuzzy logic)
Schedules
Stop & solution decoding
Repair
Chromosome
Probabilistic replacement
2 23 8 . …. 8
Solution creating & encoding
Heuristic
Random
Expert knowledge
GA-based hybrid approach
• Inoculated GA/SA is consistent in finding good solutions
Comparison of results
Average of best solutions over 10 exp
SA 146.06
GA 146.71
Heuristic -
Inoculated GA 142.67
GA/SA 145.78
Inoculated GA/SA 141.71
Best solution
140.49
137.91
139.96
138.12
222.61
137.91
GA string
Coder(Fuzzifier)
Decision making logic(Rule interpreter)
Decoder(Defuzzifier)
Rule orknowledgebase
Crisp calculation
SSR, TMV Total load violation (TLV)
Combined evaluation value (CEV)
Penalty for loadviolation
(PLV)
Evaluation function = CEV + PLV
Fuzzy logic controller
Fuzzy-GA hybrid
Comparison of results
132.95
137.91
133.4
126
130
134
138
142
nomanpowerconstraint
crisp fuzzy
SS
R (
x10e
5)
110
0
37
0
25
50
75
100
125
nomanpowerconstraint
crisp fuzzy
Ext
ra m
an-w
eeks
Manpower constraintObjective
No load violation for all cases.
Case 2: Generator schedulingCase 2: Generator scheduling
• Calculate commitment and MW output generation of each unit at each time interval
• Minimise total cost– fuel costs, start-up and shutdown costs
• Satisfy constraints– system: demand and reserve– area: import/export generation limits – unit: min & max generation, min up & down times, ramp rates, inflexibilities, shifts, transmission losses
~
~~
~
~Transmission
NetworksG1
G2
G3
G4
G5
ON/OFF? Pout?
ON/OFF? Pout?
Solution approachSolution approach
• Generation scheduling - mixed integer problem– unit commitment (discrete) – economic dispatch (continuous)
• Decomposition approach– master problem (integer) - GA string– sub-problems (real-number) - heuristic/LP
approach
• Step by step design approach starting from a simple GA to advanced hybrid GA
Comparison of resultsComparison of results
Techniques Cost of best sol. Comp. Time
Two stage GA 76328 4230sExplicit GA 76232 480sIntegrated GA 76172 300sGA-heuristic 76792 40sKnowledge-based GA 76172 45s
Knowledge-based GAKnowledge-based GAPre-Process Post process
(LP approach)
Integer variables for seeding best GA integers
Final solution
Continuous problem(heuristic approach)
Integers(GA string)
Solution qualityreal variables
GA-Heuristic approach
Alternative solutions (GA)
integer variablesevaluation value
new integer variables
Knowledge model
To further treatment
jetty
jetty
jetty
jetty
jetty
Run down line Jetty Ballast Line
Settling Time = 6 hours
1000 te/hr
30 - 1000 te/hr
10000 te
6000 te
7500 te
5000 te
Case 3: Tank scheduling in water treatment facility
Problem descriptionProblem description• Schedule filling-up and running down tanks and rates• Objectives
– Minimise delay to ships– Maximise the water quality by minimising rundown rate– Maximise uniformity of rundown rate
• Constraints– Initial conditions– Operational rules of individual elements of the facility– Operation of the network of the facility
• Mixed integer problem– tank allocation for filling and discharge (discrete)– rate calculation (continuous problem)
Hybrid GAHybrid GA
(Heuristic approach)
Determine ship unloading schedule &
calculate tank filling up rates
(GA approach)
Allocate tanks for
filling up and running down
(Heuristic approach)
Calculate tank running
down rates
Allocation of tanks for filling up
Allocation of tanks for running-down
Evaluation function
Sub-problem 1:
Sub-problem 2: Sub-problem 3:
Tank running
down rates
Ship unloading schedules
& tank filling up rates
Evaluation value determination
GA-based GA-based scheduleschedule
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 t
Tank 1 325, 325, 325, 325, 325, 325, 975, 975, 975
Filling up (& filling rate)
Settling
Stationary
Running down (& run down rate)
Tank 2
Tank 3
Tank 4
Empty
400, 500, 540, 540, 540, 540, 540
480, 480, 480, 480, 480, 480, 480, 480, 480, 480
380, 280, 180, 80, 30, 30, 30
725, 650, 650,1000,1000,1000,1000, 1000
1000 ,1000, 190 325, 325
• Feasible schedule• Average run down rate =121 te/hr, cost=67.68 units (cf. 136 te/hr and 72.2 unites of the heuristic solution)
Reclaimer
jetty
jetty
jetty
jetty
Berth
Berth
Conveyor
Conveyor
Unloader/Loader
Conveyor
Unloader/Loader
Transfer station
Stacker/Reclaimer Stockpile
Buffer
Conveyor
Steelworks
Feeder
Case 4: Optimisation in bulk Case 4: Optimisation in bulk handling systemhandling system
Optimisation problemOptimisation problem• Determine the best management strategies and
design parameters
• Objectives:– Minimise total operating cost of facility– Maximise utilisation of resources available
• Constraints:– Arrival times of ships/vessels
– Initial conditions of facility
– Operating rules of individual equipment in facility
– Physical constraints of the plant in the facility
– Demand of materials from facility
Port simulation toolkitPort simulation toolkit
• Realised using discrete event simulation
• Facilities– drag and drop objects– parameterise objects– connect objects– sanity check– reset/initialise/start/
stop simulation– view result graphs– output and save results
Optimisation frameworkOptimisation framework
Port Modelling Tool
Library of port componentsPort Model
Results display Optimisation component
Optimisation engine (GA)
Optimisation processing module
Effective technique Effective technique designdesign
• Appropriate encoding• Effective evaluation approach• Hybridisation• Problem specific operators• Selection of appropriate parameters• Pre and post- processing mechanisms
Research challengesResearch challenges
• Taxonomy of problems for tackling new application
• Suitability of techniques for particular class of problems
• Condition and contingency based problem• Optimisation in changing environment• Large computational time• Limited theoretical assessments are
available
Future researchFuture research• Investigation of novel methods for a
general class of optimisation problems– TSP, Bin packing, Yard allocation,
Timetabling
• Hybrid optimisation methods using multi-objective framework– Real-world industrial problems– Restructured electricity industries
SummarySummary• Severe penalties for non-optimum schedules and
plans
• Traditional solution techniques are limited
• Hybrid algorithms underpinned by domain knowledge show much promise
• Classification and theoretical analysis of novel techniques are limited
• Development of a taxonomy of problems - a useful reference for new applications
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