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