Presentation on theme: "School of Computer Science"— Presentation transcript:
1 School of Computer Science University of BirminghamApplication of Nature Inspired Genetic Algorithms For Job Shop SchedulingBhuvan SharmaResearch AssociateAdvanced Computation in Design and Decision Making GroupUniversity West of England, Bristol, UK
2 Aim of Presentation Understanding job shop scheduling Why Nature Inspired AlgorithmsIssues in GA, when applied to job shop problemsReview of various approaches within GAPractical Problem from Rolls RoyceMy approach
3 Job Shop Scheduling Job : A piece of work that goes through series of operations.Shop : A place for manufacturing or repairing ofgoods or machinery.Scheduling : Decision process aiming to deduce theorder of processing.
4 A typical Job Shop Problem ParametersNumber of jobsNumber of operations within each jobProcessing time of each operation within each jobMachining sequence of operations within each jobObjectivesMinimization of make spanMinimization of costMinimization of delays
5 A 3 job 3 machine problem Processing time Jobs Operations Machining SequenceJobs OperationsJ1653J24J3102J1M1M2M3J2J3
6 Why Nature Inspired Algorithms GA’s vs Other methodsEvaluation on a set of points. Better search.Better chances for global optimal solution.Suitable for Multi-objective optimisation.Flexibility, because constraints can be taken care of.Evaluation on a point each time.Often terminate into local optima.Not suited for multi-objective optimisation.Not flexible, driven by heuristics, constraints not handled easily.
7 Issues in Genetic Algorithms when applied to job shop problems Representation of schedule(phenotype) by suitablegenotype.Conversion of genotype to phenotypeChoice of Schedule BuilderType of Crossover and Mutation to be usedAvoiding Premature convergence.
8 Schedule Builder!! What’s That J1M1M2M3J2J3J1653J24J3102
9 Representation schemes for schedules in job shop Conventional Binary representationJob Based RepresentationPermutation Representation (Partitioned)Permutation Representation (Repetitive)Priority Rule Based Representation (Random /guided)
10 1. Binary Representation Genotype is binary matrix ofRows = Number of job pairsColumns = Number of machinesInterpretationMij = 0 / 1 depending on whether job1is executed later or prior to job2.
11 Job M1 M M2Job M2 M M1Job M2 M M3(a) Machine SequenceJob1 &Job1 &Job2 &(b) Binary RepresentationM/c J1 J3 J2M/c J3 J2 J1M/c J1 J2 J3(c) Symbolic Representation
12 Crossover Demerits The crossover applied is simple one point Redundancy in representation.2mj(j-1)/2 bits are required for (!j)m schedules.Forcing techniques required for replacement ofillegal schedules.
13 2. Job Based Representation Typical chromosome [ Ji Jj Jk ]For [ J2 J1 J3 ]All operations of job 2 folllowed by 1 and then by 3 are scheduled in the available processing times.
14 Merits Demerits Scheduling is very easy Always yields a feasible schedule, hence forcingnot required.DemeritsApproach is very constrainedNot many possibilities are explored
15 3. Permutation Representation (Partitioned) Chromosome is set of permutation of jobs oneach machine.M M M3Job sequence matrix for 3 X 3 problemCross Over (SXX)Subsequence Exchange CrossoverSearches for exchangeable subsequence pairsin parents, and swaps them.
17 Merits Demerits GA operators used for TSP can be applied here Simple representationDemeritsDoes not always give active schedulesRobust Schedule builder is requiredSXX does not always guarantee a crossover
18 4. Permutation Representation (Repetitive) Also known as operation based representationTypical genotype is a unpartitioned permutationwith m repetitions for each job.MMM
19 Crossover (PPX) Precedence Preservation Crossover (PPX) The offspring inherits partial characteristicof both parentsPPC
20 Merits Demerits Very simple representation All decoding leads to active schedulesSchedule building is straightforwardCrossover results in passing of characteristics fromboth parents in most cases.DemeritsProblem of Premature convergenceThis is often case with long chromosomes
21 5. Priority(Random/Guided)Rule Based Representation CharacteristicsUse of GT Algorithm, with one of priority ruleused in ith iteration to select ith operationPriority rules could be assigned randomly, orguided by heuristics.Representation[ SPT, LPT, MTPT, LTPT, MLFT, ….. ]
22 Crossover Merits Demerits Both PPX and SXX can be used Always give feasible active schedulesIncorporates heuristics to an extentDemeritsProblem of fast, premature convergence offirst few genes in the chromosome
23 Practical Problem from Rolls Royce Parameters17 batches of jobs10 operations per job4 identical machines, each can perform anyoperation subject to tool setConstraintsOnly one tool-set for each operationOpn. 2 must not begin until opn 1 is completeOpn 3-9 can be performed in any sequenceOpn 10 should be the last for each batch of job
25 My Approach Representation Crossover Permutation based The catch here is that it is permutation of machinesnot jobsFor eg. [ : | 10 ]CrossoverPrecedence Preservation Crossover (PPX)
26 Start with heuristics Schedule builder Select a set of jobs out of 17 to process first. (random)Schedule builderIdentify conflicting set of jobsSelection of one from conflicting set based onone of heuristic priority rulesChange toolset for machine as it finishes requisitejobs. Change is guided by time factor.