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Algorithms 2018,11, 68
Partiallymappedcrossover (PMX)[32,33]: Thisoperatoruses twocutpoints (Figure5). Thepart
of theďŹrstparentbetweenthe twocutpoints is copiedto thechildren. Then, the followingpartsof the
childrenareďŹlledbyamappingbetweenthe twoparents, so that theirabsolutepositionsare inherited
wherepossible fromthesecondparent.
Figure5.Partiallymappedcrossover (PMX)operator.
Figure 6 shows an example of the PMXcrossover. The cross points in bothparents serve to
formthechildchromosome.The16 listed lotsof the4 jobsarerandomlydistributedoneachparent
chromosome.Whencrossed, theyformthechildchromosomewith16 lots.
Figure6.PMXcrossoveroperatorexamplewithbatch index.
Thecrossparentsarecomposedof thebatchesof the jobs listed inTable8.
Table8.Enumerationof thebatches for jobs.
Job Batches BatchIndex
1 4 1â4
2 4 5â8
3 4 9â12
4 4 13â16
Figures7and8showrepresentationsof tasks for twoandfourmachinesperstage. Theoriginal
sequence is ordered considering the enumeration of the jobs and their batches. Eachmachine is
assignedbatches toprocess,whichformthe tasksofeach job. Eachmachinemustprocessacertainset
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Algorithms for Scheduling Problems
- Title
- Algorithms for Scheduling Problems
- Authors
- Frank Werner
- Larysa Burtseva
- Yuri Sotskov
- Editor
- MDPI
- Location
- Basel
- Date
- 2018
- Language
- English
- License
- CC BY 4.0
- ISBN
- 978-3-03897-120-7
- Size
- 17.0 x 24.4 cm
- Pages
- 212
- Keywords
- Scheduling Problems in Logistics, Transport, Timetabling, Sports, Healthcare, Engineering, Energy Management
- Categories
- Informatik
- Technik