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A research survey: heuristic approaches for solving multi objective flexible job shop problems

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Abstract

Flexible job shop scheduling problem is a relaxation of the job shop scheduling problem and is one of the well-known combinatorial optimization problems that has wide applications in the industrial fields such as production management, supply chain, transport systems, manufacturing systems. In recent years, many researches have been carried out with different approaches—ranging from mathematical models to heuristic methods—to solve multi objective flexible job shop scheduling problems (FJSSP). This study aims to present the forms of scrutiny of multi-objective FJSSPs and various heuristic techniques used to solve problems in the last decade. This review will allow the reader to select specific methods and follow the guidelines set forth in their future research.

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Abbreviations

\( \mathop \sum \nolimits_{i = 1}^{n} w_{i} f_{i} \) :

Aggregate value of the objective functions

\( t_{comp} \) :

Computation time

\( Q_{time} \) :

Queue time

\( SD(.) \) :

Standard deviation

\( RPD \) :

Relative percentage deviation

\( var(.) \) :

variance

\( PF \) :

Pareto front

\( S(PF) \) :

S-metric

\( N(PF) \) :

The size of the approximated pareto fronts

\( \chi (PF) \) :

The extent of the pareto fronts

\( d \) :

Distance

\( DistM \) :

Distribution metric

\( N_{NDS} \) :

Number of non-dominated solution

\( R_{NDS} \) :

Ratio of non-dominated solution

\( \overline{{D_{NDF/PF} }} \) :

Average distance of the obtained non-dominated front to pareto front

\( Lb \) :

Load balance

\( \overline{CD} \) :

Average crowding distance

\( \overline{NFC} \) :

Average net front contribution

\( \overline{PD} \) :

Average pareto distance

\( DT \) :

Degree of truth

\( RM \) :

Robustness measure

\( IGD \) :

Inverse generation distance

\( ER \) :

Error ratio

\( DM \) :

Diversification metric

\( SM \) :

Spacing Metric

\( MID \) :

Mean ideal distance

\( NOS \) :

Number of found solutions

\( \sum S_{{time_{i} }} \) :

Total setup time on machines

\( W_{time} \) :

Waiting time of jobs

\( EC \) :

Energy consumption

\( TOC \) :

Total operation cost

\( HVM \) :

Hyper volume metric

\( TDom \) :

Total dominance

\( RAS \) :

The rate of achievement to two objectives simultaneously

\( POD \) :

Percentage of domination

\( LimSTI \) :

Limited starting time interval

\( ConvM \) :

Convergence metric

\( CWPQ \) :

Cost-weighted processing quality

\( GC \) :

Global criterion

\( BS \) :

Best solution

\( WS \) :

Worst solution

\( GAP \) :

The gap from the best-known solution

\( WO \) :

Weak outperformance

\( CO \) :

Complete outperformance

\( NFC \) :

Net front contribution

\( TMLV \) :

Total machine load variation

\( QM \) :

Quality metric

\( \overline{{R_{idle} }} \) :

Average ratio of idle times

\( OC \) :

Operation cost

\( EUR \) :

Equipment utilization ratio

\( PrdC \) :

Production cost

\( PCT \) :

Production cycle time

\( OvrC \) :

Overtime cost

\( Stbl \) :

Stability

\( TC \) :

Total additional resource consumption

\( TAV \) :

Total availability of the system

\( TEC \) :

Total energy consumption

\( TPC \) :

Total processing cost

\( APT \) :

Adjustment processing time

\( TD \) :

Total deviation

\( \overline{AI} \) :

Average agreement index

\( AI_{min} \) :

Minimal agreement index

\( US \) :

User satisfaction

\( TCF \) :

Total carbon footprint

\( TLWC \) :

Total late work criterion

\( GD \) :

Generational distance

\( spread \) :

Spread

\( PC \) :

Processing cost

\( HVR \) :

Hyper volume ratio

\( CDom \) :

Comparison dominance

\( S_{NDS} \) :

Spread of non-dominated solutions

\( TTI \) :

Tolerated time interval

\( \sum S_{{cost_{i} }} \) :

Total setup cost on machines

\( NLO \) :

Number of late operations

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Acknowledgements

This study was supported through funds provided by Scientific Research Unit of Marmara University under Project No: “FEN-C-DRP-090518-0249”. Authors of this research are also member of Marmara University Industrial Engineering Research Group.

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  1. Department of Engineering Management, Marmara University, Göztepe Kampüsü, 34722, Istanbul, Turkey

    Alper Türkyılmaz

  2. Department of Industrial Engineering, Marmara University, Göztepe Kampüsü, 34722, Istanbul, Turkey

    Özlem Şenvar, İrem Ünal & Serol Bulkan

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Türkyılmaz, A., Şenvar, Ö., Ünal, İ. et al. A research survey: heuristic approaches for solving multi objective flexible job shop problems. J Intell Manuf 31, 1949–1983 (2020). https://doi.org/10.1007/s10845-020-01547-4

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