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Performance evaluation of proposed Differential Evolution and Particle Swarm Optimization algorithms for scheduling m-machine flow shops with lot streaming

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Abstract

We consider n-job, m-machine lot streaming problem in a flow shop with equal size sub lots where the objective is to minimize the makespan and total flow time. Lot streaming (Lot sizing) is a technique that splits a production lot consisting of identical items into sub lots to improve the performance of a multi stage production system by over lapping the sub lots on successive machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. To solve this problem, we propose a Differential Evolution Algorithm (DEA) and Particle Swarm Optimization (PSO) to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set up time. In this research, we propose the DEA and PSO algorithms for discrete lot streaming with equal sub lots. The proposed methods are tested and the performances were evaluated. The computational results show that the proposed algorithms are very competitive for the lot streaming flow shop scheduling problem.

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Abbreviations

PSO:

Particle swarm optimization

DEA:

Differential evolution algorithm

S:

Initial sequence

S’:

Generated sequence

Cmax(s) :

Makespan time for the sequence s

Cmax(s') :

Makespan time for the sequence s’

i:

Machine

j:

Job

m:

Number of machines

n:

Number of jobs

Pij :

Processing time for job j on machine i

Sij :

Setup time for job j on machine i

F1 :

Completion time for first job

F2 :

Completion time for second job

MP:

Makespan

N:

Last (final) job to be processed

M:

Last (final) machine number

Cmax :

Makespan for generated sequence

Tmax :

Total flow time for generated sequence

A:

Arrival time

S:

Setup time

P:

Processing time

Vi,G :

Velocity for the generation

Xi,G :

Position for the generation

K:

Combination factor

r1, r2, r3 :

Random population

F:

Scaling factor

CR:

Crossover Ratio

D:

Dimensions

rni :

Randomly chosen population index

uji, G + 1 :

Trial vector generation

Vji, G + 1 :

Mutant vector

qji, G :

Target vector

ranj :

Random variable

Xr1 :

Randomly chosen first population

Xr2 :

Randomly chosen second population

rand1, rand2 :

Random number between 0 and 1

C1 :

Cognitive parameter

C2 :

Social parameter

\({{\rm V}_{\rm ij}^{\rm t}}\) :

Current velocity of agent i at iteration t

\({{\rm V}_{\rm ij}^{{\rm t}+1}}\) :

Modified velocity of agent i

W:

Weight inertia for velocity of agent i

Pbesti :

Particle best of agent i

gbesti :

Global best of the group

\({{\rm x}_{\rm i}^{\rm t}}\) :

Current position of agent i at iteration t

\({{\rm x}_{\rm i}^{{\rm t}+1}}\) :

Modified position of agent i

ss :

Swarm size

Wi :

Initial weight

Wf :

Final weight

C:

Constriction function

Anm :

arrival time of the nth job on mth machine

Snm :

setup time of the nth job on mth machine

Pnm :

processing time of the nth job on mth machine

ANM :

arrival time of the Nth job on Mth machine

SNM :

setup time of the Nth job on Mth machine

PNM :

processing time of the Nth job on Mth machine

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Authors and Affiliations

  1. Department of Mechanical Engineering, Fathima Michael College of Engineering & Technology, Madurai, 625 020, India

    G. Vijay chakaravarthy

  2. Department of Mechanical Engineering, Latha Mathavan Engineering College, Madurai, 625 301, India

    S. Marimuthu

  3. Department of Mechanical Engineering, Chendhuran College of Engineering & Technology, Pudukkottai, 622 507, India

    A. Naveen Sait

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  1. G. Vijay chakaravarthy
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  2. S. Marimuthu
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  3. A. Naveen Sait
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Correspondence to G. Vijay chakaravarthy.

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Vijay chakaravarthy, G., Marimuthu, S. & Naveen Sait, A. Performance evaluation of proposed Differential Evolution and Particle Swarm Optimization algorithms for scheduling m-machine flow shops with lot streaming. J Intell Manuf 24, 175–191 (2013). https://doi.org/10.1007/s10845-011-0552-2

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  • DOI: https://doi.org/10.1007/s10845-011-0552-2

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