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A novel approach in selective assembly with an arbitrary distribution to minimize clearance variation using evolutionary algorithms: a comparative study

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Abstract

The minimization of surplus components with normal dimensional distributions while making selective assemblies was the only objective considered in the previous research works carried out by various researchers in different periods. Seldom works have been found on selective assembly by considering all dimensional distributions. In this proposed work, a novel method is developed for making assemblies with zero surplus components and minimum clearance variation by considering arbitrary distribution, to demonstrate the greater improvement in the results than the past literature. Krill Herd algorithm has been implemented for identifying the best combination of groups. Computational results showed that the proposed krill herd algorithm outperformed as compared with existing literature and as well as the results by gaining-sharing knowledge-based algorithm, differential evolution algorithm, and particle swarm optimization algorithm.

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Abbreviations

A, B and C :

Name of the components in the assembly

NP jk :

Number of parts in jth component presents in kth group

T j :

Tolerance of jth component

ng :

Number of groups

L :

Length of the best combination of the group’s string

itr :

Index for iteration number

nitr :

Number of iterations

α :

A constant value assumed between 0 and 3

N :

Number of components in the assembly

R jk :

Repetition of jth components of kth group

nk :

Number of krill

P ijk :

ith krill random combination of a group of jth component in kth group

i :

Index to represent krill number

j :

Index to represent a component number in the assembly

k :

Index to represent group number

l :

Index to represent nearby krill

gw j :

Group width of jth component

CX ik :

Maximum clearance of assembly obtained by matching the kth group components of A, B and C of ith krill

CM ik :

Minimum clearance of assembly obtained by matching the kth group components of A, B and C of ith krill

NA ik :

Number of assemblies made by matching the kth group components of A, B and C of ith krill

NA i :

Number of assemblies made in ith krill

O i :

Fitness value/Clearance variation of ith krill obtained by matching the components A, B and C based on Pijk

O max :

Minimum value of clearance variation

O min :

Maximum value of clearance variation

P b :

Best combination of groups corresponding to Omax

P w :

Worst combination of groups corresponding to Omin

O b :

Equal to Omax

O w :

Equal to Omin

pbP ij :

Previous best combination of groups of ith krill jth component

pbO i :

Previous best clearance variation value of ith krill

ds i :

Sensing distance of ith krill

P i :

ith krill combination of groups

P j :

jth krill combination of groups

nn i :

Number of krill nearby to ith krill

\( a_{i}^{t\arg et} \) :

Target effect of ith krill

Target effect of ith krill

O ib :

Normalized fitness value of ith krill with respect to best fitness value

O i :

Fitness value of ith krill

ɸ :

A constant small value assumed as 0.15

P ib :

Normalized combination of groups of ith krill concerning the best combination of groups

\( a_{i}^{local} \) :

Local effect of ith krill

O il :

Normalized fitness value concerning nearby lth krill

O l :

Fitness value of nearby lth krill

P il :

Normalized value of the combination of groups concerning nearby lth krill combination of groups value

a i :

Motion of ith krill induced by krill swamp

\( N_{i}^{o} ,N_{i}^{n} \) :

Old and new motion induced by ith krill

P f :

Location of food

C f :

Value of food concentration

\( b_{i}^{f} \) :

Movement of ith krill due to the attraction of food

O if :

Normalized fitness value of ith krill concerning the location of food

O f :

Fitness value concerning the location of food

P if :

Normalized combination of groups of ith krill concerning the location of food

\( b_{i}^{b} \) :

Movement of ith krill due to previously experienced best fitness value

pbO i :

Best fitness value of ith krill with respect to its previous experienced fitness value

pbP i :

Best combination of groups of ith krill concerning its previous experienced best fitness value

O ipb :

Normalized fitness value of ith krill concerning previous best fitness value

P ipb :

Normalized combination of groups value of ith krill concerning the previous best combination of groups

\( F_{i}^{o} ,F_{i}^{n} \) :

Old and new foraging motion induced by ith krill

δ :

Random directional vector ranges between – 1 and 1

dt :

Scale factor

\( P_{i}^{o} ,P_{i}^{n} \) :

Old and new combination of groups value of ith krill where \( P_{i}^{o} \) is equal to Pijk during initialization and after replacement \( P_{i}^{n} \) becomes Pijk

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Authors and Affiliations

  1. Department of Mechanical Engineering, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, 600 062, India

    Lenin Nagarajan & Siva Kumar Mahalingam

  2. Manufacturing Engineering, School of Mechanical Engineering, VIT University, Vellore Campus, Vellore, Tamil Nadu, 632014, India

    Jayakrishna Kandasamy

  3. Mechanical Engineering, Sri Sivasubramaniya Nadar College of Engineering, Chennai, Tamil Nadu, 603110, India

    Selvakumar Gurusamy

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  1. Lenin Nagarajan
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  2. Siva Kumar Mahalingam
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  3. Jayakrishna Kandasamy
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  4. Selvakumar Gurusamy
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Correspondence to Siva Kumar Mahalingam.

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Nagarajan, L., Mahalingam, S.K., Kandasamy, J. et al. A novel approach in selective assembly with an arbitrary distribution to minimize clearance variation using evolutionary algorithms: a comparative study. J Intell Manuf 33, 1337–1354 (2022). https://doi.org/10.1007/s10845-020-01720-9

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