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Enhanced SFLA with spectral clustering based co-evolution for 24 constrained industrial optimization problems

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Abstract

Solving real world problems with large numbers of constraints and complex optimization functions is a challenging issue. For such problems, meta-heuristic algorithms are able to provide near optimal solutions. Shuffled Frog Leaping Algorithm(SFLA) is a population based meta-heuristic algorithm which employs the concept of population division for evolving the solutions over generations. To enhance the efficacy of SFLA for solving constrained optimization, this work presents Spectral Clustering based co-evolution technique. Spectral Clustering is a graph based clustering algorithm which is used to create memeplexes or partitioning of the population in SFLA. Proposed technique is able to improve the balance between the exploration and exploitation phase of SFLA. The performance of the proposed algorithm (SCSFLA) is evaluated over 24 real world constrained optimization problems. Success rate ratio ranking reveals that proposed Spectral clustering based SFLA (SCSFLA) technique outperforms existing Seed and distance based SFLA (SEEDSFLA), Random SFLA (RSFLA), conventional SFLA and Dynamic sub-swarm number strategy (DSFLA). SCSFLA also performs better than the well-known constrained optimization algorithms IUDE, MAgES, iLSHADE44 for 22 functions out of 24.

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  1. Jaypee Institute of Information Technology, Noida, India

    Shikha Mehta

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Annexure 1

Annexure 1

Symbol

Description

SC

Spectral Clustering

SFLA

Shuffled Frog Leaping Algorithm

SCSFLA

Shuffled Frog Leaping Algorithm with Spectral Clustering

SEEDSFLA

Seed and distance based SFLA

RSFLA

Random SFLA

DSFLA

Dynamic sub-swarm number strategy based SFLA

DNS

Dynamic sub-swarm number strategy

IUDE

Improved Unified Differential Evolution Algorithm

MAgES

Matrix Adaptation Evolution Strategy

iLSHADE 44

Improved Constraint-handling Method

D

Dimension

MaxFES

Maximum fitness function evaluations

N

Population size

m

Memeplex number

Slb

local best solution

Sw

local worst solution

Sgb

global best solution

Dmax

Max value for D

Dmin

Min value for D

Fw

Fitness of worst solution

\( {\mathrm{F}}_{\mathrm{n}}^{\mathrm{w}} \)

New Fitness of worst solution

M

Similarity/affinity matrix

Dg

Diagonal Matrix

L

Laplacian Matrix

V

Matrix of largest eigen vectors

C

Cluster

K

Number of clusters

SRR

Success Rate Ratio Ranks

BFV

Best Fitness Values

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Mehta, S. Enhanced SFLA with spectral clustering based co-evolution for 24 constrained industrial optimization problems. Multimed Tools Appl 82, 17853–17878 (2023). https://doi.org/10.1007/s11042-022-13790-3

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