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Table 9 Optimum results for pressure vessel design problem

From: An advanced hybrid meta-heuristic algorithm for solving small- and large-scale engineering design optimization problems

Algorithms

Optimal values for variables

Optimal cost

Ts (\({x}_{1}\))

Th(\({x}_{2}\))

R(\({x}_{3}\))

L(\({x}_{4}\))

PSO

0.8125

0.4375

42.091266

176.7465

6061.0777

DE

0.8125

0.4375

42.098411

176.637690

6059.7340

ACO

0.8125

0.4375

42.103624

176.572656

6059.0888

ABC

0.812500

0.437500

42.098446

176.636596

6059.714339

GWO

0.8125

0.4345

42.089181

176.75731

6051.5639

DA

0.782825

0.384649

40.3196

200

5923.11

GA

0.752362

0.399540

40.452514

198.00268

5890.3279

HS

1.099523

0.906579

44.456397

179.65887

6550.0230

CS

0.812500

0.437500

42.0984456

176.6363595

6059.7143348

EO

0.7781

0.3846

40.319619

199.99999

5885.3279

CDE

0.8125

0.4375

42.098411

176.63769

6059.7340

CSDE

0.8125

0.4375

42.10

176.6

6060.0000

CPSO

0.8125

0.4375

42.091266

176.746500

6061.0777

IPSO

0.812500

0.437500

42.098445

176.6365950

6059.7143

CSKH

0.7781686

0.3846491

40.3196187

200.0000

6059.7010

aDE

0.8125

0.4375

40.32962

179.85887

5885.3279

aPSO

0.8125

0.4375

40.31962

179.85887

5885.3079

haDEPSO

0.8125

0.4375

40.31962

179.65887

5882.4387