Abstract
Genetic algorithm (GA) is used to solve a variety of optimization problems. Mutation operator also is responsible in GA for maintaining a desired level of diversity in the population. Here, a directional mutation operator is proposed for real-coded genetic algorithm (RGA) along with a directional crossover (DX) operator to improve its performance. These evolutionary operators use directional information to guide the search process in the most promising area of the variable space. The performance of an RGA with the proposed mutation operator and directional crossover (DX) is tested on six benchmark optimization problems of different complexities, and the results are compared to that of the RGAs with five other mutation schemes. The proposed IRGA is found to outperform other RGAs in terms of accuracy in the solutions, convergence rate, and computational time, which is established firmly through statistical analysis. Furthermore, the performance of the proposed IRGA is compared to that of a few recently proposed optimization algorithms. The proposed IRGA is seen to yield the superior results compared to that of the said techniques. It is also applied to solve five constrained engineering optimization problems, where again, it has proved its supremacy. The proposed mutation scheme using directional information leads to an efficient search, and consequently, a superior performance is obtained.
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- \( N \) :
-
Population size
- \( p_{\text{c}} \) :
-
Crossover probability
- \( d \) :
-
Dimensions of an optimization problem
- \( \alpha \) :
-
Multiplying factor
- \( {\text{fe}} \) :
-
Number of function evaluation
- \( t_{\text{avg}} \) :
-
Average CPU time
- \( Q_{ \hbox{min} } \) :
-
Minimum frequency
- \( D \) :
-
Mean diameter
- \( \tau \) :
-
Shear stress
- \( P_{\text{c}} \) :
-
Buckling load on the beam
- \( T_{\text{s}} \) :
-
Shell thickness
- \( r_{\text{i}} \) :
-
Inner radius
- \( b \) :
-
Face width
- \( z \) :
-
Number of teeth on the pinion
- \( d_{1} \), \( d_{2} \) :
-
Diameters of the first and second shafts, respectively
- \( r_{\text{m}} \) :
-
Mean radius of particles
- \( {\text{MRR}} \) :
-
Material removal rate
- \( \rho_{\text{w}} \) :
-
Density of work material
- \( H_{\text{dw}} \) :
-
Dynamic hardness of ductile work material
- \( (R_{\text{a}} )_{\hbox{max} } \) :
-
Permissible surface roughness
- \( p_{\text{m}} \) :
-
Mutation probability
- \( p_{\text{cv}} \) :
-
Variablewise crossover probability
- \( p_{\text{best}} \) :
-
Current best solution
- \( p_{\text{mean}} \) :
-
Average of two parents \( p_{1} \) and \( p_{2} \)
- \( \hbox{max} \_{\text{gen}} \) :
-
Maximum number of generations
- \( {\text{fe}}_{\text{avg}} \) :
-
Average number of function evaluations
- \( d_{\text{w}} \) :
-
Wire diameter
- \( n \) :
-
Number of active coils
- \( \theta \) :
-
Bending stress
- \( \delta \) :
-
End deflection of a bar
- \( T_{\text{h}} \) :
-
Thickness of head
- \( l \) :
-
Length of the cylindrical vessel
- \( m \) :
-
Module of teeth
- \( L_{1} \), \( L_{2} \) :
-
Lengths of the first and second shafts between bearings, respectively
- \( \dot{M}_{\text{a}} \) :
-
Mass flow rate of abrasives
- \( v_{\text{a}} \) :
-
Velocity of abrasives
- \( \rho_{\text{a}} \) :
-
Density of abrasives
- \( \delta_{\text{cw}} \) :
-
Critical plastic strain of ductile work material
- \( \zeta \) :
-
Amount of plastically deformed indentation volume
- \( \alpha^{\prime} \) :
-
Significance level in statistical tests
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Das, A.K., Pratihar, D.K. Solving engineering optimization problems using an improved real-coded genetic algorithm (IRGA) with directional mutation and crossover. Soft Comput 25, 5455–5481 (2021). https://doi.org/10.1007/s00500-020-05545-9
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DOI: https://doi.org/10.1007/s00500-020-05545-9