The Swine Influenza Model Based Optimization (SIMBO) family is a newly introduced speedy optimization technique having the adaptive features in its mechanism. In this paper, the authors modified the SIMBO to make the algorithm further quicker. As the SIMBO family is faster, it is a better option for searching the basin. Thus, it is utilized in local searches in developing the proposed memetic algorithms (MAs). The MA has a faster speed compared to SIMBO with the balance in exploration and exploitation. So, MAs have small tradeoffs in convergence velocity for comprehensively optimizing the numerical standard benchmark test bed having functions with different properties. The utilization of SIMBO in the local searching is inherently the exploitation of better characteristics of the algorithms employed for the hybridization. The developed MA is applied to eliminate the power line interference (PLI) from the biomedical signal ECG with the use of adaptive filter whose weights are optimized by the MA. The inference signal required for adaptive filter is obtained using the selective reconstruction of ECG from the intrinsic mode functions (IMFs) of empirical mode decomposition (EMD).
Genetic algorithm, particle swarm optimization, bacterial foraging optimization, differential evolution, evolutionary programming, and so forth are the stochastic optimizers that have drawn the attentions in recent time [
Since 1960, genetic algorithm (GA) is a potential optimizer in the field of optimization [
The hybrid algorithm tries to keep a balance in processes of exploration and exploitation achieving global optimization. Hybrid methods like leastsquarefuzzy BFO [
This paper proposal is in two ways, that is, modification of the newly introduced algorithms, Swine Influenza ModelBased Optimization (SIMBO) [
The paper is organized in seven folds. Section
The Swine Influenza ModelBased Optimization (SIMBO) developed by Pattnaik et al. [
Artificial immune system (AIS) is inspired by the immunology of the body’s immune system that categorizes all cells (or molecules) within the body as selfcells or nonselfcells [
The modifications in the SIMBO are incorporated in the proposed work as (i) constraining the individual range in the process of optimization, and (ii) new process of state change, having population diversity in the vicinity of the current individual, in SIMBOV and SIMBOQ.
The key terms and definitions used in SIMBO have been used in the modified SIMBO. These are listed below.
Day (D): current generation or iteration.
TD: total number of days or generations.
State (S): individual position.
Health (H): fitness.
Pandemic state (PS): pandemic (global) best state in all the individuals.
Pandemic health (PH): fitness value corresponding to pandemic state.
Primary symptoms of swine flu: swine flu symptoms are fever, runny nose, cough, sore throat, headache, body aches, fatigue, and chills.
Swine flu test: the laboratory testbased verification of an infected individual with swine flu.
Vaccination (V): it vaccinates against the swine flu to the susceptible/unexposed population.
Amount of vaccine (Vc): the vaccine dose supplied to the individual.
Dose: antiviral drugs supplied to individual for curing the swine flu.
Momentum factor of dose (Md): it is for controlling the individual dose.
Momentum factor of state (MS): it is for controlling the individual state.
The list of the parameters in SIMBO used in mSIMBO is shown in Table
List of the parameters in SIMBO used in mSIMBO.
Parameters of SIMBO used in mSIMBO  Value/range 

Amount of vaccine (Vc): the vaccine dose supplied to the individual  Randomly generated in the range [−0.5, 1.0) 
Quarantine factor (Vq): the state change factor to change state from best individual to new one  Randomly generated in the range [−0.5, 1.0) 






Momentum factor of dose (Md): it is for controlling the individual dose  Randomly generated in the range [0.0, 2.0) 
Momentum factor of state (MS): it is for controlling the individual state  MS = 0.2 
Fe: fever, Co: cough, fathead: fatigue and headache, NV: nausea and Vomiting, Dai: diarrhea 
(Fe × Co × fathead × NV × Dai) = random number in the range [0,1) 
The modified SIMBOT, which is named as mSIMBOT, also does optimization by treatment mechanism using probability of treatment similar to that of basic SIMBOT. Initially, all individuals are susceptible due to the infected individual and the treatment is given to all susceptible cases by antiviral drug dose. The amount of dose is dependent on primary and secondary symptoms as well as current health and pandemic health.
The mSIMBOT is also doing optimization through two steps as given below.
The health of the individual depends upon given fitness function. Initially, the health of all individuals is evaluated for checking susceptible patient to swine flu as diagnostic confirmation.
Treatment is based on symptoms and is often based on a trial and error. A physician generally begins the treatment with a typical dose and monitors for a response as well as side effects. The standardization of a dose is based on population dose response characteristics and not on individual optimal outcomes [
Similar to the basic SIMBO algorithms (i.e., SIMBOT, SIMBOV, and SIMBOQ), the modified SIMBO algorithms, which are named as mSIMBOT, mSIMBOV, and mSIMBOQ, also have the amount of dose based on primary symptoms, secondary symptoms, current health, and pandemic health, where the primary symptoms and secondary symptoms are shown in (
It does the optimization by utilizing the vaccination and treatment mechanism. The susceptible individuals go through the swine flu test. The susceptible class is presented for swine flu vaccination and acquiring immunity. The SIMBOV mechanism of optimization has four steps as shown below and mSIMBOV also utilizes these.
The explanation of Steps 2 and 3 is as follows.
Dynamic threshold is used for evaluation of the patient states due to affect of swine flu virus. When current health values of individuals are more than the dynamic threshold (
The following is the algorithm showing the application of swine flu test:
Susceptible case
Recovered case
With the application of a vaccine, the vaccination is carried out for the protection from disease with the help of immunity [
In mSIMBOV, this process of the state change of the individual is also modified and multiplicand Vc modified as in (
The following is the algorithm showing the application of modified vaccination:
It does the optimization with quarantine and treatment mechanism. Out of all susceptible individuals who undergo the swine flu test, the confirmed cases have quarantine from population. The treatment is applied to all individuals by dose amount based on current health. Similar to the basic SIMBOQ, mSIMBOQ also does optimization in four steps as given below. Steps 1 and 4 of mSIMBOQ are the same as those of mSIMBOT. Step 2 is the same as the above explanation, whereas Step 3 is explained below. Steps 1, 2, and 4 of mSIMBOQ are similar to those of mSIMBOV.
Quarantine is the separation and isolation of individuals or restriction forced on unbound reposition to prevent contagious disease spread. The confirmed cases in swine flu tests are isolated or quarantined. The original algorithm quarantines the individual by multiplying the best state of the individual with
The modification introduced in calculating the value of
The following is the algorithm that shows the application of modified quarantine:
Hybridization of genetic algorithm (GA) with local search algorithm is memetic algorithm (MA) [
The unique aspect of the MA is that the chromosomes and offspring are facilitated to gain some experience with a local search process in between regular evolutionary process [
Evolutionary algorithms follow heuristic search procedures that incorporate random selection and variation. Therefore, Swine Influenza Modelbased Optimization Algorithms (SIMBOs) are modified and used as local searches in the main algorithm GA to make MAs. In this work, the variants of MAs are named like memetic algorithm with BLX
The GA is used for the purpose of exploration and the modified SIMBOs as local search for exploitation in the metaheuristic combination of the proposed MAs. So, this gives a better converging capability to the algorithm for global convergence with better accuracy in convergence besides speed along with higher success rate. The inherent properties of basic SIMBO family are present in mSIMBOT, mSIMBOV, and mSIMBOQ and they are having the dynamic adaptation for every individual with the help of learning from its neighbours facilitating the mSIMBOT, mSIMBOV, and mSIMBOQ in dealing with complex, multimodal search landscapes efficiently. When these mechanisms are used in searching the search landscapes under limited exposure of local areas of landscapes with local boundary constraints in memetic framework, these give the capability of finding solutions in the complex local areas also. The explorationexploitation balancing adaptation in the evolutionary algorithm like modified SIMBO family inherently has its local refining characteristics and again it is utilized in refining the smaller area of landscape in MA framework making it sort of metameme in nature. This is observed in the memetic framework under consideration.
The GAs and the MAs based on real number representation are called realcoded genetic algorithms (RCGAs) and realcoded memetic algorithms (RCMAs), respectively [
Standard numerical benchmark functions (basic and CEC2005) used for experimental study [
Function  Names 

Basic standard benchmark functions  
Fsph  Sphere model (NFFE = 150000) 
Fs2.22  Schwefel’s problem 2.22 (NFFE = 200000) 
Fs1.2  Schwefel’s problem 1.2 (NFFE = 500000) 
Fs2.21  Schwefel’s problem 2.21 (NFFE = 500000) 
Fros  Generalized Rosenbrock’s function (NFFE = 500000) 
Fste  Step function (NFFE = 150000) 
Fqua  Quartic function (i.e., noise) (NFFE = 300000) 
Fs2.26  Generalized Schwefel’s problem 2.26 (NFFE = 300000) 
Fras  Generalized Rastrigin problem (NFFE = 300000) 
Fack  Ackley’s function (NFFE = 150000) 
Fgri  Generalized Griewanks function (NFFE = 300000) 
Fpen1  Generalized penalized function no. 1 (NFFE = 150000) 
Fpen2  Generalized penalized function no. 2 (NFFE = 150000) 


CEC 2005 Standard benchmark function  
F1  Shifted sphere function 
F2  Shifted Schwefel’s problem 1.2 
F3  Shifted rotated high conditioned elliptic function 
F4  Shifted Schwefel’s problem 1.2 with noise in fitness 
F5  Schwefel’s problem 2.6 with global optimum on bounds 
F6  Shifted Rosenbrock’s function 
F7  Shifted rotated Griewank’s function without bounds 
F8  Shifted rotated Ackley’s function with global optimum on bounds 
F9  Shifted Rastrigin’s function 
F10  Shifted rotated Rastrigin’s function 
F11  Shifted rotated weierstrass function 
F12  Schwefel’s problem 2.13 
F13  Expanded extended Griewank’s plus Rosenbrock’s function (F8F2) 
F14  Shifted rotated expanded Scaffer’s F6 
F15  Hybrid composition function 
F16  Rotated hybrid composition function 
F17  Rotated hybrid composition function with noise in fitness 
F18  Rotated hybrid composition function 
F19  Rotated hybrid composition function with a narrow basin for the global optimum 
F20  Rotated hybrid composition function with the global optimum on the bounds 
F21  Rotated hybrid composition function 
F22  Rotated hybrid composition function with high condition number matrix 
F23  Noncontinuous rotated hybrid composition function 
F24  Rotated hybrid composition function 
F25  Rotated hybrid composition function without bounds 
The crossovers used are BLX
This distribution is obtained by transforming with uniform random number source
The local search algorithm is evoked after a decided number of iterations or generations of evolving algorithm (known as Glocal) which is selected as 2 for better result. In the MA, local searching is of the search space around best candidate solution obtained due to the previous process of exploration. The smaller population for the refinement is generated around the current best individual by little perturbations.
Then the individuals undergo treatment, quarantine, and vaccination processes according to the threshold, state of the individual, quarantine and vaccination probabilities, and so forth. The calculated dose used for treatment depends on primary and secondary symptoms, current health and best health of individual, and previous dose for the same individual. Then the controlled dose is applied to the individual for recovery. The best individual is found out in all iterations during the refinement process. After the local refinement, the better result due to the refinement process is taken back in the evolving algorithmic process. It strengthens the algorithm for convergence of shifted and/or rotated unimodal/multimodal single/composite wellknown standard benchmark functions [
Initialization: Generate a random initial population
Number of generation:
Evaluate all individuals in the population
Find current best individual
Obtain the local population around the current best individual by small perturbation
Evaluate and sort the population
Classify the individuals in classes S, I and R
Update current_best_individual, current_best_health
Calculate dynamic threshold (DT)
Classify and tag individuals into S, I, R classes
Quarantine or vaccination S & I individuals based probability (
Calculate Dose for applying to individual
Provide treatment to S based on probability
Glocal = 0
Return best individual to evolving algorithm
Select individuals for crossover based on crossover probability
Crossover the parents by BLX
Correct the feasibility of the produced individuals
Mutate some of the descendant population based on mutation probability
Replace the old population by new preserving the elite
The experimental results on benchmark functions using modified SIMBO variants and modified SIMBObased memetic algorithms are presented here in this section.
In the genetic as well as in memetic algorithms, a population of 100 individuals of realvalued representation is used. The crossover operator used is the BLX
Comparison of the experimental results of algorithms used for dimension 10.
10D  F  Fsph  Fs2.22  Fs1.2  Fs2.21  Fros  Fste  Fqua  Fs2.26  Fras  Fack  Fgri  Fpen1  Fpen2 

GABLX  Mean 













STD 
















GASBX  Mean 













STD 
















SIMBOT  Mean 













STD 
















SIMBOV  Mean 













STD 
















SIMBOQ  Mean 













STD 
















mSIMBOT  Mean 













STD 
















mSIMBOV  Mean 













STD 
















mSIMBOQ  Mean 













STD 
















MABLXT  Mean 













STD 
















MABLXV  Mean 













STD 
















MABLXQ  Mean 













STD 
















MASBXT  Mean 













STD 
















MASBXV  Mean 













STD 
















MASBXQ  Mean 













STD 













Comparison of the experimental results of algorithms used for dimension 30.
30D  F  Fsph  Fs2.22  Fs1.2  Fs2.21  Fros  Fste  Fqua  Fs2.26  Fras  Fack  Fgri  Fpen1  Fpen2 

GABLX  Mean 













STD 
















GASBX  Mean 













STD 
















SIMBOT  Mean 













STD 
















SIMBOV  Mean 













STD 
















SIMBOQ  Mean 













STD 
















mSIMBOT  Mean 













STD 
















mSIMBOV  Mean 













STD 
















mSIMBOQ  Mean 













STD 
















MABLXT  Mean 













STD 
















MABLXV  Mean 













STD 
















MABLXQ  Mean 













STD 
















MASBXT  Mean 













STD 
















MASBXV  Mean 













STD 
















MASBXQ  Mean 













STD 













Comparison of the experimental results of algorithms used for dimension 50.
50D  F  Fsph  Fs2.22  Fs1.2  Fs2.21  Fros  Fste  Fqua  Fs2.26  Fras  Fack  Fgri  Fpen1  Fpen2 

GABLX  Mean 













STD 
















GASBX  Mean 













STD 
















SIMBOT  Mean 













STD 
















SIMBOV  Mean 













STD 
















SIMBOQ  Mean 













STD 
















mSIMBOT  Mean 













STD 
















mSIMBOV  Mean 













STD 
















mSIMBOQ  Mean 













STD 
















MABLXT  Mean 













STD 
















MABLXV  Mean 













STD 
















MABLXQ  Mean 













STD 
















MASBXT  Mean 













STD 
















MASBXV  Mean 













STD 
















MASBXQ  Mean 













STD 













Comparison of the experimental results of algorithms using statistical test.
Fsph  Fs2.22  Fs1.2  Fs2.21  Fros  Fste  Fqua  Fs2.26  Fras  Fack  Fgri  Fpen1  Fpen2  

mSIMBOT versus SIMBOT  10D 





NA  NA 

NA 



NA  NA 
10D  SL = 0.05  0  1  0  1  —  —  0  —  1  1  1  —  —  
10D  SL = 0.01  0  1  0  0  —  —  0  —  1  1  1  —  —  
30D 





NA  NA 

NA 



NA  NA  
30D  SL = 0.05  1  0  1  1  —  —  0  —  1  0  1  —  —  
30D  SL = 0.01  1  0  1  1  —  —  0  —  1  0  1  —  —  
50D 





NA  NA 

NA 



NA  NA  
50D  SL = 0.05  1  1  1  1  —  —  0  —  1  1  1  —  —  
50D  SL = 0.01  1  0  1  1  —  —  0  —  1  1  1  —  —  


mSIMBOV versus SIMBOV  10D 





NA  NA 

NA 



NA  NA 
10D  SL = 0.05  1  1  1  1  —  —  0  —  1  1  0  —  —  
10D  SL = 0.01  1  1  0  1  —  —  0  —  1  1  0  —  —  
30D 





NA  NA 

NA 



NA  NA  
30D  SL = 0.05  0  1  1  0  —  —  0  —  0  0  1  —  —  
30D  SL = 0.01  0  0  1  0  —  —  0  —  0  0  0  —  —  
50D 





NA  NA 

NA 



NA  NA  
50D  SL = 0.05  1  1  1  1  —  —  0  —  0  1  1  —  —  
50D  SL = 0.01  0  1  0  1  —  —  0  —  0  0  1  —  —  


mSIMBOQ versus SIMBOQ  10D 





NA  NA 

NA 



NA  NA 
10D  SL = 0.05  1  0  0  1  —  —  0  —  0  1  1  —  —  
10D  SL = 0.01  1  0  0  1  —  —  0  —  0  1  0  —  —  
30D 





NA  NA 

NA 



NA  NA  
30D  SL = 0.05  0  0  1  1  —  —  0  —  1  1  1  —  —  
30D  SL = 0.01  0  0  1  1  —  —  0  —  0  1  1  —  —  
50D 





NA  NA 

NA 



NA  NA  
50D  SL = 0.05  1  1  1  1  —  —  0  —  0  1  1  —  —  
50D  SL = 0.01  1  1  0  1  —  —  0  —  0  1  1  —  — 
Comparison of the experimental results of algorithms used for dimension 02.
02D  F  F1  F2  F3  F4  F5  F6  F7  F8  F9  F10  F11  F12  F13 

GABLX  Mean 













STD 
















GASBX  Mean 













STD 
















MABLXT  Mean 













STD 
















MABLXV  Mean 













STD 
















MABLXQ  Mean 













STD 
















MASBXT  Mean 













STD 
















MASBXV  Mean 













STD 
















MASBXQ  Mean 













STD 
















02D  F  F14  F15  F16  F17  F18  F19  F20  F21  F22  F23  F24  F25  


GABLX  Mean 













STD 















GASBX  Mean 













STD 















MABLXT  Mean 













STD 















MABLXV  Mean 













STD 















MABLXQ  Mean 













STD 















MASBXT  Mean 













STD 















MASBXV  Mean 













STD 















MASBXQ  Mean 













STD 












Comparison of the experimental results of algorithms used for dimension 10.
10D  F  F1  F2  F3  F4  F5  F6  F7  F8  F9  F10  F11  F12  F13 

GABLX  Mean 













STD 
















GASBX  Mean 













STD 
















MABLXT  Mean 













STD 
















MABLXV  Mean 













STD 
















MABLXQ  Mean 













STD 
















MASBXT  Mean 













STD 
















MASBXV  Mean 













STD 
















MASBXQ  Mean 













STD 
















10D  F  F14  F15  F16  F17  F18  F19  F20  F21  F22  F23  F24  F25  


GABLX  Mean 













STD 















GASBX  Mean 













STD 















MABLXT  Mean 













STD 















MABLXV  Mean 













STD 















MABLXQ  Mean 













STD 















MASBXT  Mean 













STD 















MASBXV  Mean 













STD 















MASBXQ  Mean 













STD 












Comparison of the experimental results of algorithms using statistical test.
F  MABLX_T versus GABLX  MABLX_V versus GABLX  MABLX_Q versus GABLX  

02D  02D  02D  10D  10D  10D  02D  02D  02D  10D  10D  10D  02D  02D  02D  10D  10D  10D  

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01  
F1 

0  0 

1  1 

0  0 

1  1 

0  0 

1  1 
F2 

1  0 

0  0 

1  0 

1  1 

1  0 

1  1 
F3 

1  1 

1  1 

1  1 

1  0 

1  0 

1  1 
F4 

0  0 

1  1 

0  0 

1  0 

0  0 

1  1 
F5 

0  0 

1  1 

1  1 

1  1 

1  0 

1  1 
F6 

1  1 

0  0 

1  1 

0  0 

1  1 

0  0 
F7 

1  1 

0  0 

1  1 

1  1 

1  1 

1  1 
F8 

1  1 

1  1 

0  0 

0  0 

1  1 

0  0 
F9 

0  0 

1  1 

0  0 

1  1 

1  0 

1  1 
F10 

0  0 

1  1 

0  0 

1  1 

0  0 

1  1 
F11 

1  0 

1  1 

0  0 

1  1 

0  0 

1  1 
F12 

1  0 

1  1 

1  1 

1  1 

0  0 

1  1 
F13 

0  0 

0  0 

0  0 

1  1 

1  0 

0  0 
F14 

0  0 

1  1 

0  0 

1  1 

1  0 

1  1 
F15 

0  0 

0  0 

1  0 

1  1 

0  0 

1  1 
F16 

0  0 

0  0 

1  1 

1  1 

1  1 

0  0 
F17 

0  0 

1  1 

0  0 

1  1 

0  0 

1  1 
F18 

1  1 

0  0 

1  0 

1  1 

1  1 

0  0 
F19 

0  0 

0  0 

1  0 

0  0 

1  0 

1  0 
F20 

1  1 

0  0 

1  1 

0  0 

0  0 

0  0 
F21 

1  1 

1  0 

0  0 

1  0 

0  0 

0  0 
F22 

0  0 

0  0 

1  0 

1  1 

1  1 

0  0 
F23 

1  0 

0  0 

0  0 

0  0 

1  0 

0  0 
F24 

1  1 

1  1 

0  0 

1  0 

0  0 

0  0 
F25 

1  0 

0  0 

0  0 

1  1 

0  0 

1  1 
Comparison of the experimental results of algorithms using statistical test.
F  MASBX_T versus GASBX  MASBX_V versus GASBX  MASBX_Q versus GASBX  

02D  02D  02D  10D  10D  10D  02D  02D  02D  10D  10D  10D  02D  02D  02D  10D  10D  10D  

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01 

SL = 0.05  SL = 0.01  
F1 

0  0 

1  1 

0  0 

1  0 

0  0 

0  0 
F2 

0  0 

1  0 

0  0 

1  1 

1  1 

0  0 
F3 

0  0 

1  1 

0  0 

1  1 

0  0 

1  1 
F4 

0  0 

0  0 

0  0 

0  0 

0  0 

0  0 
F5 

1  1 

0  0 

1  0 

0  0 

1  1 

0  0 
F6 

0  0 

0  0 

0  0 

0  0 

1  0 

0  0 
F7 

1  1 

1  1 

1  1 

1  0 

0  0 

1  1 
F8 

1  1 

1  0 

1  1 

1  1 

1  1 

1  1 
F9 

0  0 

1  1 

0  0 

1  1 

0  0 

1  1 
F10 

0  0 

0  0 

0  0 

1  1 

0  0 

1  1 
F11 

0  0 

0  0 

0  0 

1  1 

0  0 

0  0 
F12 

1  0 

0  0 

1  1 

0  0 

1  0 

0  0 
F13 

1  1 

1  1 

1  1 

0  0 

1  1 

1  1 
F14 

0  0 

1  1 

1  1 

1  1 

1  0 

1  1 
F15 

0  0 

0  0 

0  0 

0  0 

0  0 

0  0 
F16 

1  0 

0  0 

1  1 

1  1 

0  0 

1  0 
F17 

1  0 

1  0 

1  1 

1  1 

1  1 

0  0 
F18 

1  1 

0  0 

1  0 

0  0 

0  0 

0  0 
F19 

1  1 

0  0 

0  0 

0  0 

0  0 

0  0 
F20 

1  1 

1  1 

1  0 

0  0 

1  1 

0  0 
F21 

0  0 

1  0 

1  0 

0  0 

0  0 

1  0 
F22 

1  1 

0  0 

0  0 

0  0 

1  1 

0  0 
F23 

0  0 

1  1 

1  0 

1  1 

1  1 

1  1 
F24 

0  0 

0  0 

0  0 

1  1 

0  0 

1  1 
F25 

0  0 

0  0 

0  0 

0  0 

0  0 

0  0 
The algorithms are tested using two sets of standard benchmark functions, namely,
The algorithms are tested on wellknown basic standard benchmark functions having unimodal, multimodal properties with noise and discontinuity. Functions Fsph (sphere model), Fs2.22 (Schwefel’s problem 2.22), Fs1.2 (Schwefel’s problem 1.2), Fs2.21 (Schwefel’s problem 2.21), and Fros (generalized Rosenbrock’s function) are functions having unimodal property. Function Fste (step function) is step function, which has one minimum and which is discontinuous function. Function Fqua (quartic function) is a noisy quartic function comprising of random [0, 1) which is a uniformly distributed random variable in [0, 1). Functions Fs2.26 (generalized Schwefel’s problem 2.26), Fras (generalized Rastrigin problem), Fack (Ackley’s function), Fgri (generalized Griewank function), Fpen1 (generalized penalized function no. 1), and Fpen2 (generalized penalized function no. 2) are multimodal functions in which the number of local minima increases exponentially with the problem dimension [
From Tables
As seen from Figures
Fitness error versus number of function evaluation calls of test functions averaged over 25 runs in cases of SIMBOs and mSIMBOs for functions (a) Fs2.22, (b) Fack.
Fitness error versus number of function evaluation calls of test functions averaged over 25 runs in cases of GAs, mSIMBOs, and MAs for functions (a) Fsph, (b) Fros, (c) Fgri, and (d) Fpen2.
A statistical test, Student’s
There are various types of optimization algorithms available and used to solve realparameter function optimization problems. There is a variety of mechanisms having variations in their operators and working principles. Catering to the need of evaluating the algorithms in a more systematic manner by specifying a common termination criterion, size of problems, initialization scheme, linkages/rotation, and so forth, the CEC 2005 having 25 test problems is designed [
All functions are nonseparable and scalable except F1 and F9, which are separable, whereas F15 is separable near the global optimum (Rastrigin). The functions in the test suit are shifted and rotated. Functions F1–F5 are unimodal and functions F6–F25 are multimodal in which F6–F12 are single functions, F13F14, are expanded functions and F15–F25 are hybrid composition functions. Functions F9, F10, and F15–F25 have a huge number of local optima in their fitness landscape. In functions F15–F25, different function’s properties are mixed together to make hybrid composition functions. Functions F4 and F17 have Gaussian noise in fitness and they are similar to functions F2 and F16, respectively. Functions F15–F20 have effect due to sphere functions giving two flat areas for the function and functions F24F25 have effect due to unimodal functions giving flat areas for the function. Functions F18–F20 have a local optimum and are set on the origin. Functions F8, F20, F22F23, and F25 have Global optimum on the bound. For the performance evaluation, the function error, NFFEs, and convergence graphs for the problems are used [
From Tables
As per Figures
Fitness error versus number of function evaluation calls of test functions averaged over 25 runs in cases of MAs for functions (a) F1, (b) F5, (c) F9, and (d) F15.
When the statistical test, Student’s
The LMSbased adaptive filter having a length
Adaptive filter structure.
The stochastic optimization with proposed MAs is used to search for the optimum filter weight vector giving error. In this case to remove the noise from the ECG signal, the ECG signal
As the signal and noise are uncorrelated, then mean squared error (MSE) becomes:
The ECG contaminated by the artificial PLI with 50 Hz frequency is put forward for the PLI removal, to the LMS adaptive filter for its weights optimization by the MA using fitness function articulated in (
Mean square error  MSEor is between original and recovered ECG signal; MSEoc is between original and corrupted ECG signal by power line interference (PLI).
Record No.  MSEoc  MSEor 

sel123 


sel123 


100m 


100m 


118e00m 


118e00m 


Frequency spectrum of the ECG signal (a) having power line interference (PLI) at 50 Hz and (b) after filtering with MAbased LMS adaptive filter.
ECG—(a) corrupted by power line interference (PLI) of 50 Hz and (b) recovered.
The Swine Influenza ModelBased Optimization (SIMBO) is a faster optimization technique having the adaptive nature in its process. With the help of the threefold modifications, the algorithm is made still faster in this work. The SIMBO family is very good in searching the basin under consideration, so it is utilized in local searches to develop the memetic algorithms (MAs). The SIMBO family has high pressure in the direction of origin and hence demonstrates better results in noisy function also. But this makes it weak in case of an other type of the solution that requires more explorations. This is achieved with help of MA having balance in exploration and exploitation. So, MAs have little tradeoffs in convergence speed but are more comprehensive in solving the numerical standard benchmark test bed of functions having the different properties. The modifications in SIMBO and application of it as the local searchers in making MAs as a process exploit the properties of both the algorithms to enhance the efficiency. The ensemble strategy to tune parameters and operators can be useful to develop further the more adaptive techniques.
The developed MA is also applied to remove the power line interference (PLI) from the biomedical signal ECG with the help of adaptive filter whose weights are optimized by the MA. In this, the adaptive filter inference signal is generated with the selective reconstruction of ECG from the intrinsic mode functions (IMFs) of empirical mode decomposition (EMD). The adaptive filter with the help of the optimized weights filters the PLI from ECG effectively with reduced error (mean square error (MSE)).
The authors declare that there is no conflict of interests regarding the publication of this paper.