In industrial automation around 97% of control loops are PID and among the PID tuning methods, the most preferable are manual model free tuning such as IMC, Adaptive ^{1}. But Control engineers prefer simple tuning methods based on tuning rules ^{2} and bump test. Some of the popular PID tuning procedures are Closed loop procedure called ZN, Open loop procedure called Process reaction curve, gain and phase margin method, tuning rule based on frequency domain values , direct synthesis method etc.
Though there are various tuning methods, industry always thrive for optimized solutions. History reveals us that when it comes for optimization, trial and error (heuristic and metaheuristic) plays an important role. The optimization approach starts form Genetic Algorithm (GA) in which the solution is obtained through mutation and crossover. The next one is simulated annealing, a trajectory based algorithm, single agent algorithm, which is based on annealing of metals and used in finding the solution to traveling salesman problem. Multiple agentbased algorithms like Particle swarm optimization (PSO), Ant colony optimization and Artificial Bee Colony (ABC)^{]} are proposed by various researchers in course of time. Number of optimization algorithms come into exist like Cuckoo search (CS)
FA is more efficient than other algorithms because of its local search is superior to global search, lesser probability for premature convergence and adaptability to any search space through its parameter γ ^{7}. Among the optimization problems solved by FA, Industrial optimization tops the list ^{7}. Therefore, FA has been considered as a best solution provider for our industrial process. From ^{8, 9, 10, 11} it is evident that FA will aid in solving numerous problems viz banking, packaging, structural topology, industrial vibration etc., . The FA can be broadly classified into two categories, one is parameter control altering the algorithm parameter during algorithm’s run ^{12} and parameter tuning fixing the algorithm’s parameter well before the run ^{13}. Parameter Control method has been considered for the industrial process which is a stable and unstable bioreactor.
The sections of the paper are as follows. In Section 2 FA and its Variants have been discussed. In Section 3 proposed algorithm (SSMFAN) has been discussed. In section 4 results have been shown and reviewed. In section 5 conclusions have been drawn from the results.
Yang, in the year 2008, developed firefly algorithm that entirely depends on the behaviour of fireflies and their flashing patterns ^{6}. FA is a populationbased metaheuristic and a search algorithm. Each and every firefly in the population is a solution in the respective search space. The firefly tends to move towards the brighter firefly and the brightness is measured by the fitness functions in the search space. Let X_{i }and X_{j}_{ }be the firefly in the given search space. Here i=1, 2N; j=1, 2N. The attractiveness between the two is given by the following equation ^{6}.
Where
In the above equation (2) x_{it} is the t^{th} dimension of X_{i }and x_{jt} is the t^{th} dimension of X_{j}_{ }.
The brightness of X_{i }and X_{j} (j=1,2N and j≠i) are compared and if the brightness of Xj is greater than Xi then _{ }X_{i } is updated as ^{13}_{ }
where
Initialization of the population as general random solution through the equation (4)
Each solution in FA is obtained after comparing each X_{i (}where i=1,2N) with all the other X_{j}_{ }(where j=1,2, N and j ≠ i ) in the considered initial population. The solutions are based on the objective functions which are the fitness functions here. Henceforth, the attraction (displacement) is based on the objective functions and if the fitness values (solutions) of X_{j}_{ }is better than X_{i} then the solution of X_{i }gets updated by equation (3).
The entire process gets repeated until the stopping criteria is reached.
In ^{14} redefined the attractiveness (β) and the step size (α) of firefly in Memetic FA (MFA). In MFA the step size was adapted as per equation (6) and the firefly has been updated by eq. (5).
Where s is the length of the variable;
In ^{15} has designed an enhanced FA for steel frames in which he had replaced the distance between the fireflies with normalized distances, thereby defining a set of new equations for attractiveness, step size or randomness (α) and absorption coefficient (
and
Similarly, for the randomness or step size (α)
In ^{16} a wise strategy was proposed in which the randomness or step size had been updated with the local best (p_{best}) and global best firefly (g_{best}). In ^{17} the randomness or step size had been updated with the increasing generations. In ^{18} analysed and stated that the performance of FA mainly depends on the parameters such as brightness
In ^{19} applied FA for structural problems such as pressure vessel design, helical compression beam design, concrete beam design, cantilever beam design etc., in ^{20} applied FA in solving queuing system problems in communications, transportation networks, computer systems and manufacturing. In ^{21} did a comparative study between FA and bees algorithm, by finding the optimal solutions for continuous mathematical functions. Both in FA and a hybrid approach called FAPSO, the convergence is modified by updating the brightness alone ^{22}. As per the results it was concluded that FA had outperformed bees optimization. In ^{7} Fister et al had done a comprehensive review of FA and in that it was stated that FA was one of the most crucial technology for solving engineering problems. In addition to that it was observed that industrial optimization had topped the list of engineering areas in which FA had been used as a tool. It was also observed that Image Processing had occupied second in the list.
In FA, each and every firefly gets attracted towards the brightest one and ultimately optimal solutions are obtained. However, this sort of attraction is complex and timeconsuming. In ^{23} proposed a FA based new algorithm called FA with neighbourhood attraction (NaFA). In NAFA the brightness is updated by comparing X_{i} with X_{j}. In the comparison, instead of comparing with all the fireflies the brightness is compared with only the neighbourhood fireflies. Here j is taken as ik…k…..i+k and k << N. Also in NaFA, The parameter, step size has been updated using eq. (6) and each firefly is updated using eq. (5). Use of NaFA greatly reduces the computational time and oscillations in the optimization strategy. In the proposed algorithm the brightness is compared and updated as per NaFA and the step size (α) is updated by the following equation
Where the range of
The algorithm steps are as follows:
The initial population is considered and the solutions for each firefly is calculated for the specified objective function.
The parameter, step size has been updated using eq (6) and each firefly is updated using eq (5).
The brightness of Xi is compared with Xj where i=1, 2…. N; j= ik,….. i…..i+k and most importantly i≠j. if j<1 or j > N then j will be (j+N)%N. The solution of Xi is compared with Xj and if Xj > Xi then Xi will be updated by eq. (5).
Repeat the brightness updation till the stopping criteria is satisfied.
1. 
Initialize the population of Firefly 

2. 
Evaluate the brightness or solution by using objective functions. 

3. 
For iterations 1 to max.no of iterations 

4. 

For i =1,2N 

5. 


For j=ik,ki+k 

6. 



if j≠i then j=mod(j,N) 

7. 




if light(i) < light(j) 

8. 





update step size(α) using eq(11) 

9. 





update the solution using eq(12) 

10. 




end 

11. 



end 

12. 


end 

13. 

end 

14. 
end 
The proposed algorithm is run with 50 fireflies. The examples which are considered here are made to run in MATLAB 2013A and Simulink window with the sampling time as 0.01. The proposed algorithm (SSMFAN) has been compared with a conventional approach and an optimization approach. The objective functions considered here are PO and ITAE. It is obvious that for the continuous process the emphasis must be on steady state. Among the performance indices ITAE provides more weightage to the end of the process and PO provides more weightage to the error in the start of the process. In all the examples considered the SSMFAN is compared in terms of time domain specifications and performance indices. The processes considered here are first tuned with the conventional approaches like ZN ^{24}, HuangChen ^{25} ABB ^{26} and with an optimization approach (PSO). While running SSMFAN the minimum value and maximum value of the brightness are 0.4 and 1.0 respectively. The minimum and maximum value of the step size is 0.2 and 1.0 respectively. The adsorption coefficient is 1.0.
The example that is taken into account is a First order Plus Dead time (FOPDT) process. It has been compared with the conventional ZN method discussed in ^{24} and with the optimization method. In ^{24} discussed the conventional method called ZN method and furthermore he had shown the PID parameters as k_{p}=0.91, k_{i}=0.3309 and k_{d}=0.6188. For the optimization approach, PSO has been considered among the metaheuristic algorithms for analysis. From
Process 
Tuning Methods 
Tuning Parameters 
IAE 
ISE 
ITAE 
t_{r} 
t_{p} 
t_{s} 
PO 

ZN10% reduction in gain of the process 

3.8943 
2.8570 
13.8437 
149.1726 
474 
1605.2 
1.15 
ZNNo Change in the gain of the process 
4.3572 
2.7256 
19.5304 
128.7 
463 
2139 
1.26 

ZN10% increase in gain of the process 
5.1992 
2.9324 
31.5775 
112.95 
455 
2731.7 
1.37 

PSO10% reduction in gain of the process 

3.7795 
2.8205 
10.0708 
198.27 
609 
1221.5 
1.17 

PSONo Change 
4.0274 
2.8244 
12.7450 
174.811 
582 
1527 
1.26 

PSO10% increase in gain of the process 
4.3925 
2.8911 
16.7504 
157.0017 
562 
1819.5 
1.34 

SSMFAN 10% reduction in gain of the process 

3.5676 
2.8132 
8.4470 
238.8771 
598 
1163 
1.00 

SSMFAN No Change 
3.4750 
2.7251 
8.1167 
198.07 
568 
1123 
1.07 

SSMFAN 10% increase in gain of the process 
3.5960 
2.6859 
9.4954 
174.14 
546 
1101.4 
1.15 
The second process that is taken into account is a stable bioreactor process. It has been compared with the conventional method proposed by ABB which was discussed by ^{26} for less ITAE. The approach had been discussed in ^{26} and it was followed for less ITAE in Industries. The PID parameters for the stable bioreactor process have been found by using the method (ABB) shown in ^{26}. For the optimization approach, PSO has been considered for analysis. The robustness has been checked by increasing and decreasing the process gain by 10 percentage. From
Process 
Tuning Methods 
Tuning Parameters 
IAE 
ISE 
ITAE 
t_{r} 
t_{p} 
t_{s} 
PO 

ABB10% reduction in gain of the process 

2.34 
1.35 
4.59 
435 
 
785 
1.0 
ABBNo Change in the gain of the process 
2.11 
1.24 
3.64 
384 
 
690 
1.0 

ABB10% increase in gain of the process 
1.91 
1.14 
2.94 
343 
 
611 
1.0 

PSO10% reduction in gain of the process 

0.96 
0.56 
0.75 
177 
 
311 
1.0 

PSONo Change 
0.87 
0.52 
0.59 
157 
 
273 
1.0 

PSO10% increase in gain of the process 
0.79 
0.48 
0.48 
141 
 
242 
1.0 

SSMFAN 10% reduction in gain of the process 

0.29 
0.18 
0.11 
22 
 
165 
1.0 

SSMFAN No Change 
0.26 
0.17 
0.10 
17 
 
151 
1.0 

SSMFAN 10% increase in gain of the process 
0.24 
0.16 
0.08 
14 
 
138 
1.0 
The example that is taken into account is unstable Bioreactor. SSMFAN is compared with the conventional method proposed by ^{25} and optimization approach PSO. In ^{25} proposed the tuning procedure for unstable systems and revealed the PID parameters for the process as k_{p}=0.4498,
Process 
Tuning Methods 
Tuning Parameters 
IAE 
ISE 
ITAE 
t_{r} 
t_{p} 
t_{s} 
PO 

HC10% reduction in gain of the process 

17 
7.4 
356 
271 
1239 
6414 
1.6 
HCNo Change in the gain of the process 
16 
5.8 
334 
254 
1136 
6713 
1.5 

HC10% increase in gain of the process 
14 
4.7 
313 
240 
1051 
6832 
1.5 

PSO10% reduction in gain of the process 

3.3 
1.4 
16.3 
142 
447 
1583 
1.5 

PSONo Change 
2.9 
1.2 
12.5 
132 
415 
1478 
1.4 

PSO10% increase in gain of the process 
2.6 
1.0 
9.3 
123 
388 
1369 
1.4 

SSMFAN 10% reduction in gain of the process 

0.4 
0.18 
0.44 
15.5 
58 
338 
1.15 

SSMFAN No Change 
0.4 
0.18 
0.41 
13.4 
45 
324 
1.15 

SSMFAN 10% increase in gain of the process 
0.39 
0.17 
0.37 
11.8 
38 
312 
1.18 
From the examples considered and the tables 1 to 3 and figures 1 to 9 obtained it is well understood that the proposed SSMFAN outperforms the conventional approaches and the optimization approach (PSO) in both the time domain specifications and performance indices. Both the servo and regulatory responses of SSMFAN exceeds the performance of other two methods. The robustness has also been checked and the SSMFAN is more robust than the other two approaches. Though the objective function is PO and ITAE, all the obtained time domain specifications and performance indices are less for SSMFAN on comparing with the conventional method and the optimization method. In SSMFAN, when comparing with the optimization approach (PSO), the examined objective functions such as PO and ITAE has been truncated to 7% and 41.56% from 26% and 65.23 % respectively for FOPDT process. With respect to the optimization approach, in the stable bioreactor process, there is no PO and ITAE has been reduced to 2.7 % from 16.2%. Finally, with reference to PSO, in the unstable process, the PO and ITAE has been diminished to 15% and 0.1% form 40% and 3.74 % respectively. The step size is modified with the other FA models also. Thus, with the parameter tuning of step size the balance between the local and global search has been achieved here within 5 iterations. The updating parameters must be dynamic in nature and this requires mathematical analysis of computational algorithms. Similarly, the balance between exploration and exploitation can also be attained by varying the adsorption coefficient and combining it with the brightness tuning. The results can also be refined by adapting hybrid approaches.