If you use a combined method, answer to you question depends on what you call objective functio value. In one hand, the computational complexity of the whole algorithm depends o rhe quantity of calculations of your original objective function. Usually, in scientific papers, if someone writes 'number of obj. function calculanions' they mean the total quantity of them. In the other hand, there are at least 2 ways of joining the  metaheuristic with local search. In the 1st case, the objective (fitness) function of the metaheuristic is the result of the local search procedure (local search gives the result to your metaheuristic). In this case, there must be probably no calculations of the original objective function within the main body of the metaheuristic: all calculations must be within local search. Of course, the metric must be "number of local search starts" or "obj. function calculations" (calculations in local search procedure). The 2nd way is when the metaheuristic initially works without local search at each iteration, then some results are passed to the local search procedure. In this case, author must clearly indicate how this metric was used.

In any case, if this metric is used to show the computational complexity of the algorithm, it is always better to use the total number f the obj. f. calculations.

Yes, Number of function evaluations (NFEs) should include both metaheuristics and local search calls to objective function.

A good and highly cited  reference on memetic algorithms is 

Noman, N., & Iba, H. (2008). Accelerating differential evolution using an adaptive local search. Evolutionary Computation, IEEE Transactions on, 12(1), 107-125.

http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4358768&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4358768

Article Iba, H.: Accelerating differential evolution using an adapti...

You need to assign a large limit for number of function evaluations then in your algorithm you can define the stopping criterion. If it is not progressing then stop. 

Dear Ehsan

It seems reasonable that both algorithms in hybrid approach should be included NEF since you want to know which algorithm is better than others regarding NFE and CPU Time.

For a fair, meaningful comparison, you should include all the function evaluations, be it in the main algorithm or in the local search. If you are using a metaheuristics method COMBINED with a local search method, then what you are actually evaluating is a hybrid method. It would be unfair to leave out the local search phase when comparing among methods. Even if you want to compare several metaheuristics that use the same local method (I don't know if this is the case), it is up to the main (metaheuristics) algorithm to decide when to launch a local search, or at least to decide the starting point of the local search. Hence the subsequent number of evaluations in the local search can be dependent upon the metaheuristics, and therefore it should be taken into account when comparing.

That being said, it is a good practice to also compare the CPU time, not only the number of function evaluations, since the computational overhead (computation time not spent in function evaluations, but in inner calculations of the algorithm) can vary between methods and there may be significant differences. What the user is really interested in is usually the real, wall-clock time time that the whole computations are goind to need.

each time you refer to objective function must be included in enumeration of NFE . It is not important  this calling is performed in the main structure of algorithm or in local search phase. You use this local search method  to improve your solutions and hence this is a part of your algorithm and for fair comparison number of function evaluation in local search phase must be enumerated . 

If you combined two and or more metaheuristic algorithms in order to solve your specific problem, It would be better to comput the related objective function for each algorithm seprately and also for combined algorithm. In this connection, you can demonstrate combining of these algorithms for your problem is effectively reasonable or not. 

Hi Ehsan,

Anyhow the local search is used to find an initial solution for metaheuristic or vice versa, the output of the metaheuristic is used for starting a local search, you should consider the proposed two sections as a hybrid algorithm. So the number of function evaluations in both sections must be calculated. 

Also, an important controllable parameter in this hybrid algorithms is to determine the optimal portion of each phase in a total maximum elapsed time of the whole algorithm.

every time you use the objective function is must be counted as an evaluation it is as simple as that.

Offcourse, the local searches should be taken into account.

of course, once the function evaluation has been executed, the evaluation number should increase.

Simplest way is to add counter in Matlab for each of objective function calculation.

I have another Q..

https://www.researchgate.net/post/Why_does_Function_Evaluations_number_significant_for_the_superiority_of_an_optimization_algorithm

How can we calculate the number of function evaluations of genetic algorithm?

All the answers are great

As far as I know, the number of function evaluation of genetic algorithm can be calculated through following equation:

Number of function evaluations = Number of main population + [number of new children(from cross over) + number of mututed children(from mutation)] * number of itteration.

Save yourself the headache of numerically estimating such a value and just add an iterational counter for every time the objective function is calculated.

As for whether to include the evaluations conducted during local search, the answer is yes. Seeing as how this "local search" mechanism is incorporated into the inner workings of the algorithm, it's only logical to add the functional evaluations produced by this modification for a more wholesome algorithmic comparison process.