I observed that some algorithms obtained very small fitness values of the given optimization problems like 10^-150. and some of proposed methods obtained 10^-190. They are very small numbers. What is the significant difference between 10^-150 and 10^-190.
If you are trying to minimize the objective function, the lower is the better. However, besides the lower fitness value obtained, some other parameters need to be checked before coming to a conclusion. These include - run time for convergence, average fitness value achieved for multiple runs, etc. Moreover, one might also conduct standard statistical tests to strengthen his/her findings.
In your question, if it is a minimization problem then 10^-190 is far better than 10^-150.
For a minimization problem, the smallest is always preferable. Coming to your question, during the modeling stage, you may have modeled the cost in 10^10 dollars, for example if you are considering a huge investment, (i.e. x=1 is equivalent to 10^10 dollars) in that case there is a 'signification' difference between solution 10^10 and 10^09. However, if the variables are representing for example meters for a portfolio problem of buying a land for investment, such kind of variation on the variable can be negligible. Hence, in general the significance of the solution for a small change depends on the nature of the problem. In addition, in most cases, that is also subjective.
The other issue of getting better approximate solution needs fine-tune of the algorithm with sifficinet computational resource (memory, run time etc). Hence, getting best approximate is computationally expensive (needs more time ...) and hence based on the problem you need to decide to what extent you need to apply the metaheuristic algorithm.
Hope this helps.
Very small values of fitness in metaheuristics represents that the values of control variable is very close to its optimum values and thus the values of objective function is also very close to its optimum value.
you should perform a proper statistical test to detect significant differences between the compared algorithms, to read more about this fact, you can check the following reference:
Derrac, J., García, S., Molina, D., & Herrera, F. (2011). A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm and Evolutionary Computation, 1(1), 3-18.
The quality-measures or as so-called fitness functions, objective functions, or goodness levels are quantifiable and revolve around maximizing some desired features and/or minimizing the undesirable ones until a predefined optimization goal is achieved [6]. Generally speaking, When the fitness values are small, it means that the values of the control variable are close enough to its optimum solutions. This means that the goodness levels are high; this is unfortunately at the expense of time.
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