All metaheuristic algorithms are not cent per cent analogous to its inspired one. While converting a thought into programming we need to do many assumptions. In these assumptions some actual processes are missed and some artificial logical processes are added to ease of programming. But the main process remains very close to its inspired one.

That's why, the main process of genetic algorithm is very similar to biological evolution but some process are not similar to biological one.

My answer for your question is : yes

Hope you get the answer.

refer no free lunch theorem for getting answer to your question

Genetic Algorithms were invented to mimic some of the processes observed in natural evolution. Many people, biologists included, are astonished that life at the level of complexity that we observe could have evolved in the relatively short time suggested by the fossil record. The idea with GA is to use this power of evolution to solve optimization problems. The father of the original Genetic Algorithm was John Holland who invented it in the early 1970's.

GAs are adaptive heuristic search algorithm based on the evolutionary ideas of natural selection and genetics. As such they represent an intelligent exploitation of a random search used to solve optimization problems. Although randomised, GAs are by no means random, instead they exploit historical information to direct the search into the region of better performance within the search space. The basic techniques of the GAs are designed to simulate processes in natural systems necessary for evolution, specially those follow the principles first laid down by Charles Darwin of "survival of the fittest.". Since in nature, competition among individuals for scanty resources results in the fittest individuals dominating over the weaker ones.

Why Genetic Algorithms?

It is better than conventional AI in that it is more robust. Unlike older AI systems, they do not break easily even if the inputs changed slightly, or in the presence of reasonable noise. Also, in searching a large state-space, multi-modal state-space, or n-dimensional surface, a genetic algorithm may offer significant benefits over more typical search of optimization techniques. (linear programming, heuristic, depth-first, breath-first, and praxis.) ...

Mathematics is must for every research activity as u know all the evolutionary algorithms have a deep bath with Operation Research

Yes, they are worth to use.

Genetic Algorithms (GA) can achieve high quality solutions in a reasonable time, lower  time than exact methods. Also are easy to understand and to implemment. A wide variety of problems have been solved thanks to GA or at least have a high quality solutions.

Genetic algorithms has many variations, you can tailor cut an algorithm to your specific need, depending on randomness it can converges rapidly towards a sound and optimum solution in considerably minimum time. it is like saying everything happening for a reason and seeing order emerging out of chaos, implement it then plot it and you see what I mean.

hope it helps

best regards and keep up the good work

GAs are very usefull when you are dealing with a complex problem (a black box problem) that does not have a close analytical form... A GA is a global optimization technique. So, the solution returned by a GA is usually near optimal especially when the problem being solved is multi-modal. GAs are also used in solving combinatorial problems...

Find in attachment a real-world world problem solved with a Real-Coded Genetic Algorithm.

Conference Paper Genetic Optimization of the Multi-Location Transshipment Pro...

I feel 'mathematically not logical' is not apporpriate for GAs.

GAs are to solve complex problems especially with undeterministic data / situations. All most all Machine Learning apporaches including deep learning adopted GA methods for optimization. The ability of GAs to tackle problems especially multi objective problems made them more popular.

GA (EC in general) work, then worth it.

For specific optimization problems and problem instances, other optimization algorithms may be more efficient than genetic algorithms in terms of speed of convergence. Alternative and complementary algorithms include evolution strategies, evolutionary programming, simulated annealing, Gaussian adaptation, hill climbing, and swarm intelligence (e.g.: ant colony optimization, particle swarm optimization) and methods based on integer linear programming. 

You will find this interesting. 

GAs, like all optimization algorithms, are not useful by themselves, it depends on the problem and what you know of it. 

First, GAs, like most evolutionary algorithms, are quite general and easy to use, this means that you can use them on most combinatorial optimization problems, this is particularly useful when you lak a deep understanding of the problem. In many cases if you have a deep understanding of the problem, you might find much more efficient and exact algorithms. Nevertheless, since a GA is a very high-level algorithm,it is easy to embed domain knowledge into the design of your GA and/or combine it with other local search strategies (GA is a global searcher) , these strategies can be surprisingly competitive with traditional approaches on many real-world and difficult problems.

Genetic Algorithms (more generally, Evolutionary Computing) works!!! ... and we have a huge body of literature testifying on this!!!

At least, it works in getting a very good solution.

More so,it works in getting a, hopefully diverse, set of high quality solutions (which may not be theoretical optimal but may prove more useful in practice). A diverse set of good quality (near theoretical optimal, which not be verified readily) is something we managers/practitioners are always looking for. The reason is that all our problems are formulated under certain assumptions (some of them may not even be explicit or known to us). When we have potential solutions form our optimizer, we want to adopt the one which seems to work under the practical constraints (which may have been ignored or not present at the time of problem formulation).

One may also want to look at "automata theory" for theoretical proof of "GA works".

Genetic Algorithms is one of my favorite fields. No, they won't be exact nor follow a single representation. They instead use your skills to abstract the situation and present data in your probably own way. You can see the statistical studies on why GAs work, or just implement a few examples to see they worth it.. But again, it depends on your needs. There will be problems for wich you don't need a Genetic Algorithm. But I hope you do need them. Only your results will focus your incipient GAs knowledge on the boundaries they act within.

Please give applications of genetic algorithms to control systems.

If we put keywords "control systems" and "genetic algorithms" in Scopus, it give us 261 papers in 2015 and 489 in 2014. Here are the first twenty records (by date):

Variable step size modified P&O MPPT algorithm using GA-based hybrid offline/online PID controller. Harrag, A., Messalti, S.Renewable and Sustainable Energy Reviews

Prediction of RCF and wear evolution of iron-ore locomotive wheels. Hossein Nia, S., Casanueva, C., Stichel, S. Wear

Process simulation and dynamic control for marine oily wastewater treatment using UV irradiation. Jing, L., Chen, B., Zhang, B., Li, P.. Water Research

A bio-inspired adaptive control compensation system for an aircraft outside bounds of nominal design. Perez, A.E., Moncayo, H., Perhinschi, M., Al Azzawi, D., Togayev, A. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Teaching-learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system. Sahu, B.K., Pati, S., Mohanty, P.K., Panda, S. Applied Soft Computing Journal

Method for estimating parameters of practical ship manoeuvring models based on the combination of RANSE computations and System Identification. Bonci, M., Viviani, M., Broglia, R., Dubbioso, G. Applied Ocean Research

ACCPndn: Adaptive Congestion Control Protocol in Named Data Networking by learning capacities using optimized Time-Lagged Feedforward Neural Network. Karami, A.Journal of Network and Computer Applications.

Theoretical Analysis and Experimental Validation of a Simplified Fractional Order Controller for a Magnetic Levitation System. Folea, S., Muresan, C. I., De Keyser, R., Ionescu, C. M. IEEE Transactions on Control Systems Technology

Friction coefficient estimation in servo systems using neural dynamic programming inspired particle swarm search. Lu, Y., Yan, D., Levy, D. Applied Intelligence

Self-adjusting focus of attention in combination with a genetic fuzzy system for improving a laser environment control device system. Clemente, E., Chavez, F., Fernandez De Vega, F., Olague, G. Applied Soft Computing Journal

Embedding linear programming in multi objective genetic algorithms for reducing the size of the search space with application to leakage minimization in water distribution networks. Creaco, E., Pezzinga, G. Environmental Modelling and Software

Evolutionary algorithm enhancement for model predictive control and real-time decision support. Zimmer, A., Schmidt, A., Ostfeld, A., Minsker, B. Environmental Modelling and Software

SEMG-based prediction of masticatory kinematics in rhythmic clenching movements. Kalani, H., Moghimi, S., Akbarzadeh, A. Biomedical Signal Processing and Control

Experimental Implementation of Optimal Control of an Improved Single-Column Chromatographic Process for the Separation of Enantiomers. Medi, B., Monzure-Khoda, K., Amanullah, M. Industrial and Engineering Chemistry Research

The design of a non-minimal state space fractional-order predictive functional controller for fractional systems of arbitrary order. Bigdeli, N. Journal of Process Control

TLBO optimized sliding mode controller for multi-area multi-source nonlinear interconnected AGC system. Mohanty, B. International Journal of Electrical Power and Energy Systems

Inventory control in a centralized distribution network using genetic algorithms: A case study. Çelebi, D. Computers and Industrial Engineering

An Evolutionary Radial Basis Function Neural Network with Robust Genetic-Based Immunecomputing for Online Tracking Control of Autonomous Robots. Huang, H.-C., Chiang, C.-H. Neural Processing Letters

Optimization algorithms in scheduling problems of the rail transport. Kuznetsov, N.A., Pashchenko, F.F., Ryabykh, N.G., Zakharova, E.M., Minashina, I.K. Journal of Communications Technology and Electronics

Development of an Optimization/Simulation Model for Real-Time Flood-Control Operation of River-Reservoirs Systems. Che, D., Mays, L.W. Water Resources Management

Please refer to these articles:

https://www.researchgate.net/publication/313576646_From_PID_to_Nonlinear_State_Error_Feedback_Controller

https://www.researchgate.net/publication/312046377_Improved_Sliding_Mode_Nonlinear_Extended_State_Observer_based_Active_Disturbance_Rejection_Control_for_Uncertain_Systems_with_Unknown_Total_Disturbance

https://www.researchgate.net/publication/309655805_On_the_Improved_Nonlinear_Tracking_Differentiator_based_Nonlinear_PID_Controller_Design

Article From PID to Nonlinear State Error Feedback Controller

Article Improved Sliding Mode Nonlinear Extended State Observer base...

Article On the Improved Nonlinear Tracking Differentiator based Nonl...