This is the peculiarity of Genetic Algorithm, in fact, of every evolutionary algorithm. These algorithms are designed for those problems which can not be solved otherwise or it takes more than acceptable time to solve. These solutions are near optimal solutions. Optimum solution may be unique if no other identical solution exists. But near optimum solutions are plenty.

Of course, by varying the parameters of the algorithm, such as mutation probability, crossover fraction, etc., you may get improved solutions. But to quote the final solution you can select that solution which is optimum among the several solutions obtained in different runs. Or you may quote more than one good solutions obtained.

Genetic algorithm is a probabilistic stochastic search algorithm.Even if all the parameters are the same, the results are not the same for each operation.

Under normal circumstances, with the same set of parameters to run multiple times, take the average value of the results as the final results.

In stead of Basic GA, if you use adaptive parameter GA you can still get better results

Dear Mahdi,

                      I have a suggestion which is if you can construct theoretically the Genetic String Matching Algorithm for your problem ina manner such as my paper on "String Theory and Genetic Algorithms...." on my RG page and cosntruct the D-Branes String function from which the algorithm flows I think you will get an invariant class of results atleast within close parameter values (including probability values). I hope my suggestion works. SKM QC FEPS

You should design a weighted function where appropriate weightages is given to all the functions. the minimum value of this  weighted functionshould be treated as the solution. 

GA is a nondeterministic search algorithm, which gives you different result from different runs. This is a typical feature of heuristic optimal search algorithm. So we normally implement statistical analysis, for example analyse performance after 20-50 runs,when we evaluate a nondeterministic search algorithm. You can pick up the individual (solution) who receives the highest fitness value for your problem.

thank you all dear researchers, your answers where of a precious help. 

https://sites.google.com/site/tlborao/ ... a parameter less optimization algorithm. 

Just as many colleagues had said GA is stochastic optimization algorithm but the choice of your recombination and stopping criterion strategies helps you to get things right to some extent. I often use elitist recombination strategy and often ensure that the difference between my average fitness and best fitness are quite minimal(specifying the tolerance value). By doing this, the difference between optima you get at different runs will be negligible.

Hi,

Although GA is a probabilistic/stochastic search method, the stability of the algorithm is an important feature. It means that if you compute the standard deviations of your results, it should be negligible respect to your cost function. Otherwise, your algorithm should be improved further with tuning the parameters (e.g. number of chromosomes) or even integrating another light weight heuristic with your main GA in order to escape the algorithm from the local optima. In simple words, your algorithm may not converge completely.

GAs are stochastic global search algorithms, thus each individual of the population is expected to perform a different trajectory across the search space during each execution. The population is expected to converge to multiple (sub)optimal solutions.

Asymptotically speaking, GAs are proven to converge to the global optima of your fitness function. However, this means that the convergence is guaranteed only for an infinite number of generations.

Still, if you collect a set of optimal solutions by repeatedly executing a GA, you can still pick the best fitting individual according to its fitness value. It is wrong to consider the average value, however, because two suboptimal solutions with similar fitness value might have completely different structure, so that their average might correspond to a non fitting region of the search space.

Dear Mahdi,

                      I should congratulate you personally for having selected a very potent Econophysics problem which I have solved over time in various papers culminating in the joint Genetic Algorithm & Econophysics paper on Coal Stock Markets (which spreads the industry scientifically given that coal stocks take much less geophysical time to replenish than oil (I believe)) and the papers can be found on my RG page. Of course you need Stock Market Genetic Control in such cases.) I hope I am not at odds with the UN Millenium Goals in making this String Theoretic Geophysical Physics Modelling and ex-post experimental inference. This is very encouraging because going by the response of the learned society many of my inferences (actual or expected as the case may be) are being corroborated. Thanking you,

Yours sincerely,

Sir Ashutosh Mukherjee Chair Professor Soumitra Kumar Mallick QC EPS (Fellow Deemed)

Hi Mahdi,

Randomness concerns is one of main challenging issues with GA. To get solution within an acceptable range you could play with mutation or increase the iterations, if you problem stocked in local optimums then re-structuring the problem might be an effective solution. You can have a look at the following documents as well:

-Syswerda, Gilbert. "A study of reproduction in generational and steady state genetic algorithms." Foundations of genetic algorithms 2 (1991): 94-101.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=485989&tag=1

Since metaheuristics are not trustworthy, at least no-one I know at my math department would ever use these heuristics. There are tools that will find optima, by using mathematical optimisation tools, and only those are valid.

Well then, so can the optimiser record all the feasible solutions, as well as other things, like how many constraints are active in those solutions. To perform a local analysis can be done regardless of the method that lead to the solution.

Beauty is not easy to transform into an objective term. :-) And we would not agree on the definition.

I still have - at the back of my mind - the notion that those who use metaheuristics regularly are less eager to know what the optimum is. Why would they otherwise proudly show (especially on ResearchGate) terribly bad approximations of the optimum, while I - and plenty of my friends - would find an optimal solution? I am just curious.

It is the nature of Genetic Algorithm. But if you select suitable parameters and suitable stopping criteria, GA may give a reliable results. Furthermore , the objective function behavior is also important to give the same results in each run.

@Mahdi Abdeddaim; Were you able to solve this problem? Did you set mutation, crossover, selection parameters? Could you please explain this?