Can't you go for hybrid version, for instance select a local minima by GA and use SA (Simulated Annealing based on the initial solution found from GA.

Assuming that your implementation is ok and the parameters are well adjusted I'd recommend apply one local search method (VNS or SA) for each indivivudial in your population. If you still have availible time, re-start genetic algorithms and do it as many times as possible.

Hybridization is definitely a way to go. Other possibility is trying niching techniques (e.g. multiple island with a given migration rate between them). However, if I am understanding well you are using a built-in GA in MATLAB, aren't you? If that is the case, I assume that you cannot tweak the GA but only its parameters, am I right? If so, go brute force with a very large population (e.g. 1000 individuals), a low mutation rate (e.g. 0.001), a high crossover probability (e.g. 1.0), and set a high number of evaluations as a termination condition (e.g. 10000000)!! With that you will get an extremely inefficient GA but eventually you will hit (hopefully) the solution.

BTW, could you give some tips about your problem? Knowing the dimensionality, whether it is combinatorial or real-coded, whether a real-life problem or a benchmark (etc.) could help in providing better answers to your question.

Thanks for your valuable suggestions.

Juan Luis Jiménez Laredo , I'm scheduling taps of Voltage regulator and capacitors in order to minimize electric energy consumption.

Dear Saran, if the optimization problem is duly modeled and formulated, theoretically you just have to increase the mutation rate (at least in an initial stage of the search). In opposite to a hill-climbing algorithm, a pure random search normally easily finds the hill of the best solutions. Once you find that hill, you easily can get the global optimal solution.

My impression is that in many trials always the same optimum is recovered.  If so, then how do you know it is not a global optimum?

A good question by Marek. But if the global optimum is known then I will say you go with Juan's suggestion with increasing population size but i suggest higher probability of mutation as we are interested in unexplored area and more exploration is needed than exploitation just as Antonio suggested. If the problem dimension is too big parallel computing can be considered (i m not sure if it is ok in the toolbox)

To,

Marek Wojciech Gutowski,

I have M+N control variables. After optimal solution, I have taken M without modifications and modified 'N' (set N = Nmax). Then I found that this solution gives me minimum objective value as compared to previous one. Its means GA is not able to set N at Nmax after so many trials.

Try to apply Genetic algorithm as the initial seed for ur problem.Then apply the tabulated search for globalization,Which is good at both exploration and exploitation.At the same it will address the too much exploration and exploitation problem as well.Hybridization is the best way of avoiding the local optima.

Situation is still unclear for me.  After running GA with M+N unknowns and finding optimum another run is attempted but this time with some (M) unknowns fixed.  Doing so another (better or the same?) optimum is found.  Is it so?  Or are you running GA always with a subset of searched parameters fixed? After fixing some unknown parameters we are automatically working within only the part of search space and this is the main reason for the so called premature convergence .  Fixing another subset will allow to find better solution.  Imagine that you are searching minimum of f(x,y) = x2 + y2 with fixed x=x0 (with x0 not equal to zero!), then with fixed y=y0 (again y0 is not equal to zero).

But there might be two other reasons of your problems. 1) The optimum of objective function (be it local or global) is reached at the extended subset of search space, not at single, isolated point, or 2) the problems arise due to inexact computer arithmetic (rounding errors).  I don't know anything about your electric circuit except that it contains capacitors.  Now, if the operating currents are or order of kA then C = 22 pF will act practically the same way as C=47 pF - as an open circuit.  Contrary, for small currents, of order of nA, very high capacitance, say 1 mF or 10 mF will behave as a well conducting wire.  This is NOT GA's fault.

It all depends on the problem at hand, but in my experience a lot of trouble comes from casting a multi-objective optimisation into a single-objective representation using arbitrarily chosen weight factors. Running a full-fledged multi-objective optimisation might solve your problem.

To,

Marek Wojciech Gutowski,

Not like this ! I have a objective function which takes input as optimum (X=Xm+Xn). Once, I run GA with Xm as variable (in the range of -16 to +16) and Xn fixed (fixed to its maximum bound), then I got objective value 'F0'. In second case, I have Xm+Xn variable (where Xm  and Xn bound remains same as per previous case), now objective value is 'F1' and what I observed F1 is greater than F0(F1>F0).  Why? As per my opinion it should be either F1=F0 or F1

To,'

Bas Van der Geer,

Its not a multi-objective problem. It is simple minimization of electric energy consumption of a feeder.

Indeed, one should expect F1=0 or F1

To,

Marek Wojciech Gutowski,

I'm actually modelling voltage dependent loads. If voltage supplied by transformer increases/decreases then power consumption will also increases/decreases.  Here transformer secondary side voltage is controlled by taps (16 taps for increasing the voltage and 16 taps for decreasing the voltage from rated voltage). Therefore my objective is to determine optimal setting of these taps in a period of 24-hours for a particular feeder. In second case I'm trying to do the same with taps of transformer and capacitors (shunt capacitor bank).  

It seems that multiple runs with different seeds of initial chromosomes may escape the local minima in the present case. Further, population size may play the key role in this regard. Try the following two sets of population size 20~60 and 200~250. Even if you are facing the same problem, then it is better to move for the other algorithms like PSO and HS.

Hybridized Ga with a local search. You please go through memetic algorithm.

Sasan,

after your last explanation I understand that you have 31 x 31 = 961 variants of setting your 'taps'.  This is not a big number, so I'm wondering why you are resorting to GA instead of simply solving (most likely analytically) 961 problems and see which (numerically exact) solution is most satisfying for a given load.

Thanks all of you for your expert advice.

I'll try your suggestions.

Dear Sasan

if still you have problem with GA you can utilize RPLNN technique, I used it for different optimization processes and really it is faster and in some cases gives more accurate results. please check the attached articles.

regards

Aydin

1.https://www.researchgate.net/publication/306048088_Optimizing_radio_frequency_identification_network_planning_through_ring_probabilistic_logic_neurons?ev=prf_pub

2.https://www.researchgate.net/publication/303402995_Modeling_Mechanical_Properties_of_FSW_Thick_Pure_Copper_Plates_and_Optimizing_It_Utilizing_Artificial_Intelligence_Techniques?ev=prf_pub

Article Optimizing radio frequency identification network planning t...

Article Modeling Mechanical Properties of FSW Thick Pure Copper Plat...

https://stackoverflow.com/questions/31215003/genetic-algorithm-selection-method-stuck-at-local-minimum-after-few-generations

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.8662&rep=rep1&type=pdf

https://cs.stackexchange.com/questions/54828/how-to-avoid-getting-stuck-on-local-optimum-for-genetic-algorithms