Evolutionary Algorithms - Science topic

Definitely use the number of evaluations if you can't guarantee that the algorithms consume the same number of evaluations per generation/iteration.

Hello Sofia,

It is indeed possible that for some instances of your problem, the objectives are not conflicting. For example, in a shortest path problem, the path with the shortest distance may also be the fastest in terms of travel time, resulting in no trade-off between the objectives.

However, the lack of a diverse Pareto front in some instances does not always imply non-conflicting objectives. It could also be due to factors such as:

If you describe your problem, we can help you more easily and as Roy already stated, you can verify whether your objectives are conflicting by calculating the correlation coefficient.

There was a similar question already asked here:

I hope this helps!

Dear Zohre Sajjadi ,

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Regards,

Shafagat

website: https://www.inderscience.com/jhome.php?jcode=ijcast

Dear Maoqing Zhang ,

Neuroevolution is a paradigm that leverages evolutionary algorithms to train neural networks. Unlike traditional gradient-based optimization methods, which rely on backpropagation, neuroevolution evolves neural network architectures and parameters over generations.

https://vinaykumarmoluguri.medium.com/neuroevolution-training-neural-networks-using-evolutionary-algorithms-27487634d3bb#:~:text=Neuroevolution%20is%20a%20paradigm%20that,architectures%20and%20parameters%20over%20generations.

Regards,

Shafagat

I recommend studying the following systematic review.

I am from Ethiopia and happy to participate on this conference.

Hello,

I think it would be better if you gave more complete information about your question. For example, is your output data one-dimensional (i.e. a vector) or two-dimensional (matrix) and... or were you explaining that the optimal value in your opinion is the lowest value or the highest value?

However, I offer a general trend. If your output dataset is one-dimensional (and your goal is to find the minimum or maximum value), you can use MATLAB's max or min functions. But if your output data is multi-dimensional, although the problem can be solved with MATLAB and command codes, I suggest you use optimization algorithms such as PSO. ​But the bigger the search space, the more optimization-based algorithms are felt.

Usually the code can be optimised: same algorithm but less computing time, less memory (well, sometimes _far_ less). Now, for the quality of the results if you find a _sure_ way to improve it ((for a given search effort, of course, like a number of evaluations) publish it quickly!

Note that a different initialisation method might improve the algorithm on some problems, but not always. See for example

Omran, Mahamed G. H., Salah al-Sharhan, Ayed Salman, and Maurice Clerc. ‘Studying the Effect of Using Low-Discrepancy Sequences to Initialize Population-Based Optimization Algorithms’. Computational Optimization and Applications, 2013, 1–24.

Sometimes the problem can be reformulated. Using different formulae to take constraints into account or rewriting a discrete problem as binary.

No, a Pareto front produced by an evolutionary algorithm does not necessarily include both global and local optima. The Pareto front represents the set of non-dominated solutions in multi-objective optimization problems. These solutions are not dominated by any other solution in terms of all the objective functions simultaneously.

In a multi-objective optimization problem, there can be multiple optimal solutions, known as Pareto optimal solutions, that represent trade-offs between conflicting objectives. These solutions lie on the Pareto front and are considered efficient solutions because improving one objective would require sacrificing performance in another objective.

The Pareto front typically contains a mixture of global and local optima. Global optima are solutions that provide the best performance across all objectives in the entire search space. Local optima, on the other hand, are solutions that are optimal within a specific region of the search space but may not be globally optimal.

The evolutionary algorithm aims to explore the search space and find a diverse set of Pareto optimal solutions across the entire front, which may include both global and local optima. However, the algorithm's ability to discover global optima depends on its exploration and exploitation capabilities, the problem complexity, and the specific settings and parameters of the algorithm.

It's important to note that the distribution and representation of global and local optima on the Pareto front can vary depending on the problem and algorithm used. Analyzing the Pareto front and its solutions can provide valuable insights into the trade-offs and optimal solutions available in multi-objective optimization problems.

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Thank you.

I would be surprised if you will find any "hard" rule on this since hyperparameters of optimization routines are typically quite application specific. For meta-heuristic algorithms you can often find the rule of the thumb to use 10 search entities (e.g., 10 particles for PSO) per optimization variable in some lecture books, but this is definitely not a hard rule.

In terms of required iterations, you might just want to monitor the cost curve during optimization. If it stalls for a certain number of function evaluations, you can stop the optimization. Otherwise or additionally, you might want to consider a simple time constraint allowing your algorithm to optimize as long as you like it.

In fcat to a problem, we can propose many apporoaches of resolutions, and aalso Lagrange can not solve any kind of problem, another thing is the computation time a method can use to solve the problem, is the computation time good or appropriated ? Some problems can easily be solved in a short time using evolutionnary computation like GA, PSO, ABC, SA etc

Genetic algorithms have the several characteristics over others such as , (1) Natural selection and natural genetics are at the heart of the Genetic Algorithm. -(2)These are simple to comprehend and use. -(3) These are frequently encountered in optimization issues. (4)These are based on a population of points rather than a single point. -(5) Instead of deterministic rules, these utilize probabilistic transition rules. -(6)Genetic algorithms can handle a large number of variables efficiently. - (7)No derivative information is required for these methods. -(8)These are more successful when dealing with complicated difficulties than when dealing with basic problems.

It's a good idea to learn how to code. On the other hand ``bilevel optimization problem'' doesn't provide any relevant information, so it would be better to just ask about how to code evolutionary algorithms. This: https://towardsdatascience.com/introduction-to-evolutionary-algorithms-a8594b484ac might be a good place to start.

@Helei Kang please search the concept "Global neighborhood algorithm". I cannot find the paper at the moment, but that is more or less what you are looking for.

Here is the link to the original paper: https://www.researchgate.net/publication/269826478_A_New_Optimization_Algorithm_For_Combinatorial_Problems

Good luck

You most certainly can. In fact, there may be an advantage in employing such a method since we know that some algorithms are better suited for some problems over others (NFL theorem). Just be sure to properly select the correct MH for any given objective function. This may require some experimentation on your part, but whatever you do, don't let the algorithm selection process be randomized. A methodological approach needs to be adopted here.

Personally, I would advise using Pareto-based techniques instead of conventional non-Pareto-based approaches like Lexicographic or sum weighted optimization. Nonetheless, good luck!

Dear Anil,

In this paper, four optimisation methods were applied, including GA, DE, ES, and BBO. I know there are many different available source codes for these methods. Which one is most interesting for you to use?

Yarpiz (2022). Biogeography-Based Optimization (BBO) (https://www.mathworks.com/matlabcentral/fileexchange/52901-biogeography-based-optimization-bbo), MATLAB Central File Exchange. Retrieved March 18, 2022.

Dear Muhammad,

In the website of Professor Mirjalili who is one of the pivotal pioneers in Swarm Intelligence, you can find several modern meta-heuristics' source codes which have been developed in different languages like Python. Matlab, R, and C++ and so on. Please find the codes in the below website:

Good luck

(Chaotic initialization)

(Opposition-based initialization)

Of the two, initialization with chaotic mappers is superior. Distributing the population evenly across the search space is key for the algorithm to have the best start possible. Opposition-based techniques have been found, at least in my personal experience, to reduce population diversity in this crucial phase.

Dear Dr Sajid,

In each iteration, after computing the average fitness of all solutions, the difference between each solution's fitness and the average fitness can be calculated. Next, the minimum difference shows the solution with the highest similarity with the average fitness.

Most LPs arising in practice can be solved quickly using simplex. For very large and/or degenerate instances, interior point methods (IPMs) may be faster. Many solvers (e.g., CPLEX, Gurobi, Xpress, MOSEK) allow the user to try several methods.

Hello Abhinav Kumar Sharma

I think that these papers may help you

1-Burachik, R. S., Kaya, C. Y., & Rizvi, M. M. (2021). Algorithms for generating Pareto fronts of multi-objective integer and mixed-integer programming problems. Engineering Optimization, 1–13. doi: 10.1080 / 0305215x.2021.1939695

2- Sujeet Kumar Singh & Mark Goh (2018): Multi-objective mixed integer programming and an application in a pharmaceutical supply chain, International Journal of Production Research, DOI: 10.1080/00207543.2018.1504172

3- Tušar, T., Brockhoff, D., & Hansen, N. (2019). Mixed-integer benchmark problems for single- and bi-objective optimization. Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO ’19. doi:10.1145/3321707.3321868

All the genes play an important rolein in the optimization process, The likely good genes contribute information for improving the qulity of new ones and the likely bad genes could help to avoid non factible solutions and to re-direct the search to new areas of the domain. So, I think that all the genes must to participate in the solution search process.

Miha Ravber : for me, [-2, 2] was enough because I fixed the first atom at (0, 0, 0), the second at (>= 0, 0, 0), etc. If you don't, you get free coordinates between your bounds.

You can definitely start at [-10, 10] and see what the results are, then adjust.

Arash Mazidi PSO is also in various classification problems. I particularly use it for Phishing website datasets.

In the following article, the performance of a new metaheuristic algorithm named QANA was compared with ten comparative algorithms using three statistical tests, Wilcoxon signed-rank sum, analysis of variance (ANOVA), and mean absolute error (MAE).

Dear Azhagumathi Ma

These links might be useful, have a look:

1. https://kushalvyas.github.io/gen_8Q.html

2. https://jeroenpelgrims.com/solving-8-queens-problem-on-an-8x8-board-with-a-genetic-algorithm/

Kind Regards

Qamar Ul Islam

Dear Amirhosein Fardi

First you may check two sources of the optimal fronts of 3-D DTLZ instances:

<< Coello, Lamont, & Van Veldhuizen, Evolutionary Algorithms for Solving Multi-Objective Problems: Appendix E >> http://www.cs.cinvestav.mx/~emoobook/apendix-e/apendix-e.html

<< Durillo & Nebro's jMetal Framework >> http://jmetal.sourceforge.net/problems.html Those could help you to evaluate your MOEAs on the 3-D instances. =====================================

As for more than three objectives, we can generate the optimal fronts by ourselves. In this case, let us check the problem descriptions in the original paper:

<< Deb, Thiele, Laumanns, & Zitzler, Scalable Test Problems for Evolutionary Multiobjective Optimization >> http://link.springer.com/content/pdf/10.1007%2F1-84628-137-7_6.pdf

According to the descriptions, the optimal front of DTLZ4 is the same as those of DTLZ2 and DTLZ3. A simple way to generate the optimal front is to generate a set of decision vectors by setting the values of the first M-1 variables randomly and set the remaining k variables by 0.5. Evaluate these decision vectors by DTLZ2, and the obtained objective vectors could serve as the reference optimal front (,though not very evenly distributed). Another way is to generate the objective vectors directly by making the sum of the square of objective values as one (f1^2 + f2^2 + ... + fM^2 = 1). The DTLZ5 and DTLZ6 instances have the same optimal front. You can generate a set of decision vectors by setting the first variable randomly and set all remaining variables by 0.5. Evaluate these decision vectors by DTLZ5, and the obtained objectives will form a reference optimal front. For the implementation of DTLZ5, you could check the PISA implementation or jMetal implementation.

MOEAFramework provides the PF of DTLZ1-4 and DTLZ7 with 2, 3, 4, 6, and 8 objectives. You can download them here:

If you still need to generate PF of DTLZ1-4 by yourself, the paper of Li et al. [1] describes one method in details in Section IV-B. Just check equations (14) and (17). You may also use the PF generator included in nsga3cpp [2], which is an unofficial implementation of NSGA-III by me. Note that for 8 and more objectives, the number of Pareto optimal solutions could be very large.

In this case, the 2-layer methoed mentioned in [3] is adopted. Li et al. [4] proposed another complex method to generate PF of DTLZ functions.

If you want to generate PF of other test functions, MOEAFramework provides a way to do so. Please check the discussions here [5].

I guess that you are generating PF of DTLZ and other functions since you want to measure algorithm performance by the inverted generational distance (IGD) indicator. In this regard, you may want to check Ishibuchi et al.' study [6] on an improved indicator called IGD+, which is weakly Pareto compliant (but IGD is not).

Finally, Ishibuchi et al. [7] indicated that DTLZ1-4 and WFG4-9 are similar functions with respect to the shape of PF and mentioned the necessity of more general test problems. Cheng et al. [8] proposed a new set of test functions with an open-source software platform PlatEMO [9], which may also be interesting to you.

Hope the above information is useful to you. :)

-------------------------------------

[1] Li et al., An evolutionary many-objective optimization algorithm based on dominance and decomposition, t-EC 2015, https://doi.org/10.1109/TEVC.2014.2373386

[2] nsga3cpp: http://web.ntnu.edu.tw/~tcchiang/publications/nsga3cpp/nsga3cpp.htm

[3] Deb and Jain, An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: solving problems with box constraints, tEC 2014. https://doi.org/10.1109/TEVC.2013.2281535

[4] Li et al., A method for distributing reference points uniformly along the Pareto front of DTLZ test functions in many-objective evolutionary optimization, ICIST 2015. https://doi.org/10.1109/ICIST.2015.7289031

[5] https://github.com/MOEAFramework/MOEAFramework/issues/49

[6] Ishibuchi et al, Modified distance calculation in generational distance and inverted generational distance, EMO 2015, http://doi.org/10.1007/978-3-319-15892-1_8

[7] Ishibuchi et al., Performance of decomposition-based many-objective algorithms stronly depends on Pareto front shapes, tEC 2017. https://doi.org/10.1109/TEVC.2016.2587749

[8] Cheng et al., A benchmark test suite for evolutionary many-objective optimization, CIS 2017. https://doi.org/10.1007/s40747-017-0039-7

[9] PlatEMO: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html

Kind Regards

Qamar Ul Islam

PyGAD: https://pygad.readthedocs.io

It is an open-source library for general-purpose optimization using the genetic algorithm. It is very easy to learn.

I'm not keen on calling anything "smart". Any method will fail under some circumstances, such as for some outlier that no-one have thought of.

Dear Mahdi Ansari

This thread might be helpful. Have a look

Kind Regards

Qamar Ul Islam

Dear Neeru Ahuja

You can find a lot of ready algorithms from this website.

This reference might be helpful:

I recommend you to check also the CCSA algorithm implemented by a Conscious Neighborhood-based approach which is an effective mechanism to improve other metaheuristic algorithms as well. The CCSA and its full source code are available here:

Yes there are, but most of them focus on the very simple optimisation problems.

such as

Also, if you prefer using predefined functions in Matlab, check this link:

https://www.mathworks.com/help/gads/genetic-algorithm-options.html

I am a bit muddled up with respect to tournament selection..

Should the population set size be the same as the size of the offspring?

If that is the case, why do we need a tournament selection strategy to form a mating pool- we might as well as directly use the entire population as a whole?

Iago Augusto Carvalho sorry for the late response. I saw this approach in some papers. I can't remember all of them, but I found at least one where they used this method:

Knapsack problems of economic type can be easily solved by Genetic algorithm see the following sites for an example of knapsack business problems:

Knapsack Problem Using Genetic Algorithm With Source Code | by Muzamil Shahbaz | Medium

Genetic algorithm for knapsack problem in Matlab - Free Open Source Codes - CodeForge.com

The premature convergence of a genetic algorithm arises when the population for an optimization problem converged too early. In order to avoid this situation, the following link may be helpful in this context:

Bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010 and BA has been found to be very efficient .

Please read this article:

Medical Image Registration Using Evolutionary Computation: An Experimental Survey By: S. Damas; O. Cordón; J. Santamaría

By: Thomas Jansen

Metaheuristic can be categorized upon their common features into at least nine basic categories:

N. K. T. El-Omari, "Sea Lion Optimization Algorithm for Solving the Maximum Flow Problem", International Journal of Computer Science and Network Security (IJCSNS), e-ISSN: 1738-7906, DOI: 10.22937/IJCSNS.2020.20.08.5, 20(8):30-68, 2020.

Dear Harish Garg

Here is you are:

Ali Sadollah, Hassan Sayyaadi, Anupam Yadav (2018) “A dynamic metaheuristic optimization model inspired by biological nervous systems: Neural network algorithm”, Applied Soft Computing, 71, pp. 747-782

There are some technical programming points you should take care of them regardless of the above answers: first, you can follow what has been proposed above directly, as in such a case, maybe your solution goes infeasible when you keep a unique cell. So, your analysis will be a misleading chain of function feedbacks. Another mistake can be due to monitoring of weakly-defined fitness function, instead of monitoring the loss of a function that is sensitive to all independent genes. So, you can also change the definition of fitness function to be a another valid function, and also, it can track (sensing) each cell instead of the whole solution block. If you protect your model from these flaws or not able to redefine the objective function, you can focus on the way you programmed your code (functional programming or not). Then, you can simply eliminate the set of selected elements one by one (using a conditional selection scheme) and re-test the evaluations in the loop.

A hint: it is not OK to be ignorant of nonlinear mathematical optimisation. First you absolutely need to understand optimality criteria - as those conditions are the goal to fulfill. Mathematical optimisation tools are DESIGNED such that accumulation points from the iterative scheme WILL satisfy the optimality criteria, and in most cases you will be able to see the "fault" in the optimality criterion shrinking.

In contrast metaheuristics have no such "guiding light" at all - they fumble in the dark! Few sensible scholars with knowledge in mathematical optimisation would use these tools.

We can optimise mixed continuous and categorical variables with Bayesian Optimisation. Please check out our paper Bayesian Optimisation over Multiple Continuous and Categorical Inputs and the code below.

Paper: https://arxiv.org/pdf/1906.08878.pdf

Code: https://github.com/rubinxin/CoCaBO_code

The response from those who know about both - such as me - is that PSO and other meta things will very unlikely be as robust and accurate as a modern branch-and-bound code. I have always been puzzled why people seem to not be interested in what the optimum actually is - I thought that finding an optimum was the whole idea with using optimisation in the first place!

And yet there are more people here that seem to be content with non-optimal points. I would not be, and therefore I do not use meta things, and instead use tools that guarantee that the final output always is optimal. I have always thought that that is the whole purpose with the use of optimisation tools. But for some I guess not. I can't understand why - it seems to be a waste of time.

Following

Matlab and Adams easily coupled to each other. you should just write an appropriate objective function in matlab which can use the date in simulink. then use this function in GA tools. your objective function should go to simulink and run the box of Adams/Car in simulink then Return the response to objective function output.

If you write such an objective function you can use GA tools in matlab and optimize your problem easily.

Dear Rachid,

The optimization problem in the pv system where it is required to locate the point of maximum power point is characterized by a relativity broad maximum not a sharp maximum so it will be not very critical for the resolution issue. I think the speed of convergence to the global maximum is important and distinguishing for such a problem. Also the oscillations around the steady sate solution is an other performance parameters of the optimization method.

Best wishes

Saifullah Khalid What is the objective function? I do not find it in your description That would otherwise be very handy to have. Also, you need to restrict E_i to be non-negative.

I can - with almost certainty - say that this problem is a standard resource allocation problem, for which there are solvers that guarantee to provide an optimal solution, within a second. (My papers on it describe a great variety of models and approaches.) Hence, skip the metaheuristic, please - I do not think it is going to provide an optimum, while using the simple tools described in my papers will always yield optimal solutions.

Below material can be useful:

To me, the best optimal solutions to such problems are use:

1) Convectional neural works.

2) Multivariate exponential families of distributions.

use weka software

With nonlinear problems there may be multiple local solutions which will "attract" the algorithm, preventing it from finding the optimum global solution. Your boundaries will impact the starting point and also the first few provisional steps, so that the outcome may depend on the boundaries. Even if they include the global optimum, this doesn't assure that the algorithm will find it. This problem is too complex for a simple solution that will work in any case. I have solved many such problems. When I don't get an adequate solution with Excel's solver, I resort to C code, which I have tons of. If you have a particular problem or data set, I'd be glad to solve it for you and send you the solution. I wrote a book on the subject, https://www.amazon.com/dp/B07FL7JR1J, which contains many examples. It will free on 1/7/2020.

Each optimization problem ( in any type ) has the exact same components:

1- Upper and Lower Bounds for the search space.

2- Number of dimensions (D) or the size of the problem (number of Xs).

3- Type of the problem (Discrete , Continuous, Binary).

4- One (or more) Objective Function.

5- An optimal solution.

All solutions, or all generated Xs in Range (UperrBound, LowerBound) are correct. However, The better solution is the solution with near cost/fitness value to the optimal solution (component no. 5). Therefore, (in my opinion and based on so many research papers) you can not specify a range for LOA. However, we said that the algorithm (A) is better than algorithm (B) when the cost/fitness is near more than B to the optimal solution in that optimization problem.

You wrote two examples ( Rastrigin and Schwefel ) , these two problems (I think) have been widely tested.. What about "Quartic" test function ? It is a noisy function (i.e., contains a random part). This is a very challenging and interesting test problem, the average solutions for most of evolutionary algorithms and swarm intelligence algorithm reached to something around 10^-5, while the optimal solution is 0. You can not say there is a specific range for LOA for quartic test function, however, you just check how much your algorithm is near to 0.

One more thing, in some research papers, they said, "Any algorithm reached to cost value less than 10^-12, it will be converted to/considered as Zero, because it is a very low value". In this case, they used a very low value. In my opinion, I think this is not fare. For example in Algorithm (A) we reached to 10^150 using 500 iterations, while in algorithm (B) we reached to 10^30 in 500 iterations. Both of them will be Zero, however, A was faster and better than B when reached the optimal solution.

Comparing an algorithm with others should be done based on different evaluation measurements , such as the following:

Note: (after executing the algorithms R run times, R could be 10, 20, 30 )

1- The best (B) and worst (W) results.

2- The mean (Avg) and median (Med).

3- Standard deviation (Std.) .

4- Mean absolute error (MAE) between the algorithms.

5- Statistical analysis (Willxcon, Fridman .... ) between the algorithms.

6- Convergence analysis between the algorithms.

7- Time Complexity.

8- Execution Time (if you have executed all algorithms on the exact same machine).

Based on the above 8 measurements, you can discuss that the range of your algorithm (B,W) is better than the range of the algorithm (B, W). The low value of Std. means that your algorithm is stable more than the others. Statistical analysis methods show how much your algorithm is different to the others. The rest show how much your algorithm is fast as compared to the others in terms of (iterations/fitness evaluation, Algorithmic time, and execution time).

In any run time, you should specify your stop condition:

1- Fixed number of iterations.

2- Fixed number of fitness evaluation.

3- A value represents the algorithm is trapped (sometimes called "Tolerance"). For example, Tolerance = 100, means 100 iterations and the algorithm has not been enhanced/ found new better solution.

Hope I answered your question and did not explain something outside what you needed..

Regards ..

Hi, if you run the algorithm using all the samples of the different sub populations you increase the size of the initial population and mutations will occur between the different samples. At the opposite you can perform different runs using a different sub population for each run. Mutations between sub populations need still to be defined in your approach.

Hi, instead of modifying the mutation rule it would be better in a first step to generate a larger initial population. Indeed, the new mutation rule will be adapted to a particular problem only.

Thank you for the question and replies so far. My experience is that evolutionary algorithms (metaheuristics) are good for inequality constraints but not so for equality constraints. So, it is better to eliminate equality constraints to reduce the problem dimension before using evolutionary algorithms. When one equality constraint is eliminated to calculate one (dependent) variable, then inequality constraints may have to be added if there are lower and/or upper bounds on the (dependent) variable.

See the following book chapter for our study on using differential evolution for solving optimization problems with equality constraints.

Sharma S. and Rangaiah G.P., Improved Constraint Handling Technique for Multi-Objective Optimization with Application to Two Fermentation Processes in “Multi-Objective Optimization in Chemical Engineering: Developments and Applications” edited by G.P. Rangaiah and A. Bonilla-Petriciolet, John Wiley, 2013.

If I understand correctly, you are facing the "exploration vs exploitation" problem. In essence you should experiment with the parameters that affect "exploration". Parameters depend on the algorithm you use. For example you could try with (listed in no particular order)

- representation

- population size (increase)

- mutation operators

- crossover operators

- selection operators

...

Probably you should run a lot of experiments to find the set of parameters that suits you. Also, you should be aware that none of the metaheuristic algorithms in practice (limited execution time) guarantees convergence to the optimal solution. However, with the proper parameters you might get the solutions that are good enough.

I hope that this helps!

This question, like many others you have posted in the last few days, can all be answered in the same way: it depends on the problems you are wanting to solve.

I would suggest looking at the results of the Black Box Optimisation Benchmarks (BBOB).

There are many different algorithms that are compared and many are freely available via github, or from the authors of the codes. The tremendous advantage is that you can see how they perform on many different types of problems, some of which might be similar to what are wanting to solve in your own work. Furthermore, you won't have to trawl through reams of cloying self-assessment and self-appraisal of many commercial products which, not surprisingly, are always fulsome in praise of their own product.

I am not sure if I understand your question clearly but if you are having a problem that your evolutionary algorithm (EA) gets stuck on local optimum, this is called as "premature convergence" and yes this can happen if the problem is too complex, local optima is too good, or your algorithm is designed badly.

You may try to redesign/change your genetic operators (selection, crossover, mutation). For example, selection operator of Excel EA may be allowing only good individuals to survive which decreases the diversity and after a number of generations the algorithm gets stuck in the same region.

Using a selection operator which also allows a small number of bad individuals to survive during the generations can increase diversity of the population. You may also increase the mutation rate but since mutation is a random process, it may take too long to leave the solution region you stucked in. Moreover, increasing randomness will decrease your convergence time.

I recommend you to use Python or R programming languages, which has well designed EA packages, or any programming language you are famililar. This will give you chance to modify the operators when neccessary.

Optimization algorithms are really pretty simple. Just keep climbing up the hill until you get to the top. Take some precautions to make sure your step size isn't too big and try many different starting points far away form the optimum to make sure you have found the true optimum an not just a local optimum.

You problem is equivalent to (if I understand your notation):

X=k1(z1+y1+q1)+k2(z2+y2+q2)+k3(z3+y3+q3)->max

If z, y, q are given constants, then their sums are also given constants, say K1, K2, K3

X=k1*K1 + k2*K2 +k3*K3 ->max

There are no constraints for the decision variables k1, k2, k3.

This is a linear form that is maximized as these variables take unlimited max values......, hence there is no unique solution. Something is missing in your problem statement.

Sounds great!

Thank you Salah Mortada for your explanation. However, I would like to draw a figure that compares different methods that used in the experiment result and clearly show the overfitting, under-fitting methods. If you have an example of such an experimental result will be grateful.

Simple:

1) Open optimization toolbox

2) Select GA solver (and enter your objective function and constraint file detail)

3) Set lower bound as 0 upper bound as 1 (this set must be as many variable)

4) Under integer variable put index of all the variable whose values to be either 0 or 1

5) Run

You can get the result.

You may require basic knowledge of how to use optimization toolbox.

Hope that you can do it now.

Sincerely,

Alam

Thank you very much Raael Sir, I am doing Same and trying to minimize Error

Please see