Solve Multi-Objective Optimization Problems Using GA Solver in Matlab

In this video, I’m going to show you a simple but effective way to solve various multi-objective optimization problems. This approach is very easy to implement, and it is based on multi-objective genetic algorithm solver (multi-objective GA solver) in Matlab. Let’s see how to use this optimization solver to solve a simple multi-objective optimization problem.
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HERE ARE 6 LISTS OF MY VIDEOS YOU MAY BE INTERESTED IN:
1. Optimization Using Genetic Algorithm:
• Optimization Using Gen...
2. Optimization Using Particle Swarm Optimization:
• Optimization Using Par...
3. Optimization Using Simulated Annealing Algorithm:
• Optimization Using Sim...
4. Optimization Using Optimization Solvers:
• Optimization Using Opt...
5. Optimization Using Matlab:
• Optimization Using Matlab
6. Optimization Using Python:
• Optimization Using Python
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[@nightknight8070]

This video really help me a lot! Thano you! I don't have any problem when try to run the optimization. However, when the optimization running, it won't show the graph as in the video. How can i fix it?

[@nightknight8070]

*Thank you

[@SolvingOptimizationProblems]

Please try run the exact function as shown in the video first and you should get the same result. And then update and try other functions later. Good luck!

[@ghazijumaa1648]

Dear Sir, How we can optimize the constants in equations Like : Y=c1*X1+ C2 *X2^c3 I mean finding the optimum values for c1, c2, c3 based on data set?

[@SolvingOptimizationProblems]

Hi, what is the objective function? Y, X, or other thing?

[@ghazijumaa1648]

@@SolvingOptimizationProblems Y is a target variable and X is a predictor variable,

[@SolvingOptimizationProblems]

So, in this case, consider c1, c2, c3 as decision variables to optimize your objective function

[@ghazijumaa1648]

@@SolvingOptimizationProblems Can you share a video about this type of problem, really I searched all the KZbin and I did not find any one.

[@SolvingOptimizationProblems]

There are several videos on my channel which solve similar problems. The solving principle is the same; although, it is not possible to find exact problem. Please let me know if you still have any difficulty!

[@techno-wonders]

If we want to save show the values of pareto front variables and decision variables along with plot how can we save this

[@SolvingOptimizationProblems]

Export the results to work space and then save it

[@techno-wonders]

By export we get code in workspace

[@techno-wonders]

Do we get that table also then how to retrieve it in presentable eformat

[@SolvingOptimizationProblems]

Hi, please have a look at my video related to triple objective optimization for how to do so. Thanks

[@severnsevern1445]

Please in the pareto front graph do we have possibility to visualize more than objectives functions?

[@SolvingOptimizationProblems]

Yes, it is possible to visualize 3 objectives. Have a look at my video named: "How to solve triple-objective optimization problems using Matlab". Thanks for your interest!!!

[@tekesteaman5105]

thanks a lot for clear and supportive video. please help me if any video related to the method of changing multi objective to single objective and how to solve by genetic algorithm

[@SolvingOptimizationProblems]

Thank you for watching and suggestions!

[@ssirailsiuofstso9332]

Your explanation is great. Can you talk about how to use the NSGA-|| algorithm for multi-objective optimization? Thank you.

[@SolvingOptimizationProblems]

I will upload NSGA_II soon. Thanks for watching

[@ssirailsiuofstso9332]

@@SolvingOptimizationProblems Thank you very much and look forward to your update！

[@severnsevern1445]

Great video! Please can you make a video on Kigring surrogate model.

[@SolvingOptimizationProblems]

Thanks for your suggestions! I will try it as soon as possible.

[@siwanedi2243]

Optimization running. Error running optimization. Undefined function 'nonlinear_constraints' for input arguments of type 'double'. why like that sir?

[@SolvingOptimizationProblems]

Check the format of all related functions

[@siwanedi2243]

how to check the format ??

[@yousrat4396]

hello sir, I have a question please in the table we get of pareto front variables and decision variables why do we get multiple results ? are they in order ? like is the results of index 1 the optimal one to choose ?

[@SolvingOptimizationProblems]

In multi objective optimization, multiple optimal solutions exist

[@veniciabond1058]

Thanks a lot professor, this is the only video I have found so far with similar problem to what am stuck on and uses gamultiobj toolbox- your video is so much better and easy to follow. However being new to Matlab and self studying. am stuck on this after a few hours and readings. I am attempting to graph a bi-objective problem: ie maximize f1 = x1 & f2 = x2; with these two constraints (one quadratic and one linear inequality): 𝑥1^2 + 𝑥2^2 - 1 ≤ 0 & 2𝑥1 + 𝑥2 - 2≤0. How do you set it up and graph it in gamultiobj? The graphs I am getting compared to what I expect are too different. Do you write both constraint equations in one script like you did for your two quadratic constraints? Most importantly how do you enter the objective functions and constraints in the toolbox window? Tried several variations. Thanks

[@SolvingOptimizationProblems]

Hi, thanks for watching! All of your questions will be answered in this video. Your problem is 99% similar to the problem in this video. Just follow the instruction in this video, you should be able to solve it. Good luck!

[@veniciabond1058]

@@SolvingOptimizationProblems Thanks for taking your time to respond. Yes, as I said earlier it is similar, I followed it step by step to the end but the graph is totally different from expected. I created two scripts like you did: first script I just replace your functions with the f1 & f2 I typed above (your question is minimize, mine is maximize- so I put a negative infront of both f1/f2, note even if I dont put a negative the graph plotted still comes out wrong). for the second script I wrote it as: function [C Ceq] = nonlinear_constraints(Input) x1 = Input(1); x2 = Input(2); C(1) = x1^2 + x2^2 - 1; Ceq(1) = 2*x1 + x2 - 2; Tried others such as using C instead of C(1), entering 2*x1 + x2 - 2 as a matrix (A= [2 1], b =[2]) under Constraints in the linear inequality constraints section, etc. There are no bounds given so I tried several bounds (feasible region is within circle of radius 1). Any ideas on what I am doing wrong? Thanks and happy holidays

[@SolvingOptimizationProblems]

Hi, in your problem, there is no equality constraint, so Ceq = []. If you still have some difficulty, just let me know, so that, I will make a video on solving multi objective max problems

[@veniciabond1058]

​@@SolvingOptimizationProblems the first attempt I made was: C(1) = x1^2 + x2^2 - 1; C(2) = 2*x1 + x2 - 2; Ceq = []; everything else is as you did but the graph of f1/f2 was still not as expected. So as mentioned I tried other versions including since C(2) is linear I entered it as a matrix in the linear inequality constraints of the toolbox ((A= [2 1], b =[2]) with the nonlinear script altered as - C = x1^2 + x2^2 - 1; Ceq = [];

[@veniciabond1058]

@@SolvingOptimizationProblems Thanks, i think it will definitely help some people even if they may not be in a situation similar to mine

[@nadhirmehellou9403]

Thanks a lot,

[@SolvingOptimizationProblems]

You are most welcome

[@ShathaAlhamad]

thank you , can you please help me in solving the base station placement problem in mobile communication using GA , the fitness function has two objective functions ,and the binary encoding is used to select the active or non active base station from the possible set of the base stations

[@SolvingOptimizationProblems]

thanks for your suggestions

[@nishantdhiman3361]

Hello sir, Thanks for this helpful video. I just want to know if this can directly be used for a dataset or do I need to get a regression equation first. I have a dataset with 3 input and two outputs

[@SolvingOptimizationProblems]

I think with your dataset, we need to do the regression

[@worshipacademy6402]

if I have absolute values? for example: | x(1)-x(2) | . What is the comand?

[@SolvingOptimizationProblems]

Hi, abs(x(1)-x(2))

[@준-m4t]

I have seen a lot of your videos. I have seen that most of the functions (when there are 2 variables) are solved with genetic algorithms. But I have 10 variables, and I want to solve a multipurpose function. I have organized the equation, and I don't know how to assign it and how to specify it. I want to talk in detail.

[@SolvingOptimizationProblems]

Hi, I prefer to use 2 dimensional problems to test my algorithm because it is possible to visualise the search space. To extend from 2 varibles to 1000 variables, it is not very much different.

[@putrafallo3074]

sir,, i want to ask you how to get power generation unit scheduling with power target for example 40 MW load on 5 power plant units using multi objective genetic algorithm optimizing tool...thankyou sir 🙏

[@SolvingOptimizationProblems]

We need the problem formulations, objective function and constraints, and then follow the instruction in this video. Thanks for watching

[@putrafallo3074]

@@SolvingOptimizationProblems thankyou sir 🙏

[@tatianamoreira2753]

Hi, thank you for the helpful video. I am only receiving one solution point on my pareto front, do you know how to fix this? And, can you use linear constraints in the gamultiobj?

[@SolvingOptimizationProblems]

Hi, increase the population size, you will have more chance to get more solutions. Thanks for watching!

[@tatianamoreira2753]

@@SolvingOptimizationProblems Hi, thanks for the response. I increased the population size, even to 10,000, and still have the same issue.

[@SolvingOptimizationProblems]

Check the constraints, what happens if you remove all the constraints?

[@aminebenrhouma9287]

hi can i change a parameter in the objective fonction in every run of the genetic algorithm?

[@SolvingOptimizationProblems]

Hello, for that, we need to develop our own GA code. This GA solver in Matlab. It is not possible to do so.

[@aminebenrhouma9287]

@@SolvingOptimizationProblems thank you

[@ismailamara4431]

Hi I'm using the built-in function (ga) in MATLAB. I want to make a constraint on a variable RD which is not one of the inputs variables (xi), as A.x

[@SolvingOptimizationProblems]

That constraint can be nonlinear constraint. Look at my m.file regarding nonlinear_constraints in this video for how to do it.

[@s.vinothjohnprakash5957]

I need to minimize x2,x4,x6 using GA toolbox matlab For the function f(x)=(x1*x2)+(x3*x4)+(x5*x6) Subject to constraints 0≤x2≤100 0≤x4≤ 20 0≤x6≤ 10

[@SolvingOptimizationProblems]

You mean: finding x2, x4, x6 to minimize f(x)? If that's the case, find my video about single objective GA solver in Matlab

[@indrajithkatkar3236]

Are the constraints used of equality or in equality type??? And what are the design variables

[@SolvingOptimizationProblems]

Yes, for constrained problems, please check other videos on this channel. Thanks

[@indrajithkatkar3236]

@@SolvingOptimizationProblems My doubt is which type of constraints are used here?

[@indrajithkatkar3236]

@@SolvingOptimizationProblems Can u send me the link of multi objective and minimization problem solved in matlab with the point of application purporse

[@SolvingOptimizationProblems]

Here it is: kzbin.info/www/bejne/roaUn4Fji91ojs0

[@yugao-yv7gi]

Hello sir,Your video is of great help to me. Do you know how to use gpops2 software package to realize adaptive h pseudo-spectral method and adaptive p pseudo-spectral method? I would appreciate it if you could answer it for me

[@SolvingOptimizationProblems]

Hello, I don't know that software. Thanks for watching!

[@selcukkizilcaoglu6595]

When I put run and answer to me this problem; Optimization running. Error running optimization. Undefined function 'nonlinear_constants' for input arguments of type 'double' what is soluition for this message?

[@SolvingOptimizationProblems]

Hi, the format of the "nonliear_constraints" is not correct.

[@selcukkizilcaoglu6595]

@@SolvingOptimizationProblems thank you for answer. I passed read to note on video about constraints.

[@SolvingOptimizationProblems]

Ok, thanks

[@kalimullah2773]

Hello Error running optimization. Undefined function 'nonlinear_constraints' for input arguments of type 'double'. I facing the above error, why?

[@kalimullah2773]

its solved, thanks

[@SolvingOptimizationProblems]

Great! Good luck.

[@kalimullah2773]

@@SolvingOptimizationProblems Thanks

[@miaadrina]

@@SolvingOptimizationProblems hi. I'm facing the same problem. What should i do?

[@imambayuprasetya2435]

@@kalimullah2773 i facing the s same problem, how to solve it?

[@nadiarizkys]

what if i want to use discrete values for some variables?

[@SolvingOptimizationProblems]

We need to update the objective function

[@lalitgrover4581]

Hi, I tried with the same example as you gave in a video but I receive an error. Error: File: ga.m Line: 4 Column: 14 Function with the duplicate name "ga" cannot be defined.

[@SolvingOptimizationProblems]

Maybe because of matlab version. I used matlab version 2016a

[@amianifineug1353]

Thank you lot! please I am working on structue transistor using Silvaco I want to use GA using matlab, Please how use matlab as an inteface with silvaco (Thank you)

[@SolvingOptimizationProblems]

I don't know how to connect Matlab to Silvaco

[@selvarajp1703]

Sir could you please add a multi objective pso algorithm

[@SolvingOptimizationProblems]

Great suggestion! Many thanks

[@selvarajp1703]

@SolvingOptimizationProblems I am waiting for your vedio

[@kelzangmpee8496]

Hello sir , How do we optimize with summation objected function ? I have sent the image of the formula in the Facebook. Waiting for your response Thankyou sir

[@SolvingOptimizationProblems]

Let me check. Thanks

[@كهرباءوميكانيكاالمصانع]

If you found the

[@sudiptamishra4297]

Hello sir, Please help me. I can't rectify the error. Undefined function 'nonlinear constraints' for input arguments of type 'double'

[@SolvingOptimizationProblems]

Your format of the function is not correct

[@hamidmehrabi8853]

I did it but I received this error: Undefined function 'nonlinear_constraint' for input arguments of type 'double' How can I fix this error?

[@SolvingOptimizationProblems]

Check the format of the m file

[@sagnikbhattacharya6071]

I had the same problem today. Then I realised that I have not added the path of folder (in which I saved those files) to matlab. So open "home" Open "Set path" Click "add folder" Find the folder where you saved these two files. Save and close And it should work.

[@SolvingOptimizationProblems]

Great to hear that. Good luck!

[@sharadinduroy3430]

please give some helpful video for coding multi objective simulated annealing

[@SolvingOptimizationProblems]

Many thanks for the interesting suggestion!

[@nihith323]

sir for me it is showing gaplot pareto not supported for thisalgorithm

[@SolvingOptimizationProblems]

Hello, I don't understand what you mean. Can you be more specific?

[@techno-wonders]

How to save parento front function values and variables

[@SolvingOptimizationProblems]

We can export the results to work space and then save it.

[@alsaidalmetwally5671]

can u provide me the Matlab code for multi objective optimization for 3 responses and 3 independent variables. I have conducted 3 power of 3 full factorial design applied to three different responses. Thus I have 27 treatments and 27 for each variable

[@SolvingOptimizationProblems]

Hi, please have a look at video about triple objective optimization on this channel. We can generate Matlab code as well

[@kssb-k2o]

I have a bunch of constrains for the constraints in inventory problem. How do I sort it?

[@SolvingOptimizationProblems]

For constrained problems, we need to add a constraint handling mechanism.

[@meditationmusicmahimam3690]

Same here... Can you please help me?

[@bkarthikeya4438]

@@meditationmusicmahimam3690 I'll

[@imexmaven7071]

Hello sir, how do I use suitable niching method to solve discrete multi model TSP using GA in matlab? Sir, if you can share suitable code, it is a big help for my research.

[@SolvingOptimizationProblems]

I often use Taguchi experiment design to select the optimal parameters of the algorithm. This is GA solver in Matlab. Just install Matlab and you will have it. No need to download the code.

[@imexmaven7071]

Is Taguchi experiment design a niching method?? Sir, I want to combine GA with nicing method and get multiple soutions.

[@SolvingOptimizationProblems]

Hi, I use Taguchi method to select the optimal parameters of my genetic algorithm to maximize its performance

[@keyrusalia6735]

what if the function contains symbolic variable?

[@SolvingOptimizationProblems]

In this method, all variables must have some numerical values, like 2, 2.5, 8, etc. If not, we need to convert them to.

[@soumialahfair3171]

thank you , please can you help me in this ziggurat method x1= 3.44 v=9.958e-3 (v:surface of one stairs and they have all same v ) n =128 (n:number of my stairs ) function f= exp(-(x^2)/2) using j=randi(n) ( j; normal distributio) u=2* rand([0,1]) (u ;uniform distribution ) how can i find x2 x3 x4... and y1 y2 y3 .... (y1 : wz can find it with this v/x1 )

[@SolvingOptimizationProblems]

I think you need to do regression before applying the solver

[@midhunap3779]

How to do ANN-GA optimization in Matlab

[@SolvingOptimizationProblems]

I don't know ANN.

[@mandal143]

If variable is binary, it is possible

[@SolvingOptimizationProblems]

Yes, but a small modification is required.

[@vipuldave8866]

Clearly of video is not proper

[@SolvingOptimizationProblems]

Thanks for your feedback.