I can see more than one possible reason:

1. The problem may perhaps not have a unique solution, and different solvers could therefore - because of their different strategies - converge to different optima.

2. The solvers themselves perhaps are not guaranteed to find an optimal solution to your problem. Heuristics - such as metaheuristics or greedy approaches - are almost never guaranteed to converge to an optimum.

Article A Review on different optimization techniques used to optimi...

For the same problem and the same heuristic optimization algorithm with its settings unchanged, different set of answers can be obtained every time you seek an optimal answer. This is attributed to the random variables used in the algorithm and the limits on the runs to reach an answer. For example,

https://www.researchgate.net/publication/307583888_Implementation_and_Analysis_of_Genetic_Algorithms_GA_to_the_Optimal_Power_Flow_OPF_Problem

More intense differences may be happened when the setting of an algorithm changed, or the another algorithm is used.

In the particular case of the paper you included in your first comment, Table 10 didn't show such behavior. The reasons of differnce between the answer of the first row and the rest answers are well explained by the authors.

Hello,

Simply, because the purposes of the driven optimizations are different (costs minimization, quality service maximization, minimization of greenhouse gas emissions...) and because the associated parameters are it automatically.

Dear Sudhir Kumar, we always teach our students that the optimum, is by definition unique. But this does not rule out situations, such as those presented by Michael Patriksson, Mohamed EL-Shimy or Bruno Durand.

I would add that, in general, it is the responsibility of the established model. To different models, different solutions.

What should be taken into account is if the model we propose resolves the true situation that interested us. In other words, the optimal solution for the real problem.

I hope that my reflections will be of some use.

Best regards,

José Hernández.

Hence, José, you should defiinitely *not* teach that optimization models have unique optima.

Dear Michael Patriksson, the observation is very interesting, but I would not risk so much.

I agree with your statement “perhaps not have a unique solution,” and I am clear, we see that in Linear Programming, that an optimal solution can be obtained from different combinations (10 = 3 + 7 = 5 + 5). But none of these cases denies that the optimum is unique. I will also agree that different models can generate different optima. But of those optimal ones only one solves the real problem situation. (Again, this does not deny that this optimum is achieved through different strategies).

Thanks for the reflection.

Best regards,

José Hernández.

I did not refer to the optimal *objective function* value - which is always unique - but to the case that the vector of optimal variable values x^*_j might be non-unique. It is very easy to illustrate the fact that the optimal values x_j, j=1, 2, 3, ..., n are not necessarily unique. Here is a link to an RG post with a simple example:

Article On the uniqueness of solutions to linear programs

In fact you can illustrate this in one dimension, or, trivially, max x_2 subject to 0

Dear Michael Patriksson, I think that now we agree.

Best regards,

José Hernández.

The best way to compare different optimization techniques is to provide the same initialization points and see how the final solution compares. Of course, each optimization strategy is best suited for certain class of problems and behave differently thus the reason they converge to different solutions. Michael Patriksson pretty much said it all

Again, greetings to all the esteemed colleagues who are followers of this question. Last week I submit to the Research Gate platform, the Spanish version and the English version of the work: Multicriteria models to evaluate social development projects [New version], what we assume may be in the interest of all of you.

I apologize to those who receive this information multiple times, since I am sending it to several questions related to the subject.

Thank you for your attention and I hope you find the information useful.

Best regards,

José Hernández.

https://www.researchgate.net/publication/330205251_Modelos_multicriterio_para_evaluar_proyectos_de_desarrollo_social_Nueva_version?_sg=-kvK9X0bzxMahqSlW07QkmzFnhDBAoWH5RgS2uwZvCOL_CMOE2P-9-0hA85EG7X4l-4GTMNWR2uMTJ5B8Ks5hxVMxEy9iULap7QfAfUz.SDl1CjD-_Gc_FAvKYD1YlNXOXTMLbA4_iR5GwJ4xApIdL-NR_6HdVD_kinFOZ7hC4_bsbjKiYmbltNswb_XAvg

https://www.researchgate.net/publication/330354600_Multicriteria_models_to_evaluate_social_development_projects_New_version_Modelos_multicriterio_para_evaluar_proyectos_de_desarrollo_social?_sg=-kvK9X0bzxMahqSlW07QkmzFnhDBAoWH5RgS2uwZvCOL_CMOE2P-9-0hA85EG7X4l-4GTMNWR2uMTJ5B8Ks5hxVMxEy9iULap7QfAfUz.SDl1CjD-_Gc_FAvKYD1YlNXOXTMLbA4_iR5GwJ4xApIdL-NR_6HdVD_kinFOZ7hC4_bsbjKiYmbltNswb_XAvg

Hi

Each of us seeks to achieve the best values ​​through the optimization algorithms and so we start compositions and change them to get what we should, those we get through these structures we integrate them with some.

Greetings