What do you mean by saying “targeted minimum”?

If it is the global minimum, then the optimizer will not see that point, and thus it will converge to the closest point.

If it is the value that you are targetting for (i.e., you want to reach that value), then you are defining an equality constraint in your model. Thus, the optimization algorithm will not reach that point because its search space doesn’t contain that point. This means that if you are initiating your optimizer using a while-loop with a stopping criteria, then the algorithm will have infinite number of iterations (i.e., it will run forever without stopping).

What do you mean by saying “targeted minimum”?

If it is the global minimum, then the optimizer will not see that point, and thus it will converge to the closest point.

If it is the value that you are targetting for (i.e., you want to reach that value), then you are defining an equality constraint in your model. Thus, the optimization algorithm will not reach that point because its search space doesn’t contain that point. This means that if you are initiating your optimizer using a while-loop with a stopping criteria, then the algorithm will have infinite number of iterations (i.e., it will run forever without stopping).

Thanks Ali R. Al-Roomi . Yes, it is the global optimal value (22).

Does " converge" mean the optimizer will choose the closest feasible point upper 20 ( which we assume 20>= 22 )automatically without have to enlarge the upper bound?

The mathematical model is divided into two parts:

1) objective function

2) design constraints

The second part is divided into two sub-parts:

a) side constraints (also called variable bounds, limits, domain, search space, etc)

b) functional constraints

The second sub-part is divided into two sub-sub-parts:

i) equality constraints

ii) inequality constraints

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As you can see, the objective function is different than the side constraints. You, as a designer, have to define the variable bounds (i.e., the lower and upper limits of the independent variables that need to be optimized). The lower and upper limits of the objective function are automatically defined based on the variable bounds you have defined before.

If you want to define your own lower and upper bounds on the objective function, then these are not side constraints. Instead, you have to treat them as inequality constraints. From its name, objective function, it is a function of one or more independent variables. This phenomenon is frequently seen in the topic of "optimal coordination of directional overcurrent relays" where the operating time of a relay (which is a function of pick-up and time-dial settings) should not less than the minimum operating time of the device and not more than the critical clearing time of circuit breaker to preserve the system stability.

Hi Shrouq Gamal

The closest point is the most optimal point available in the user-defined search-space. We're not saying global optima, because - from the question - the user wants to modify the original lower and upper bounds. This point can also be called the modified or feasible global optima since the original global optima become infeasible within the new cropped search-space.

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Regarding the best meta-heuristic optimization algorithm, no one can give you an exact answer! Algorithm X could be the best choice for some types of problems and/or under some specific conditions, and algorithm Y could win if it is applied to other problems and/or under different conditions. It is better to read about "No Free Lunch Theorem".

Regards,

Ali