In some practical problems, some equations which are valid under ideal conditions are problematic due to external influences. These equations can lead to large errors in the results. More accurate results can be obtained by removing these equations and using the other equations.
Are there any existing optimization algorithms that can achieve more accurate results by using only part of the equations (or serve a similar purpose)？
Based on my understanding of your question, I guess that if you don't think of using other approaches other than the equation that requires ideal constraints in order to work, then you need to adapt the optimization method that you choose to your problem, where you restrict the search space to those solutions that work well with this equation.
Dear Jizhou
I agree with Aymen, that is, work with what you have.
What if you add to your set of ideal equations other criteria that can reflect the intensity of external factors?
For example, one criterion or equation may refer to values of a series of products to export
There are external factors that you can't control, for instance, the international pricing of a commodity you are exporting.
Normally, you have acces to the seriers of values of this commodity alog time. Thus, work with both extreme values in the two new criteria and keep the old criterion as your information at present.
If you use the apprpriate MCDM method, it will work simultaneously with the three equations, and will find a balance.
Still, more complex, you can work with the utility curves of the three criteria,and the comparison will tell you probabilistically how much you can earn or lose.
Yes, there are optimization algorithms that consider the equation trade-off in an overdetermined system as an optimization parameter. These algorithms are designed to balance the number of equations with the number of variables to achieve a more robust solution.
These algorithms can be used to optimize the equation trade-off in an overdetermined system by adjusting parameters such as the regularization term or the reweighting scheme to achieve a more robust solution.
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