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I am implementing a code that would like to sort some objects.

Each object has 5 attributes, which some of them I would like to maximize and at the same time minimize others attributes. Consider that I have the following attributes: $a$, $b$, $z$, $w$, and $y$. I would a function that returns a value $v$ that maximize $a$ and $b$ values and minimize $z$, $w$, and $y$. That is, a function $f(a, b, z, w, y) = v$.

For instance, I would like a to do a balance between these values. For my application, sometimes it is better to choose an object that has high $a$ and $b$ values. However, sometimes it is better to choose an object that has low $z$, $w$, and $y$ values.

Any recommendation, tip to do it?

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    You typically want to optimize $v$ (max or min) with respect to the features - where we can use weights to adjust the combinations to your desire. This is a classical setting for optimization an objective. If the features are independent, then you can create rankings for each column and then combine them with some heuristic rule - but the beauty of this is that you can rank $a,b$ and $c,z,w$ and $y$ accordingly. – 2017-02-13
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    @Chinny84 I think I understood your idea. But, in this case I would like to "transform" all the features into a value $v$. Does it make sense if I sum/multiple the variables that I would like to maximize ($a$ and $b$) and then subtract the variables that I would like to minimize ($z$, $w$, and $y$)? That is, $f(a, b, z, w, y) = v = a * b - (z + w + y)$ – 2017-02-13
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    Well depending on the sizes of these features then probably not - you may not have any dependence on the sum and instead all dependence of z comes from the multiple. If you could reframe your problem to state some notation of what the variables are .. – 2017-02-13
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    $a$ is an variable to indicate the number of modifications of an object; $z$ is when the last modification was done; $w$ and $y$ are quantity variables about the characteristics of the object; $b$ is more like a weight, which means that we have preference for high $b$ values. Perhaps, we can change the $f$ to $(a - (z + w + y)) * b$. My problem is that: I would like to pick objects with higher number of modifications but with old modifications (i.e., a small $z$ value). In addition, I would prefer objects with $w$ and $y$ that are very small. In this case, $b$ is like an intensifier. – 2017-02-13
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    @Chinny84 do you think that an implementation of a Multi-objective optimization would help me? I did not completely understand this concept or how to develop my problem using this concept, but I think the idea of "tradeoffs" fits with the multi-objective optimization. – 2017-02-14

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