Composite objectives

Often we use a composite objective, built from two simple objectives A and B. Then we write A***B for the composite. The general meaning is: Take the winners under objective A, and apply objective B to them,

some examples from the shopping mall:

A | B | A***B |
---|---|---|

select all the red dresses | the cheapest dress | the cheapest red dress |

the 10 cheapest dresses | select all the red dresses | red dresses among the 10 cheapest, if any |

simply the best | select all the prices | the best together with its price |

The first two examples show that A***B can be different from B***A.

The third example shows that objectives like select all
the scores (rather than choosing one or a few) can make a lot of sense when combined with other objectives.