>for each of those there is a best solution. This isn't necessarily true. For instance, if A and B are each measurable characteristics of potential solutions a

>for each of those there is a best solution. This isn't necessarily true. For instance, if A and B are each measurable characteristics of potential solutions and your goal values A and B equally, if all other characteristics of solutions X and Y are equal, but X={A:2, B:7, ...} and Y={A:7, B:2, ...}, then X and Y are equally "good" solutions according to your goal.