1.4 Statement of an Optimization Problem 7
Figure 1.3 Gear pair in mesh.
thedesign variable spaceor simplydesign space. Each point in then-dimensional
design space is called adesign pointand represents either a possible or an impossible
solution to the design problem. In the case of the design of a gear pair, the design
point{ 1. 0 , 20 , 40 }T, for example, represents a possible solution, whereas the design
point{ 1. 0 ,− 20 , 40. 5 }Trepresents an impossible solution since it is not possible to
have either a negative value or a fractional value for the number of teeth.
1.4.2 Design Constraints
In many practical problems, the design variables cannot be chosen arbitrarily; rather,
they have to satisfy certain specified functional and other requirements. The restrictions
that must be satisfied to produce an acceptable design are collectively calleddesign
constraints. Constraints that represent limitations on the behavior or performance of
the system are termedbehavior orfunctional constraints. Constraints that represent
physical limitations on design variables, such as availability, fabricability, and trans-
portability, are known asgeometricorside constraints. For example, for the gear pair
shown in Fig. 1.3, the face widthbcannot be taken smaller than a certain value, due
to strength requirements. Similarly, the ratio of the numbers of teeth,T 1 /T 2 , is dictated
by the speeds of the input and output shafts,N 1 andN 2. Since these constraints depend
on the performance of the gear pair, they are called behavior constraints. The values
ofT 1 andT 2 cannot be any real numbers but can only be integers. Further, there can
be upper and lower bounds onT 1 andT 2 due to manufacturing limitations. Since these
constraintsdepend on the physical limitations, they are called sideconstraints.
