163
tion systems work that way, but it is not a good idea because there
is no guidance in deciding the relative importance of the limits on
stiffness, strength, weight, and cost. This is not a trivial difficulty; it
is exactly this relative importance that makes aluminum the prime
structural material for aerospace and steel that for ground-based
structures.
These problems of relative importance are old; engineers have
sought methods to overcome them for at least a century. The traditional approach is that of assigning weight factors to each constraint and objective and using them to guide choice in ways that
are summarized in the following discussion. Experienced engineers
can be good at assessing relative weights, but the method nonetheless relies on judgment, and judgments can differ. For this reason,
this section focuses on systematic methods. But one should know
about the traditional methods because they are still widely used.
We start with them.
the Method of Weight Factors
Weight factors seek to quantify judgment. The method works like
this: The key properties are identified and their values M i are tabulated for promising candidates. Since their absolute values can differ
widely and depend on the units in which they are measured, each
is first scaled by dividing it by the largest value of its group, (M i ) max ,
so that the largest, after scaling, has the value 1. Each is then multiplied by a weight factor, w i , with a value between 0 and 1, expressing its relative importance for the performance of the component.
This give a weighted index W i :
W w
M
M
i
i
i
i
= ( ) min
(5.5)
For properties that are not readily expressed as numerical values,
such as weldability or wear resistance, rankings such as A to E are
expressed instead by a numeric rating, A = 5 (very good) to E =
1 (very bad), then dividing by the highest rating value as before.
For properties that are to be minimized, such as corrosion rate,
scaling uses the minimum value (M i ) min , expressed in the form
W w
M
M
i
i
i
i
=
( ) min
(5.6)
The weight factors w i are chosen such that they add up to 1, that is,
w i < 1 and Σw i = 1. There are numerous schemes for assigning their
values (see Further Reading); all require, in varying degrees, the use
Resolving Conflicting Objectives
tion systems work that way, but it is not a good idea because there
is no guidance in deciding the relative importance of the limits on
stiffness, strength, weight, and cost. This is not a trivial difficulty; it
is exactly this relative importance that makes aluminum the prime
structural material for aerospace and steel that for ground-based
structures.
These problems of relative importance are old; engineers have
sought methods to overcome them for at least a century. The traditional approach is that of assigning weight factors to each constraint and objective and using them to guide choice in ways that
are summarized in the following discussion. Experienced engineers
can be good at assessing relative weights, but the method nonetheless relies on judgment, and judgments can differ. For this reason,
this section focuses on systematic methods. But one should know
about the traditional methods because they are still widely used.
We start with them.
the Method of Weight Factors
Weight factors seek to quantify judgment. The method works like
this: The key properties are identified and their values M i are tabulated for promising candidates. Since their absolute values can differ
widely and depend on the units in which they are measured, each
is first scaled by dividing it by the largest value of its group, (M i ) max ,
so that the largest, after scaling, has the value 1. Each is then multiplied by a weight factor, w i , with a value between 0 and 1, expressing its relative importance for the performance of the component.
This give a weighted index W i :
W w
M
M
i
i
i
i
= ( ) min
(5.5)
For properties that are not readily expressed as numerical values,
such as weldability or wear resistance, rankings such as A to E are
expressed instead by a numeric rating, A = 5 (very good) to E =
1 (very bad), then dividing by the highest rating value as before.
For properties that are to be minimized, such as corrosion rate,
scaling uses the minimum value (M i ) min , expressed in the form
W w
M
M
i
i
i
i
=
( ) min
(5.6)
The weight factors w i are chosen such that they add up to 1, that is,
w i < 1 and Σw i = 1. There are numerous schemes for assigning their
values (see Further Reading); all require, in varying degrees, the use
Resolving Conflicting Objectives