Harmony Search Applications in Mechanical, Chemical and Electrical Engineering - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 81

cuts are used to complete the part and achieve the final dimension, tolerances, and
surface smoothness. In production machining jobs, one or more roughing cuts are
usually performed on the work, followed by one or two finishing cuts. The total pro-
duction cost ( C T ) for multi-pass milling is expressed as:

n

∑
=

C = C + C + C

(10)

T f ri tp

i 1

where C f is the cost of the finishing pass, C ri is the cost of the i th roughing pass, and
C tp is the cost of tool preparation. The objective function, Eq. (10), is subjected to
various constraints such as tool-life, available cutting speeds, surface roughness, and
cutting power.

4.2 Example of Machining Process

An illustrative example is used to demonstrate the ability of the HS algorithm for
solving machining optimization problems. For validation purpose, GA is also used to
solve this problem. The data for this problem are available from Zarei et al. [58].
Table 5 shows the best HS and GA results for a total cutting depth of 8 mm.

Table 5. Optimal results for machining process example

Cost per pass

Total Cost
GA $0.5366 $0.3716 $0.5047 $1.4129
HS $0.4446 $0.4446 $0.5047 $1.3939
Both HS and GA find the solutions with three passes (two rough passes and a fin-
ish pass). It can be seen from the results that the total cost obtained from HS is lower
than GA.

Algorithms

1 st 2 nd 3 rd

5 Conclusions

Three types of engineering optimization problems were studied in this chapter. The
first type is related to the design optimization of thermal systems; the second type
concerns the economic utilization of electric power systems; and the third deals with
the selection of cutting parameters in machining process. The ability of the HS algo-
rithm was demonstrated using several test problems and its performance was compared
with other conventional methods. The results reveal that HS outperforms other ap-
proaches not only in terms of the quality of the obtained solutions but also in terms of
the elapsed computational time. Generally, it can be concluded that the HS simplicity
of implementation, good computational efficiency, high quality solution, along with
the lower number of setting parameters makes it an ideal method when dealing with
complex engineering optimization problems. Future research can be directed towards
HS implementation in diverse areas of mechanical/chemical/electrical engineering
fields such as synthesis of heat exchanger networks, utilization of distributed
generation sources (i.e. photovoltaic and pump storage generators) and more.