Harmony Search Applications in Mechanical, Chemical and Electrical Engineering - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 75

This problem was formulated as an unconstrained, multiple-objective optimization
problem having five continuous design variables:

GL L t t T (, , , , ) − G

*

M L L t t (, , , ) − M

*

f c f b p f c f b

min Z = +

(1)

* *

G M

where G is the thermal conductance; M is the mass; and G * and M * are the optimal
values of G and M determined by optimizing each function separately. The result ob-
tained using HS is compared with those of Broyden-Fletcher-Goldfarb-Shanno
(BFGS) [27] in Table 3.

Table 3. Optimal results for satellite heat pipe design example

Algorithms G (W/K) M (kg)
BFGS 0.3750 26.854
HS 0.3810 26.704
As seen from Table 3, HS can find better solutions compared to those of gradient-
based technique BFGS. The mass obtained by HS is 0.6% lower while thermal con-
ductance by HS is 1.6% higher, when compared with BFGS.

3 Economic Power Dispatch

Economic dispatch is the method of determining the most efficient, low-cost and reli-
able operation of a power system by dispatching the available electricity generation
resources to supply the load on the system. The primary objective of economic dis-
patch is to minimize the total cost of generation while honoring the operational con-
straints of the available generation resources [28].
Various mathematical programming methods such as linear programming, homoge-
nous linear programming, and nonlinear programming [29-34] have been applied so far
for solving the ED problems. These methods use gradient information to search solution
space near an initial starting point. In general, gradient-based methods converge faster
and can obtain solutions with higher accuracy compared to stochastic approaches in ful-
filling the local search task. However, for effective implementation of these methods,
the variables and cost function of the generators need to be continuous. Furthermore, a
good starting point is crucial for these methods to function successfully. In a realistic
operation, to provide completeness for the ED problem formulation, prohibited operat-
ing zones, ramp-rate limits, and non-smooth or non-convex cost functions arising due to
the use of multiple fuels should be considered. The resulting ED formulation is a non-
convex optimization problem, which is a challenging one and cannot be solved by the
traditional mathematical programming methods. Therefore, dynamic programming [35]
and mixed integer nonlinear programming [36], and their modifications have been