Harmony Search Applications in Mechanical, Chemical and Electrical Engineering - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 79

(vi) Feasible operating region
In combined heat and power (CHP) units the power capacity limits of units are func-
tions of the unit heat productions. Respectively the heat capacity limits are functions
of the unit power generations. Usually these constraints are expressed by a closed
boundary curve as shown in Fig. 6 (i.e. curve ABCDEFA).

Fig. 6. Feasible operation region for a typical cogeneration unit

3.2 Example of ED Problem

One of the most challenging ED problems is emerged in CHP systems. Cogeneration
systems have now been extensively utilized by the industry, because they offer a reli-
able, efficient and economic mean to supply both thermal and electrical energy. To
show the effectiveness of the HS algorithm in solving ED problems, a benchmark
problem is considered here.
This problem was originally proposed by Gou et al. [47]. The problem includes a
conventional power unit, two cogeneration units and a heat-only unit. The objective is
to find the minimum overall cost of units subject to constraints on heat and power
production. Table 4 presents the best solution of this problem obtained using the HS
algorithm and compares the HS results with those obtained from improved genetic al-
gorithm (IGA) [51], genetic algorithm [48], Lagrangian Relaxation (LR) [47], ant
colony search algorithm (ACSA) [49] and a hybrid of genetic algorithm with tabu
search (GT) [50].

Table 4. Optimal results for ED problem example

Algorithms Minimum Cost

LR [47] $9257.10

GA [48] $9267.20

ACSA [49] $9452.20

GT [50] $9207.64

IGA_ MU [51] $9257.07

HS $9186.97