Most important steps in proposed meta-heuristic techniques is the evaluation of the obtained solutions. In this step, the goodness (or fitness) of the solution is calculated, and based on the result, the solution may be deleted, kept, or marked as good. The TS algorithm maintains a tabu list to track the already evaluated solutions and tracks the ever best solution found in the process of execution. SA procedure also keeps the record of best solution encountered accordingly with the temperature reducing function. When a new solution is obtained, the goodness (fitness) function is applied, and based on the result, algorithms decide to add the solution to the elite list, or omit the solution and generate another one. During the TS and SA
iterations, the goodness of each solution is calculated using equation (1) which is the objective function and performance measure as well.

Similarity coefficient based techniques are massively practiced in formation of manufacturing cells over the last few decades (Yin and Yasuda, 2005). In this article Complete Linkage (C-Linkage) technique is used along with a similarity metric method to generate a quick solution. When this technique develops the feasible solution to form initial part families, generation of initial solution is therefore accomplished.

3.4.1.

 Similarity metric for part family formation In this research a similarity measure method based on part family identification technique is utilized
(Offodile, 1992). It is presented as,

$$S_{i j}={\frac{\sum_{k=1}^{K}S_{i j k}}{K}}$$  $$S_{i j k}=1-{\frac{\left|b_{i k}-b_{j k}\right|}{R_{k}}}$$
$$\mathrm{(2)}$$

$$\mathrm{(3)}$$

Where Where Sijk is Similarity measured between part i and part j on attribute k ,
K is total number of attributes considered, b ik is part coding for part i on attribute k ,
b jk is part coding for part j on attribute k ,
R k is range of possible part codings for all parts on attribute k .

Therefore sum of similarities is derived using the formula,

$$\left({}^{4}\right)$$

Where

$$f=\sum_{n=1}^{N}S_{n}$$

$S_{n}=\frac{\sum_{i\in n,j\in n}S_{ij}}{0.001+C_{2}^{Pn}}$
$$\quad(5)$$

where S ij = similarity measure between part i and part j C P = Number of pair-wise combinations formed in part family n , and P n is the number of parts in family n (in the denominator a small value of 0.001 is added to avoid the division by zero rule).

In order to facilitate the computation in Matlab the similarity matrix obtained using equation (2)
further transformed into distance matrix using equation (5).