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The initialization example reveals several important points.

(b) Initialization example for k-center with and without using k-means.

(a) Initialization example for k-means with and without using k-center.

Figure 3 Initialization examples for k -means and k -center.

The problem of getting stuck into local minima can be minimized by "good" initialization, for example, iterating the equalizer weights the minimum BER algorithm can be started from an initial weight vector obtained from the MMSE solution.

Since the results of using neutral initialization and inheritance initialization in data generation are very similar, we only show results with the neutral initialization model.

Ant Colony System works as follows: m ants are initially positioned on n nodes chosen according to some initialization rule, for example randomly.

Based on this observation, the best performance are obtained using hybrid algorithms combining probabilistic solution construction by a colony of ants with local search algorithms as 2 3 opt, tabu-search etc. m ants are initially positioned on n nodes chosen according to some initialization rule, for example randomly.

Table 3 Initialization population No. Example of heuristic initialization z 1 z 2 z 3     1 First edge is removed z 2 z 3       2 Second edge is removed z 1 z 3       3 Third edge is removed z 1 z 2       4 One edge is randomly added z 1 z 2 z 3 A   5 Two edges is randomly added z 1 z 2 z 3 B C. Next, the first objective function is calculated based on (1) for each initial population.

An example graph initialization is shown in Figure  1.

A more explicit example for an initialization is: In contrast to a's data type which is integer we enforce the distributed_data_object to be complex.