38.

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Page 131

Figure 3.14 A Hopfield network constructed of a set of 4×4 neurones to solve the travelling salesman problem. See text for details.

3 All the cities must be visited which means the total number of active units m must be equal to the total number of cities (in our case, m=4).

According to constraint condition (1), one can code the constraint element of energy E₁ as:

(3.38)

where v_Xi denotes output neurones at location (X, i), i.e. city X and visit sequence i. Constraint (2) can be coded in a similar way as:

(3.39)

The third constraint can be expressed as

(3.40)

The objective part of the energy function, denoted by E₄, can be coded as:

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