499
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501
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503
\ a +b - c
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509
= Net addition to the existing network due to new point ‘O’.
As seen above for the section A1O, A2O is the adding distances & A1A2 is the subtracting distance from the network, see [Fig.3]. We find this value for all segments
We repeat the process for new joined branches till we reach a network that looks like [Fig.4]
510
511
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521
Space for Fig. 4
522
523
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525
526
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531
The above network has following properties.
This is the shortest route or the optimal tour (local optimal tour) between the points on the network joined so far. No confusion about the term local optimal tour should stem out. This is the optimal tour for the points joined so far w.r.t. themselves but this is a local optimal tour w.r.t. the points all the points as better combination may exist between these and other points in the optimal tour. We would take this case under the heading virtual segments or hypothetical diagonals. The virtual segment case puts each point under testimony, and each point is considered vulnerable to a change in position,
after application of point to segment (Section 6.1) and segment to segment rule (Section 6.2).