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Table 3 Example solutions computed by phase 2

From: An algorithm for solving the bi-objective median path-shaped facility on a tree network

λkPath PD(P)Comment
 1\(\left \{\begin {array}{c}P_{v_{7},v_{12}} \\ P_{v_{7},v_{11}}\end {array}\right. \)\(\left \{\begin {array}{c}s^{3}=(169,474) \\ s^{1}=(131,689)\end {array}\right. \)\(\begin {array}{c}\textrm {Supported point lies in the first V.R.} \\ \textrm {Supported point lies in the first V.R.}\end {array}\)
\(\lambda =\frac {215}{253}\)2\(\left \{\begin {array}{c}P_{v_{6},v_{11}} \\ P_{v_{6},v_{12}}\end {array}\right. \)\(\left \{\begin {array}{c}s^{4}=(139, 676) \\ s^{5}=(177,461)\end {array}\right. \)\(\begin {array}{c}\textrm {Unsupported point lies in the first V.R.}\\ \textrm {Unsupported point lies out in the first V.R.}\end {array}\)
 3\(P_{v_{5},v_{12}}\)s6=(194,447)Unsupported point lies out in the first V.R.
 1\(P_{v_{1},v_{12}}\)s2=(219,350)Supported point lies in the second V.R.
\(\lambda =\frac {124}{174}\)2\(P_{v_{6},v_{12}}\)s5=(177,461)Unsupported point lies in the second V.R.
 3\(P_{v_{5},v_{12}}\)s6=(194,447)Unsupported point lies out in the second V.R.
 4\(P_{v_{2},v_{12}}\)(201,482)Dominated point lies out in the second V.R.