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. Author manuscript; available in PMC: 2022 Jun 16.
Published in final edited form as: Ind Eng Chem Res. 2021 Jun 4;60(23):8493–8503. doi: 10.1021/acs.iecr.1c01175

Table 4:

Optimal solution and Critical Region definition of Problem (7).

Critical Region Definition Optimal Binary Solution Objective Function
CR1 2.800 ≤ ≤ 3.044 y = [0 0 0 1 0 0 1]T f1 = 272.6 + 9, 930.7 f2 =
CR2 3.044 ≤ ≤ 3.080 y = [0 0 0 1 0 0 1]T f1 = 10,671 f2 = 3.080
CR3 3.080 ≤ ≤ 3.960 y = [0 0 0 1 0 0 1]T f1 = 454.4 + 9, 360.8 f2 =
CR4 3.960 ≤ ≤ 6.660 y = [0 0 0 1 0 1 1]T f1 = 124.63 + 10, 931 f2 =
CR5 6.660 ≤ ≤ 6.735 y = [0 0 0 1 0 1 1]T f1 = 11, 761 f2 = 6.735
CR6 6.735 ≤ ≤ 8.660 y = [0 0 0 1 0 1 1]T f1 = 207.8 + 10, 361 f2 =
CR7 8.660 ≤ ≤ 16.580 y = [1 0 0 0 1 1 1]T f1 = 16, 478 f2 = 16.580
CR8 16.580 ≤ ≤ 17.065 y = [1 0 0 0 1 1 1]T f1 = 2, 476.8 − 24.589 f2 =
CR9 17.065 ≤ ≤ 18.454 y = [1 0 0 1 1 1 1]T f1 = 17, 678 f2 =
CR10 18.454 ≤ ≤ 20.196 y = [1 0 0 1 1 1 1]T f1 = 229.6 + 13, 342 f2 =
CR11 20.196 ≤ ≤ 20.240 y = [1 0 0 1 1 1 1]T f1 = 18, 078 f2 =
CR12 20.240 ≤ ≤ 21.283 y = [1 0 0 1 1 1 1]T f1 = 382.8 + 10, 332 f2 =
CR13 21.283 ≤ ≤ 23.461 y = [1 0 0 1 1 1 1]T f1 = 2,476.8 − 34, 236 f2 =
CR14 23.461 ≤ ≤ 25.872 y = [1 0 0 1 1 1 1]T f1 = 4, 828.6 − 89, 389 f2 =