An Improved Geometric Programming Approach for Optimization of Biochemical Systems

Table 4

Comparisons between the proposed algorithm and the method in [14] for Case study 2.

Proposed method			[14]
Initial auxiliary; variable 𝑠𝑖^(0)	Iterations	Objective value	Initial auxiliary; variable 𝑡𝑖^(0)	Iterations	Objective value
1	5	1577.4227	0^b	—	—
1.1	5	1577.4227	0.1	15	1577.422623
1.2	5	1577.4227	0.2	15	1577.422627
1.3	5	1577.4227	0.3	15	1577.422632
1.4	5	1577.4227	0.4	15	1577.422625
1.5	5	1577.4227	0.5	15	1577.422626
1.6	5	1577.4227	0.6	15	1577.422629
1.7	5	1577.4227	0.7	15	1577.422629
1.8	5	1577.4227	0.8	15	1577.422625
1.9	5	1577.4227	0.9	15	1577.422631
1.99	5	1577.4227	0.99	15	1577.422630

bThe method in [14] does not allow 𝑡_𝑖⁽⁰⁾=0 (𝑖=2,3,5) because of the auxiliary variables 𝑡_𝑖>0 being imposed in the implementation of this algorithm.