Table 36 CI–SAPF results solving linear and nonlinear problems

From: Cohort intelligence with self-adaptive penalty function approach hybridized with colliding bodies optimization algorithm for discrete and mixed variable constrained problems

Sr. No Test functions Solver Search space Function Value Optimum variables
Lower limit Upper limit
1 Dynamic problem (Maximization) Srivastava and Fahim [82] [0, 0, 0] [10, 10, 10] 16 [0, 1, 2]
CI–SAPF 16 [0, 1, 2]
CI–SAPF–CBO 16 [0, 1, 2]
CBO 15 [0, 2, 1]
2 Transportation problem Srivastava and Fahim [82] [0,…,0] [100,…,100] 40.5 [5, 15, 0, 0, 0, 15, 0, 5, 5]
CI–SAPF 40.8 [2,18, 0, 3, 0,12, 0, 2]
CI–SAPF–CBO 40.8 [2,18, 0, 3, 0,12, 0, 2]
3 Multistage oroblem (Maximization) Srivastava and Fahim [82] [0,0,0] [100,100,100] 55.2 [3, 1, 0]
CI–SAPF 55.2 [3,1,0]
CI–SAPF–CBO 55.2 [3,1,0]
CBO 32.7 [0,1,1]
4 Rosen-Suzuki test problem convex programming problem (Minimization) Srivastava and Fahim [82] [− 10,− 10,− 10,− 10] [20, 20, 20, 20] 44 [0,1, 2,- 1]
CI–SAPF − 44 [0,1, 2,− 1]
CI–SAPF–CBO − 44 [0, 1, 2, − 1]
CBO − 32 [− 1, 1, 2, 0]
5 Knapsack problem (maximization) Srivastava and Fahim [82] [0,…,0] [100,…,100] 19,979 [32, 2, 1, 0, 0, 0, 0]
CI–SAPF 20,059 [16, 18, 9, 0, 2, 8,0 ]
CI–SAPF–CBO 20,240 [27, 3, 4, 4, 8, 1, 5]
CBO 18,428 [16, 10, 8, 0, 19, 8, 38]
6 Integer linear problem
(a) (maximization)
Srivastava and Fahim [82] [0,…,0] [200,…,200] 316 [4, 87, 34, 149, 0]
CI–SAPF 1037 [200, 199, 67, 104, 0]
CI–SAPF–CBO 1040 [200, 200, 67, 106, 0]
CBO 393 [111, 138, 27, 0,136]
7 (b) (Maximization) Srivastava and Fahim [82] [0, 0] [100,1 00] 33 [3,6]
CI–SAPF 33 [3,6]
CI–SAPF–CBO 33 [3,6]
CBO 33 [3,6]
8 Non-convex Integer problem (formulation 1) Tsai et al. [89] [1, 1, 1] [5, 5, 5] 75.7579 [1, 2, 5]
CI–SAPF − 75.7579 [1, 2, 5]
CI–SAPF–CBO − 75.7579 [1, 2, 5]
CBO − 75.7579 [1, 2, 5]
(formulation 2) Tsai et al. [89] [0, 0, 0] [5, 5, 5] 125 [5, 4, 0]
CI–SAPF − 328.3159 [0, 5, 5]
CI–SAPF–CBO − 328.3159 [0, 5, 5]
CBO − 131.3264 [0, 2, 5]
9 Global nonlinear mixed
discrete programming
Tsai et al. [89] [3, 3] [6, 5] 246 [5, 4]
CI–SAPF − 275 [5, 5]
CI–SAPF–CBO − 275 [5, 5]
CBO − 275 [5, 5]
10 Three-bar truss design problem Shin et al. [80] [0.1, 0.2, 0.3, 0.5, 0.8, 1.0, 1.2] 3.0414 [1. 2, 0.5, 0.1]
CI–SAPF 3.0414 [1.2, 0.5, 0.1]
CI–SAPF–CBO 3.0414 [1.2, 0.5, 0.1]
CBO 3.0414 [1.2, 0.5, 0.1]
11 Monotone functions Lawler and Bell [53] [0, 0, 0, 0, 0] [3, 3, 3, 3, 3] 8 [1, 1, 1, 1, 2]
CI–SAPF 16 [1, 1, 2, 1, 3]
CI–SAPF–CBO 16 [1, 1, 2, 1, 3]
CBO 16 [1, 1, 2, 1, 3]
12 Lawler and Bell [53] [0, 0, 0, 0, 0, 0, 0] [7, 7, 7, 15, 15, 7, 15] 16 [1, 4, 1, 0, 2, 1, 2]
CI–SAPF 14 [0, 2, 4, 0, 2, 1, 6]
CI–SAPF–CBO 14 [0, 2, 4, 0, 2, 1, 6]
CBO 22 [2, 3,1, 1, 2, 1, 2]
13 Lawler and Bell [53] [0,0,0,0,0,0,0] [7,7,7,15,15,7,15] 10 [0,6,0,1,1,1,1]
CI–SAPF 11 [1,3,2,1,1,1,2]
CI–SAPF–CBO 11 [2,4,0,1,1,1,2]
14 Lawler and Bell [53] [0, 0, 0, 0, 0, 0, 0] [7, 7, 7, 15, 15, 7, 15] 46 [0, 7, 0, 0, 0, 2, 1]
CI–SAPF 92 [2,4, 0, 0, 1, 2, 2]
CI–SAPF–CBO 92 [2,4, 0, 0, 1, 2, 2]
15 Lawler and Bell [53] [0, 0, 0, 0, 0, 0, 0] [7, 7, 7, 15, 15, 7, 15] 25 [1, 4, 1, 1, 1, 1, 2]
CI–SAPF 21 [2,3, 1, 1, 1, 1, 2]
CI–SAPF–CBO 21 [2, 3, 1, 1, 1, 1, 2]
16 Lawler and Bell [53] [0, 0, 0, 0, 0, 0, 0] [7, 7, 7, 15, 15, 7, 15] 1000 [0, 7, 0 ,0, 0, 2,1]
CI–SAPF 1331 [1, 3, 2, 1, 1, 1, 2]
CI–SAPF–CBO 1331 [1, 3, 2, 1, 1, 1, 2]