Comparison of Results on the 2017 CEC Competition on Constrained Real Parameter Optimization
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1 Comparison of Results on the 07 CEC Competition on Constrained Real Parameter Optimization GuohuaWu, R. Mallipeddi, P. N. Suganthan National University of DefenseTechnology, Changsha, Hunan, P.R. China Kyungpook National University, Daegu, South Korea Nanyang Technological University, Singapore
2 The 8 benchmarked constrained optimization problems can be transformed into the following format: Reference: f ( X ), X ( x, x,..., x n ) and X S Minimize: Subject to: g ( X ) 0, i,..., p i () h ( X ) 0, j p,..., m () j Equality constraints are transformed into inequalities of the form h ( X) 0, for j p,..., m (3) j Solution X is regarded as feasible if g ( X ) 0, i,..., p and h ( X) 0, for j p,..., m ( =0.000 j i ). GuohuaWu, R. Mallipeddi, P. N. Suganthan, "Problem Definitions and Evaluation Criteria for the CEC 07 Competition and Special Session on Constrained Single Objective Real-Parameter Optimization", Technical Report, NanyangTechnological University, Singapore, December 06.
3 Problem Properties Problem/Search Range Type of Objective Number of Constraints E I C0 Non Separable 0 [-00,00] D Separable C0 Non Separable, Rotated 0 [-00,00] D Non Separable, Rotated C03 Non Separable [-00,00] D Separable Separable C04 Separable 0 [-0,0] D Separable C05 Non Separable 0 [-0,0] D Non Separable, Rotated C06 0 Separable 6 [-0,0] D Separable C07 Separable [-50,50] D Separable 0 C08 Separable [-00,00] D Non Separable 0 C09 Separable [-0,0] D Non Separable 0
4 Problem Properties Number of Constraints Problem/Search Range Type of Objective E I C0 Separable 0 [-00,00] D Non Separable C Separable [-00,00] D Non Separable Non Separable C Separable 0 [-00,00] D Separable C3 3 Non Separable 0 [-00,00] D Separable C4 Non Separable [-00,00] D Separable Separable C5 Separable [-00,00] D C6 Separable [-00,00] D Non Separable Separable C7 Non Separable [-00,00] D Non Separable Separable C8 Separable [-00,00] D Non Separable
5 Problem Properties Number of Constraints Problem/Search Range Type of Objective E I C9 Separable 0 [-50,50] D Non Separable C0 Non Separable 0 [-00,00] D C Rotated 0 [-00,00] D Rotated C 3 Rotated 0 [-00,00] D Rotated C3 Rotated [-00,00] D Rotated Rotated C4 Rotated [-00,00] D Rotated Rotated C5 Rotated [-00,00] D Rotated Rotated C6 Rotated [-00,00] D Rotated Rotated C7 Rotated [-00,00] D Rotated Rotated C8 Rotated 0 [-50,50] D Rotated
6 Evaluation Criteria () Rank all algorithms on one problem with multiple runs The procedure for ranking algorithms based on mean values: Rank the algorithms based on feasibility rate; Then rank the algorithms according to the mean violation amounts; 3 At last, rank the algorithms in terms of mean objective function value. The procedure for ranking the algorithms based on the median solutions: A feasible solution is better than an infeasible solution; Rank feasible solutions based on their objective function values; 3 Rank infeasible solutions according to their constraint violation amounts.
7 Evaluation Criteria () Rank all algorithms on multiple problems For each problem, algorithm ranks are determined in terms of the mean values and median solutions at the maximum allowed number of evaluations, respectively. The total rank value of each algorithm is calculated as below. 8 8 Rank value = rank (using mean value) rank (using median solution) i i i i
8 Algorithms CAL-SHADE LSHADE44 + IDE LSHADE44 UDE Ales Zamuda. Adaptive Constraint Handling and Success History Differential Evolution for CEC 07 Constrained Real-Parameter Optimization, CEC 07 Josef Tvrdik and Radka Polakova. A Simple Framework for Constrained Problems with Application of L-SHADE44 and IDE, CEC 07 Radka Polakova. L-SHADE with Competing Strategies Applied to Constrained Optimization, CEC 07 AnupamTrivedi, Krishnendu Sanyal, PranjalVerma and Dipti Srinivasan. A Unified Differential Evolution Algorithm for Constrained Optimization Problems, CEC 07
9 Table Ranks based on mean values on the 8 functions of 0 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
10 Table Ranks based on median solution on the 8 functions of 0 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
11 Table 3 Ranks of the four methods on problems of 0 dimensions based on mean value and median solution CAL-SHADE LSHADE44 + IDE LSHADE44 UDE Total rank values Rank 4 3
12 Table 4 Ranks based on mean values on the 8 functions of 30 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
13 Table 5 Ranks based on median solution on the 8 functions of 30 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
14 Table 6 Ranks of the four methods on problems of 30 dimensions based on mean value and median solution CAL-SHADE LSHADE44 + IDE LSHADE44 UDE Total rank values Rank 4 3
15 Table 7 Ranks based on mean values on the 8 functions of 50 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
16 Table 8 Ranks based on median solution on the 8 functions of 50 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
17 Table 9 Ranks of the four methods on problems of 50 dimensions based on mean value and median solution CAL-SHADE LSHADE44 + IDE LSHADE44 UDE Total rank values Rank 4 3
18 Table 0 Ranks based on mean values on the 8 functions of 00 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
19 Table Ranks based on median solution on the 8 functions of 00 dimensions Problems CAL- SHADE LSHADE44 + IDE LSHADE UDE
20 Table Ranks of the four methods on problems of 00 dimensions based on mean value and median solution CAL-SHADE LSHADE44 + IDE LSHADE44 UDE Total rank values Rank 4 3
21 Table 3 Ranks of the four methods on problems of all considered dimensions CAL-SHADE LSHADE44 + IDE LSHADE44 UDE Total rank values Rank 4 th 3 rd st nd
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