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Table 3

Details of optimal for AS and algorithms for different values of probabilities and separately for each study area, and the difference between the results of the algorithm and the optimal results obtained from the LINGO software

AS
LINGO results
Diff (%)
Time-consuming
Probability exceedanceCanal bedCanal depthObjective functionCanal bedCanal depthObjective functionCanal bedCanal depthObjective functionAS & LINGO & LINGOASLINGO
First canal 0.01 6.95 3.72 20.061 6.97 3.68 19.765 7.00 3.67 19.724 1.71 0.21 0:04:04 0:03:46 0:08:45 
0.013 6.95 3.50 18.296 6.95 3.50 17.681 6.98 3.41 17.618 3.85 0.36 0:03:19 0:03:27 0:07:16 
0.02 6.73 3.16 15.294 6.71 3.16 15.266 6.71 3.15 15.187 0.70 0.52 0:04:23 0:04:14 0:07:08 
0.04 6.71 2.60 10.949 6.65 2.55 10.456 6.70 2.53 10.385 5.43 0.68 0:04:15 0:04:12 0:08:56 
0.1 6.45 2.00 6.323 6.33 2.00 6.094 6.30 2.00 6.039 4.70 0.91 0:04:23 0:03:50 0:07:48 
Second canal 0.01 8.81 4.90 13.785 8.97 4.81 13.327 9 4.79 13.241 4.11 0.65 0:04:01 0:03:09 0:07:25 
0.013 8.71 4.50 10.894 8.93 4.39 10.362 8.97 4.37 10.268 6.10 0.91 0:04:42 0:04:39 0:07:06 
0.02 8.66 4.10 8.049 8.90 3.99 7.549 8.94 3.97 7.473 7.71 0.14 0:04:34 0:04:22 0:08:02 
0.04 8.64 3.49 3.796 8.87 3.41 3.507 8.89 3.40 3.483 8.99 0.69 0:03:15 0:03:05 0:07:29 
0.1 8.60 3.19 1.669 8.77 3.13 1.564 8.80 3.12 1.557 7.10 0.45 0:04:18 0:03:50 0:08:29 
Third canal 0.01 10.90 4.06 43.458 10.93 4.04 43.139 11 4.01 42.770 1.61 0.86 0:04:36 0:04:35 0:08:05 
0.013 10.5 3.84 39.172 10.64 3.80 38.610 10.6 3.80 38.570 1.56 0.11 0:04:14 0:04:05 0:07:11 
0.02 10.45 3.50 33.152 10.43 3.50 33.126 10.49 3.47 32.660 1.51 1.43 0:04:20 0:04:17 0:08:44 
0.04 10.38 2.98 23.946 10.39 2.96 23.606 10.41 2.95 23.448 2.12 0.67 0:04:22 0:04:21 0:08:08 
0.1 10.36 2.57 16.746 10.38 2.55 16.419 10.37 2.55 16.408 2.06 0.07 0:04:38 0:04:29 0:07:48 
AS
LINGO results
Diff (%)
Time-consuming
Probability exceedanceCanal bedCanal depthObjective functionCanal bedCanal depthObjective functionCanal bedCanal depthObjective functionAS & LINGO & LINGOASLINGO
First canal 0.01 6.95 3.72 20.061 6.97 3.68 19.765 7.00 3.67 19.724 1.71 0.21 0:04:04 0:03:46 0:08:45 
0.013 6.95 3.50 18.296 6.95 3.50 17.681 6.98 3.41 17.618 3.85 0.36 0:03:19 0:03:27 0:07:16 
0.02 6.73 3.16 15.294 6.71 3.16 15.266 6.71 3.15 15.187 0.70 0.52 0:04:23 0:04:14 0:07:08 
0.04 6.71 2.60 10.949 6.65 2.55 10.456 6.70 2.53 10.385 5.43 0.68 0:04:15 0:04:12 0:08:56 
0.1 6.45 2.00 6.323 6.33 2.00 6.094 6.30 2.00 6.039 4.70 0.91 0:04:23 0:03:50 0:07:48 
Second canal 0.01 8.81 4.90 13.785 8.97 4.81 13.327 9 4.79 13.241 4.11 0.65 0:04:01 0:03:09 0:07:25 
0.013 8.71 4.50 10.894 8.93 4.39 10.362 8.97 4.37 10.268 6.10 0.91 0:04:42 0:04:39 0:07:06 
0.02 8.66 4.10 8.049 8.90 3.99 7.549 8.94 3.97 7.473 7.71 0.14 0:04:34 0:04:22 0:08:02 
0.04 8.64 3.49 3.796 8.87 3.41 3.507 8.89 3.40 3.483 8.99 0.69 0:03:15 0:03:05 0:07:29 
0.1 8.60 3.19 1.669 8.77 3.13 1.564 8.80 3.12 1.557 7.10 0.45 0:04:18 0:03:50 0:08:29 
Third canal 0.01 10.90 4.06 43.458 10.93 4.04 43.139 11 4.01 42.770 1.61 0.86 0:04:36 0:04:35 0:08:05 
0.013 10.5 3.84 39.172 10.64 3.80 38.610 10.6 3.80 38.570 1.56 0.11 0:04:14 0:04:05 0:07:11 
0.02 10.45 3.50 33.152 10.43 3.50 33.126 10.49 3.47 32.660 1.51 1.43 0:04:20 0:04:17 0:08:44 
0.04 10.38 2.98 23.946 10.39 2.96 23.606 10.41 2.95 23.448 2.12 0.67 0:04:22 0:04:21 0:08:08 
0.1 10.36 2.57 16.746 10.38 2.55 16.419 10.37 2.55 16.408 2.06 0.07 0:04:38 0:04:29 0:07:48 
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