A Passenger-Oriented Optimization Model for Implementing Energy-Saving Strategies in Railway Contexts
Abstract
:1. Introduction
2. Literature Review
3. The Proposed Methodology
3.1. Optimization Problem Formulation
3.2. Theoretical Properties of the Optimization Problem
- Objective function is defined in a non-empty and compact (i.e., closed and limited) set;
- Objective function is continuous in its definition set, that is:
- according to a non-decreasing function (since an increase in provides an increase in corresponding layover time which may imply an increase in running times);
- according to a non-increasing function (since an increase in provides a decrease in corresponding layover time which may imply a decrease in running times);
- according to a strictly decreasing function (since an increase in provides an increase in corresponding layover time which allows a reduction in energy consumption);
- according to a strictly increasing function (since an increase in provides a decrease in corresponding layover time which limits reductions in energy consumption).
- Objective functions and are defined in nonempty and compact (i.e., closed and limited) sets;
- Objective functions and are continuous in their definition sets, that is:
3.3. Solution Algorithm Development
- A master algorithm for solving the upper level;
- A slave algorithm for solving the lower level.
- Approach 1 (see Figure 2), where running times and energy consumptions are calculated by a train movement simulator at any iteration of the slave algorithm;
- Approach 2 (see Figure 3), where all feasible speed profiles are preliminary calculated by a train movement simulator and all results in terms of running times and energy consumption are collected in a performance matrix. In this case, the slave algorithm queries the performance matrix without the need of implementing again the train movement simulator.
3.3.1. The Proposed Master Algorithm
- Phase 1: Definition of the initial analysis set;
- Phase 2: Partition of the analysis set;
- Phase 3: Objective function calculation;
- Phase 4: Identification of the optimal solution;
- Phase 5: Stop test or definition of a new analysis set.
3.3.2. The Proposed Slave Algorithm
- Phase 1: Definition of the initial value of the speed limits;
- Phase 2: Calculation of the subsequent Total Running Times;
- Phase 3: Stop test or definition of new speed limits.
4. Application to a Real Network
5. Conclusions and Research Prospects
Author Contributions
Funding
Conflicts of Interest
References
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Values | ||
---|---|---|
Naples-Sorrento Direction | Sorrento-Naples Direction | |
Total Running Times | 3262 s [54.4 min] | 3220 s [53.7 min] |
Total Dwell Times | 1080 s [18.0 min] | 1080 s [18.0 min] |
Inversion times | 180 s [3.0 min] | 180 s [3.0 min] |
Buffer times [90th percentile] | 225 s [3.8 min] | 228 s [3.8 min] |
Planned Cycle Time [90th percentile] | 9455 s [157.6 min] | |
Buffer times [95th percentile] | 252 s [4.2 min] | 253 s [4.2 min] |
Planned Cycle Time [95th percentile] | 9507 s [158.5 min] | |
Buffer times [97.5th percentile] | 275 s [4.6 min] | 275 s [4.6 min] |
Planned Cycle Time [97.5th percentile] | 9552 s [159.2 min] | |
Minimum headways | 374 s [6.2 min] | 359 s [6.0 min] |
Travel distance | 42.6 km | 42.6 km |
Energy consumption in Time Optimal (TO) condition | 621.2 kWh | 564.2 kWh |
H [min] | NC | Feasibility | |||||||
---|---|---|---|---|---|---|---|---|---|
6.5 | 25 | 25 | 25 | 4.92 | 45.1% | 55.9% | 48.0% | 12.34 | NO |
7.0 | 23 | 23 | 23 | 3.42 | 6.3% | 95.1% | 47.1% | 11.59 | NO |
7.5 | 22 | 22 | 22 | 7.42 | 50.1% | 50.6% | 48.7% | 13.59 | NO |
8.0 | 20 | 20 | 20 | 2.42 | 0.0% | 100.0% | 45.9% | 11.09 | NO |
8.5 | 19 | 19 | 19 | 3.92 | 0.0% | 100.0% | 47.4% | 11.84 | NO |
9.0 | 18 | 18 | 18 | 4.42 | 0.0% | 100.0% | 47.7% | 12.09 | NO |
9.5 | 17 | 17 | 17 | 3.92 | 0.0% | 100.0% | 47.4% | 11.84 | NO |
10.0 | 16 | 17 | 16 | 2.42 | 0.0% | 100.0% | 45.9% | 11.09 | NO |
10.0 | 16 | 17 | 17 | 12.42 | 50.1% | 50.3% | 49.2% | 16.09 | NO |
10.5 | 16 | 16 | 16 | 10.42 | 35.7% | 64.8% | 49.0% | 15.09 | NO |
11.0 | 15 | 15 | 15 | 7.42 | 2.9% | 97.8% | 48.7% | 13.59 | NO |
11.5 | 14 | 15 | 14 | 3.42 | 0.0% | 100.0% | 47.1% | 11.59 | NO |
11.5 | 14 | 15 | 15 | 14.92 | 48.4% | 52.0% | 49.3% | 17.34 | NO |
12.0 | 14 | 14 | 14 | 10.42 | 21.3% | 79.2% | 49.0% | 15.09 | NO |
12.5 | 13 | 14 | 13 | 4.92 | 0.0% | 100.0% | 48.0% | 12.34 | YES |
12.5 | 13 | 14 | 14 | 17.42 | 50.0% | 50.2% | 49.4% | 18.59 | NO |
13.0 | 13 | 13 | 13 | 11.42 | 19.4% | 81.0% | 49.1% | 15.59 | NO |
13.5 | 12 | 13 | 12 | 4.42 | 0.0% | 100.0% | 47.7% | 12.09 | YES |
13.5 | 12 | 13 | 13 | 17.92 | 45.9% | 54.4% | 49.4% | 18.84 | NO |
14.0 | 12 | 12 | 12 | 10.42 | 2.1% | 98.4% | 49.0% | 15.09 | NO |
14.5 | 11 | 12 | 11 | 1.92 | 0.0% | 100.0% | 44.8% | 10.84 | YES |
14.5 | 11 | 12 | 12 | 16.42 | 34.8% | 65.5% | 49.4% | 18.09 | NO |
15.0 | 11 | 12 | 11 | 7.42 | 0.0% | 100.0% | 48.7% | 13.59 | YES |
15.0 | 11 | 12 | 12 | 22.42 | 50.0% | 50.2% | 49.6% | 21.09 | NO |
16.0 | 10 | 11 | 10 | 2.42 | 0.0% | 100.0% | 45.9% | 11.09 | YES |
16.0 | 10 | 11 | 11 | 18.42 | 33.8% | 66.5% | 49.5% | 19.09 | NO |
17.0 | 10 | 10 | 10 | 12.42 | 0.0% | 100.0% | 49.2% | 16.09 | YES |
18.0 | 9 | 10 | 9 | 4.42 | 0.0% | 100.0% | 47.7% | 12.09 | YES |
18.0 | 9 | 10 | 10 | 22.42 | 36.7% | 63.6% | 49.6% | 21.09 | NO |
19.0 | 9 | 9 | 9 | 13.42 | 0.0% | 100.0% | 49.3% | 16.59 | YES |
20.0 | 8 | 9 | 8 | 2.42 | 0.0% | 100.0% | 45.9% | 11.09 | YES |
20.0 | 8 | 9 | 9 | 22.42 | 27.7% | 72.5% | 49.6% | 21.09 | NO |
25.0 | 7 | 8 | 7 | 17.42 | 0.0% | 100.0% | 49.4% | 18.59 | YES |
25.0 | 7 | 8 | 8 | 42.42 | 50.0% | 50.1% | 49.8% | 31.09 | NO |
30.0 | 6 | 7 | 6 | 22.42 | 0.0% | 100.0% | 49.6% | 21.09 | YES |
30.0 | 6 | 7 | 7 | 52.42 | 50.0% | 50.1% | 49.8% | 36.09 | NO |
H [min] | NC | Feasibility | |||||||
---|---|---|---|---|---|---|---|---|---|
6.5 | 25 | 25 | 25 | 4.05 | 43.6% | 56.8% | 47.1% | 12.34 | NO |
7.0 | 23 | 23 | 23 | 2.55 | 0.0% | 100.0% | 45.4% | 11.59 | NO |
7.5 | 22 | 22 | 22 | 6.55 | 49.9% | 50.4% | 48.2% | 13.59 | NO |
8.0 | 20 | 20 | 20 | 1.55 | 0.0% | 100.0% | 42.5% | 11.09 | NO |
8.5 | 19 | 19 | 19 | 3.05 | 0.0% | 100.0% | 46.2% | 11.84 | NO |
9.0 | 18 | 18 | 18 | 3.55 | 0.0% | 100.0% | 46.7% | 12.09 | NO |
9.5 | 17 | 17 | 17 | 3.05 | 0.0% | 100.0% | 46.2% | 11.84 | NO |
10.0 | 16 | 17 | 16 | 1.55 | 0.0% | 100.0% | 42.5% | 11.09 | NO |
10.0 | 16 | 17 | 17 | 11.55 | 49.9% | 50.2% | 49.0% | 16.09 | NO |
10.5 | 16 | 16 | 16 | 9.55 | 34.2% | 66.0% | 48.8% | 15.09 | NO |
11.0 | 15 | 15 | 15 | 6.55 | 0.0% | 100.0% | 48.2% | 13.59 | NO |
11.5 | 14 | 15 | 14 | 2.55 | 0.0% | 100.0% | 45.4% | 11.59 | NO |
11.5 | 14 | 15 | 15 | 14.05 | 48.2% | 52.0% | 49.2% | 17.34 | NO |
12.0 | 14 | 14 | 14 | 9.55 | 18.5% | 81.7% | 48.8% | 15.09 | NO |
12.5 | 13 | 14 | 13 | 4.05 | 0.0% | 100.0% | 47.1% | 12.34 | YES |
12.5 | 13 | 14 | 14 | 16.55 | 49.9% | 50.2% | 49.3% | 18.59 | NO |
13.0 | 13 | 13 | 13 | 10.55 | 16.7% | 83.4% | 48.9% | 15.59 | NO |
13.5 | 12 | 13 | 12 | 3.55 | 0.0% | 100.0% | 46.7% | 12.09 | YES |
13.5 | 12 | 13 | 13 | 17.05 | 45.6% | 54.5% | 49.3% | 18.84 | NO |
14.0 | 12 | 12 | 12 | 9.55 | 0.0% | 100.0% | 48.8% | 15.09 | NO |
14.5 | 11 | 12 | 11 | 1.05 | 0.0% | 100.0% | 38.9% | 10.84 | YES |
14.5 | 11 | 12 | 12 | 15.55 | 33.9% | 66.2% | 49.2% | 18.09 | NO |
15.0 | 11 | 12 | 11 | 6.55 | 0.0% | 100.0% | 48.2% | 13.59 | YES |
15.0 | 11 | 12 | 12 | 21.55 | 50.0% | 50.1% | 49.5% | 21.09 | NO |
16.0 | 10 | 11 | 10 | 1.55 | 0.0% | 100.0% | 42.5% | 11.09 | YES |
16.0 | 10 | 11 | 11 | 17.55 | 32.9% | 67.2% | 49.3% | 19.09 | NO |
17.0 | 10 | 10 | 10 | 11.55 | 0.0% | 100.0% | 49.0% | 16.09 | YES |
18.0 | 9 | 10 | 9 | 3.55 | 0.0% | 100.0% | 46.7% | 12.09 | YES |
18.0 | 9 | 10 | 10 | 21.55 | 36.0% | 64.0% | 49.5% | 21.09 | NO |
19.0 | 9 | 9 | 9 | 12.55 | 0.0% | 100.0% | 49.1% | 16.59 | YES |
20.0 | 8 | 9 | 8 | 1.55 | 0.0% | 100.0% | 42.5% | 11.09 | YES |
20.0 | 8 | 9 | 9 | 21.55 | 26.8% | 73.3% | 49.5% | 21.09 | NO |
25.0 | 7 | 8 | 7 | 16.55 | 0.0% | 100.0% | 49.3% | 18.59 | YES |
25.0 | 7 | 8 | 8 | 41.55 | 50.0% | 50.1% | 49.7% | 31.09 | NO |
30.0 | 6 | 7 | 6 | 21.55 | 0.0% | 100.0% | 49.5% | 21.09 | YES |
30.0 | 6 | 7 | 7 | 51.55 | 50.0% | 50.0% | 49.8% | 36.09 | NO |
H [min] | NC | Feasibility | |||||||
---|---|---|---|---|---|---|---|---|---|
6.5 | 25 | 25 | 25 | 3.30 | 41.9% | 58.1% | 46.2% | 12.34 | NO |
7.0 | 23 | 23 | 23 | 1.80 | 0.0% | 100.0% | 43.1% | 11.59 | NO |
7.5 | 22 | 22 | 22 | 5.80 | 49.7% | 50.3% | 47.8% | 13.59 | NO |
8.0 | 20 | 20 | 20 | 0.80 | 0.0% | 100.0% | 34.4% | 11.09 | NO |
8.5 | 19 | 19 | 19 | 2.30 | 0.0% | 100.0% | 44.6% | 11.84 | NO |
9.0 | 18 | 18 | 18 | 2.80 | 0.0% | 100.0% | 45.5% | 12.09 | NO |
9.5 | 17 | 17 | 17 | 2.30 | 0.0% | 100.0% | 44.6% | 11.84 | NO |
10.0 | 16 | 17 | 16 | 0.80 | 0.0% | 100.0% | 34.4% | 11.09 | NO |
10.0 | 16 | 17 | 17 | 10.80 | 49.8% | 50.2% | 48.8% | 16.09 | NO |
10.5 | 16 | 16 | 16 | 8.80 | 32.8% | 67.2% | 48.6% | 15.09 | NO |
11.0 | 15 | 15 | 15 | 5.80 | 0.0% | 100.0% | 47.8% | 13.59 | NO |
11.5 | 14 | 15 | 14 | 1.80 | 0.0% | 100.0% | 43.1% | 11.59 | NO |
11.5 | 14 | 15 | 15 | 13.30 | 48.0% | 52.0% | 49.1% | 17.34 | NO |
12.0 | 14 | 14 | 14 | 8.80 | 15.7% | 84.3% | 48.6% | 15.09 | NO |
12.5 | 13 | 14 | 13 | 3.30 | 0.0% | 100.0% | 46.2% | 12.34 | YES |
12.5 | 13 | 14 | 14 | 15.80 | 49.9% | 50.1% | 49.2% | 18.59 | NO |
13.0 | 13 | 13 | 13 | 9.80 | 14.1% | 85.9% | 48.7% | 15.59 | NO |
13.5 | 12 | 13 | 12 | 2.80 | 0.0% | 100.0% | 45.5% | 12.09 | YES |
13.5 | 12 | 13 | 13 | 16.30 | 45.3% | 54.7% | 49.2% | 18.84 | NO |
14.0 | 12 | 12 | 12 | 8.80 | 0.0% | 100.0% | 48.6% | 15.09 | NO |
14.5 | 11 | 12 | 11 | 0.30 | 0.0% | 100.0% | 8.3% | 10.84 | YES |
14.5 | 11 | 12 | 12 | 14.80 | 33.0% | 67.0% | 49.2% | 18.09 | NO |
15.0 | 11 | 12 | 11 | 5.80 | 0.0% | 100.0% | 47.8% | 13.59 | YES |
15.0 | 11 | 12 | 12 | 20.80 | 49.9% | 50.1% | 49.4% | 21.09 | NO |
16.0 | 10 | 11 | 10 | 0.80 | 0.0% | 100.0% | 34.4% | 11.09 | YES |
16.0 | 10 | 11 | 11 | 16.80 | 32.0% | 68.0% | 49.3% | 19.09 | NO |
17.0 | 10 | 10 | 10 | 10.80 | 0.0% | 100.0% | 48.8% | 16.09 | YES |
18.0 | 9 | 10 | 9 | 2.80 | 0.0% | 100.0% | 45.5% | 12.09 | YES |
18.0 | 9 | 10 | 10 | 20.80 | 35.5% | 64.5% | 49.4% | 21.09 | NO |
19.0 | 9 | 9 | 9 | 11.80 | 0.0% | 100.0% | 48.9% | 16.59 | YES |
20.0 | 8 | 9 | 8 | 0.80 | 0.0% | 100.0% | 34.4% | 11.09 | YES |
20.0 | 8 | 9 | 9 | 20.80 | 25.9% | 74.1% | 49.4% | 21.09 | NO |
25.0 | 7 | 8 | 7 | 15.80 | 0.0% | 100.0% | 49.2% | 18.59 | YES |
25.0 | 7 | 8 | 8 | 40.80 | 50.0% | 50.0% | 49.7% | 31.09 | NO |
30.0 | 6 | 7 | 6 | 20.80 | 0.0% | 100.0% | 49.4% | 21.09 | YES |
30.0 | 6 | 7 | 7 | 50.80 | 50.0% | 50.0% | 49.8% | 36.09 | NO |
H [min] | NC | [km/h] | [km/h] | [s] | [s] | [kWh] | [kWh] | [kWh] | Reduction in Energy Consumption | |
---|---|---|---|---|---|---|---|---|---|---|
12.5 | 13 | 49.52% | 67 | 68 | 129 | 147 | −136.8 | −139.8 | −21,019 | −23.33% |
13.5 | 12 | 37.04% | 70 | 67 | 87 | 163 | −110.9 | −149.1 | −18,315 | −21.91% |
14.5 | 11 | 43.21% | 74 | 76 | 49 | 65 | −80.6 | −80.3 | −10,544 | −13.58% |
15.0 | 11 | 58.71% | 61 | 66 | 241 | 180 | −186.5 | −156.2 | −21,587 | −28.91% |
16.0 | 10 | 34.57% | 74 | 73 | 49 | 90 | −80.6 | −103.5 | −10,943 | −15.51% |
17.0 | 10 | 38.55% | 60 | 55 | 263 | 434 | −193.0 | −242.9 | −24,166 | −36.72% |
18.0 | 9 | 37.04% | 70 | 67 | 87 | 163 | −110.9 | −149.1 | −13,783 | −21.94% |
19.0 | 9 | 58.30% | 54 | 59 | 436 | 320 | −237.7 | −211.8 | −22,478 | −37.93% |
20.0 | 8 | 33.33% | 75 | 73 | 41 | 90 | −73.5 | −103.5 | −8,389 | −14.89% |
25.0 | 7 | 55.56% | 51 | 55 | 542 | 434 | −261.6 | −242.9 | −19,172 | −42.56% |
30.0 | 6 | 46.96% | 50 | 49 | 588 | 668 | −265.2 | −283.8 | −17,285 | −46.26% |
H [min] | NC | [km/h] | [km/h] | [s] | [s] | [kWh] | [kWh] | [kWh] | Reduction in Energy Consumption | |
---|---|---|---|---|---|---|---|---|---|---|
12.5 | 13 | 41.43% | 70 | 69 | 87 | 134 | −110.9 | −132.8 | −18,523 | −20.56% |
13.5 | 12 | 39.51% | 71 | 70 | 79 | 123 | −103.8 | −124.2 | −16,064 | −19.22% |
14.5 | 11 | 54.32% | 77 | 82 | 29 | 27 | −61.8 | −42.9 | −6869 | −8.84% |
15.0 | 11 | 61.32% | 62 | 68 | 218 | 147 | −178.7 | −139.8 | −20,067 | −26.87% |
16.0 | 10 | 27.85% | 79 | 76 | 21 | 65 | −48.8 | −80.3 | −7669 | −10.87% |
17.0 | 10 | 34.57% | 62 | 55 | 218 | 434 | −178.7 | −242.9 | −23,369 | −35.51% |
18.0 | 9 | 45.68% | 70 | 71 | 87 | 113 | −110.9 | −118.2 | −12,144 | −19.33% |
19.0 | 9 | 66.67% | 53 | 63 | 473 | 233 | −247.8 | −179.8 | −21,378 | −36.07% |
20.0 | 8 | 27.85% | 79 | 76 | 21 | 65 | −48.8 | −80.3 | −6119 | −10.86% |
25.0 | 7 | 84.22% | 46 | 68 | 780 | 147 | −296.2 | −139.8 | −16,567 | −36.78% |
30.0 | 6 | 33.33% | 55 | 46 | 402 | 814 | −232.5 | −304.9 | −16,892 | −45.20% |
H [min] | NC | [km/h] | [km/h] | [sec] | [sec] | [kWh] | [kWh] | [kWh] | Reduction in Energy Consumption | |
---|---|---|---|---|---|---|---|---|---|---|
12.5 | 13 | 50.89% | 70 | 73 | 87 | 90 | −110.9 | −103.5 | −16,294 | −18.09% |
13.5 | 12 | 37.04% | 73 | 72 | 59 | 100 | −87.8 | −108.2 | −13,809 | −16.52% |
14.5 | 11 | 100% | 80 | 90 | 18 | 0 | −41.0 | 0.0 | −2708 | −3.49% |
15.0 | 11 | 67.90% | 62 | 72 | 218 | 100 | −178.7 | −108.2 | −18,077 | −24.21% |
16.0 | 10 | 6.17% | 88 | 79 | 2 | 43 | −5.2 | −61.3 | −3932 | −5.57% |
17.0 | 10 | 41.98% | 60 | 58 | 263 | 350 | −193.0 | −222.0 | −23,018 | −34.97% |
18.0 | 9 | 60.08% | 70 | 76 | 87 | 65 | −110.9 | −80.3 | −10,136 | −16.13% |
19.0 | 9 | 48.42% | 58 | 58 | 315 | 350 | −211.2 | −222.0 | −21,661 | −36.55% |
20.0 | 8 | 6.17% | 88 | 79 | 2 | 43 | −5.2 | −61.3 | −3133 | −5.56% |
25.0 | 7 | 66.67% | 50 | 60 | 588 | 298 | −265.2 | −204.0 | −17,830 | −39.58% |
30.0 | 6 | 43.21% | 52 | 49 | 507 | 668 | −251.3 | −283.8 | −16,839 | −45.06% |
H [min] | NC | [€/Daily] | [€/Daily] | [€/Daily] | Master Algorithm Iterations | Slave Algorithm Iterations | Approach 1 Computing Times [h] | Approach 2 Computing Times [s] | |
---|---|---|---|---|---|---|---|---|---|
12.5 | 13 | 49.52% | 13,814 | 150,511 | 164,325 | 31 | 1473 | 2.70 | 13.71 |
13.5 | 12 | 37.04% | 13,056 | 154,000 | 167,056 | 21 | 938 | 1.72 | 8.00 |
14.5 | 11 | 43.21% | 13,425 | 156,664 | 170,089 | 31 | 995 | 1.77 | 8.99 |
15.0 | 11 | 58.71% | 10,618 | 161,367 | 171,985 | 31 | 1724 | 3.21 | 8.04 |
16.0 | 10 | 34.57% | 11,923 | 162,469 | 174,392 | 21 | 358 | 1.30 | 5.33 |
17.0 | 10 | 38.55% | 8330 | 171,736 | 180,066 | 31 | 1074 | 3.98 | 6.44 |
18.0 | 9 | 37.04% | 9808 | 171,797 | 181,606 | 21 | 479 | 1.72 | 4.57 |
19.0 | 9 | 58.30% | 7358 | 180,661 | 188,019 | 31 | 2131 | 4.08 | 5.62 |
20.0 | 8 | 33.33% | 9589 | 177,513 | 187,102 | 21 | 727 | 1.30 | 3.82 |
25.0 | 7 | 55.56% | 5174 | 206,508 | 211,683 | 21 | 1563 | 3.03 | 2.89 |
30.0 | 6 | 46.96% | 4016 | 227,726 | 231,743 | 41 | 3430 | 6.72 | 3.60 |
H [min] | NC | [€/Daily] | [€/Daily] | [€/Daily] | Master Algorithm Iterations | Slave Algorithm Iterations | Approach 1 Computing Times [h] | Approach 2 Computing Times [s] | |
---|---|---|---|---|---|---|---|---|---|
12.5 | 13 | 41.43% | 14,313 | 149,897 | 164,210 | 41 | 1817 | 3.31 | 15.49 |
13.5 | 12 | 39.51% | 13,507 | 153,461 | 166,968 | 21 | 859 | 1.56 | 7.60 |
14.5 | 11 | 54.32% | 14,160 | 156,033 | 170,194 | 21 | 507 | 0.89 | 6.77 |
15.0 | 11 | 61.32% | 10,922 | 160,751 | 171,673 | 31 | 1627 | 3.02 | 8.93 |
16.0 | 10 | 27.85% | 12,578 | 161,868 | 174,446 | 31 | 877 | 1.55 | 8.02 |
17.0 | 10 | 34.57% | 8490 | 171,232 | 179,722 | 21 | 1347 | 2.56 | 5.26 |
18.0 | 9 | 45.68% | 10,136 | 171,217 | 181,353 | 21 | 861 | 1.56 | 4.79 |
19.0 | 9 | 66.67% | 7578 | 180,084 | 187,663 | 21 | 1383 | 2.64 | 4.34 |
20.0 | 8 | 27.85% | 10,043 | 176,984 | 187,027 | 31 | 877 | 1.55 | 5.24 |
25.0 | 7 | 84.22% | 5696 | 205,669 | 211,365 | 31 | 2197 | 4.24 | 3.84 |
30.0 | 6 | 33.33% | 4095 | 227,409 | 231,504 | 21 | 1676 | 3.28 | 2.32 |
H [min] | NC | [€/Daily] | [€/Daily] | [€/Daily] | Master Algorithm Iterations | Slave Algorithm Iterations | Approach 1 Computing Times [h] | Approach 2 Computing Times [s] | |
---|---|---|---|---|---|---|---|---|---|
12.5 | 13 | 50.89% | 14,759 | 149,409 | 164,168 | 31 | 1251 | 2.26 | 11.81 |
13.5 | 12 | 37.04% | 13,958 | 152,995 | 166,953 | 21 | 778 | 1.40 | 7.54 |
14.5 | 11 | 100% | 14,992 | 155,634 | 170,626 | 21 | 277 | 0.48 | 6.33 |
15.0 | 11 | 67.90% | 11,320 | 160,227 | 171,547 | 21 | 1028 | 1.90 | 6.25 |
16.0 | 10 | 6.17% | 13,325 | 161,469 | 174,795 | 31 | 562 | 0.98 | 7.30 |
17.0 | 10 | 41.98% | 8560 | 170,801 | 179,361 | 21 | 1315 | 2.49 | 4.89 |
18.0 | 9 | 60.08% | 10,538 | 170,657 | 181,195 | 31 | 1155 | 2.08 | 5.92 |
19.0 | 9 | 48.42% | 7522 | 179,699 | 187,221 | 31 | 2051 | 3.90 | 5.38 |
20.0 | 8 | 6.17% | 10,640 | 176,585 | 187,225 | 31 | 562 | 0.98 | 5.03 |
25.0 | 7 | 66.67% | 5443 | 205,414 | 210,857 | 21 | 1503 | 2.90 | 2.87 |
30.0 | 6 | 43.21% | 4106 | 226,873 | 230,979 | 31 | 2509 | 4.90 | 2.89 |
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D’Acierno, L.; Botte, M. A Passenger-Oriented Optimization Model for Implementing Energy-Saving Strategies in Railway Contexts. Energies 2018, 11, 2946. https://0-doi-org.brum.beds.ac.uk/10.3390/en11112946
D’Acierno L, Botte M. A Passenger-Oriented Optimization Model for Implementing Energy-Saving Strategies in Railway Contexts. Energies. 2018; 11(11):2946. https://0-doi-org.brum.beds.ac.uk/10.3390/en11112946
Chicago/Turabian StyleD’Acierno, Luca, and Marilisa Botte. 2018. "A Passenger-Oriented Optimization Model for Implementing Energy-Saving Strategies in Railway Contexts" Energies 11, no. 11: 2946. https://0-doi-org.brum.beds.ac.uk/10.3390/en11112946