Summary:
Paper shows an approach to solve Transit Network Design Problem. Considered problem covers regional transport system (Lublin region in Poland). Input data were GIS transport network and population distribution. Complex optimization problem was simplified by means of graph theory methods. Final optimization problem was poli-criterial genetic algorithm. Result of solving problem was Pareto frontier, being a set of non-dominated solutions. Optimization process was continuation of Visum Zone definition described here.
Background:
I got GIS database consisting of:
· Location of place with information about their population (fig.1)
· Transport network (roads + railway) (fig.2)
· Administrative division (zones) (fig.1+2) (each zone was about 50k inhabitants, 2k km2)
I presented the network as a graph consisting of 82 edges:
fig.3 |
Method:
I solved poli-criteria problem of Network Layout Optimization. Two contrary criteria were:
1) Operator cost minimization criteria: Total network length (km) and
2) Passenger Cost minimization criteria: Total passenger kilometers (paskm) represented via two separate criteria:
a. Travel times to get co central points of the network
b. Overall accessibility, being DistanceMatrix x OD Matrix ^(-1) (reciprocal was employed to transform criteria into minimization)
Decisive vector was 82 element Boolean vector. Each element of vector was reflecting graph edge.
I solved problem using Multi-objective Genetic Algorithm, minimizing three given criteria. Result was Pareto Frontier. Pareto frontier final population is shown here. Additional criteria being standard deviation of accessibility is proposed:
Nuber In Pareto final population (Lp) | Passenger cost 1 | Operator Cost | Passenger Cost 2 | Additional Criteria |
Passenger kms[1000 paskm] | Network Length [km] | Accessibility [pop./km] | Standard Deviation of Accessibility for Zones | |
8 | 161 000 | 1 218 | 732 902 | 99,3 |
22 | 161 000 | 1 282 | 733 704 | 99,3 |
10 | 161 000 | 1 276 | 733 447 | 99,3 |
28 | 128 000 | 1 423 | 723 114 | 66,2 |
2 | 122 000 | 1 851 | 640 084 | 62,8 |
20 | 123 000 | 2 241 | 653 834 | 63,7 |
15 | 122 000 | 2 457 | 667 836 | 62,8 |
1 | 133 000 | 1 624 | 814 889 | 71,1 |
23 | 132 000 | 1 707 | 823 710 | 67,5 |
19 | 126 000 | 2 400 | 882 689 | 68,2 |
27 | 121 000 | 2 700 | 900 210 | 59,6 |
17 | 121 000 | 3 521 | 921 467 | 59,6 |
21 | 136 000 | 2 445 | 886 533 | 72,6 |
18 | 122 000 | 2 556 | 900 101 | 62,8 |
7 | 122 000 | 2 898 | 908 254 | 62,8 |
Network diagrams for selected solutions are shown here:
network no 8 |
network no 17 |
network no 22 |
Conclusion:
User friendly tools combined with good quality of input data can perform much more than you expect with basic transport models. Built-in optimization for tranpsport modeling - sounds good.
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