Academia.eduAcademia.edu

Figure 3 – uploaded by Maurizio Bielli

See full PDFdownloadDownload figure
Fig. 5. A solution procedure for the urban network design problem — Cantarella and Vitetta (1994). M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34

Figure 5 A solution procedure for the urban network design problem — Cantarella and Vitetta (1994). M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34

Related Figures (16)

Fig. 1. Layout of a GA implementation. M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 e GA uses objective function information and not derived or auxiliary knowledge; e GA uses probabilistic transition rules and not deterministic ones.
Fig. 1. Layout of a GA implementation. M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 e GA uses objective function information and not derived or auxiliary knowledge; e GA uses probabilistic transition rules and not deterministic ones.
The second operator denoted simple crossover (see e.g., Chambers, 1995; Goldberg, 1989; Michalewicz, 1992) works as follows: the members reproduced in the new mating pool are mated randomly and afterward each pair of strings undergoes a cross-change. In order to do this, an integer position k (cut point) is selected uniformly at random among the strings between position | and the string length / less one. Two new strings are created swapping all genes (with the cor- responding al elic values) between the selected position k and the end of the string. Fig. 3 shows a simple crossover operator.
The second operator denoted simple crossover (see e.g., Chambers, 1995; Goldberg, 1989; Michalewicz, 1992) works as follows: the members reproduced in the new mating pool are mated randomly and afterward each pair of strings undergoes a cross-change. In order to do this, an integer position k (cut point) is selected uniformly at random among the strings between position | and the string length / less one. Two new strings are created swapping all genes (with the cor- responding al elic values) between the selected position k and the end of the string. Fig. 3 shows a simple crossover operator.
Fig. 6. The simple genetic algorithm — Xiong and Schneider (1993). M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34
Fig. 6. The simple genetic algorithm — Xiong and Schneider (1993). M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34
Fig. 8. The transit planning process — Ceder and Wilson (1986). Referring to the framework proposed by Ceder and Wilson (1986) on the transit planning process (Fig. 8) this work tries to unify the planning activities at level A and level B. In fact,
Fig. 8. The transit planning process — Ceder and Wilson (1986). Referring to the framework proposed by Ceder and Wilson (1986) on the transit planning process (Fig. 8) this work tries to unify the planning activities at level A and level B. In fact,
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 Fig. 7. The cumulative genetic algorithm — Xiong and Schneider (1993).
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 Fig. 7. The cumulative genetic algorithm — Xiong and Schneider (1993).
Fig. 9. Genetic representation: chromosome and cut points (network).
Fig. 9. Genetic representation: chromosome and cut points (network).
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 Fig. 11. Crossover operator implementation.
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 Fig. 11. Crossover operator implementation.
(2) The second phase is a routine that aggregates the output of the assignment phase in order to btain a set of performance indicators (Bielli et al., 1996) reported in Table 1. The first column in he table reports indicators and the second their abbreviations. The third column contains two ymbols: W means that the lowest the value, the best the indicator, while A means that the highest he value, the best the indicator. The fourth column defines the type of the indicator: effectiveness
(2) The second phase is a routine that aggregates the output of the assignment phase in order to btain a set of performance indicators (Bielli et al., 1996) reported in Table 1. The first column in he table reports indicators and the second their abbreviations. The third column contains two ymbols: W means that the lowest the value, the best the indicator, while A means that the highest he value, the best the indicator. The fourth column defines the type of the indicator: effectiveness
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 Fig. 13. The network representation for the flow assignment phase.
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 Fig. 13. The network representation for the flow assignment phase.
The performance indicators
The performance indicators
quency represented by the value of the other allele in that gene. Finally two further considerations can be done (Fig. 16). The first one is related to the intro- duction of a n-best solutions container, that during the whole process stores a predefined number of good solutions generated. This container is very useful to perform an off-line sensitivity analysis on the weights used in the multicriteria analysis, in order to accept the results obtained or perform a new run with a new set of weights. rest 1 4 1+, 4 oq °4e, 7 4 41 7 1 . 1
quency represented by the value of the other allele in that gene. Finally two further considerations can be done (Fig. 16). The first one is related to the intro- duction of a n-best solutions container, that during the whole process stores a predefined number of good solutions generated. This container is very useful to perform an off-line sensitivity analysis on the weights used in the multicriteria analysis, in order to accept the results obtained or perform a new run with a new set of weights. rest 1 4 1+, 4 oq °4e, 7 4 41 7 1 . 1
Fig. 15. Details of the fitness function evaluation. M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34
Fig. 15. Details of the fitness function evaluation. M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34
Best fitness function values for different combinations of crossover and mutation probability
Best fitness function values for different combinations of crossover and mutation probability
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 geometrical structures. Parma? is formed by 20 circular lines, involving 1130 nodes, 3006 arcs and 459 stops. Parma3 is constituted by 20 semicircular lines, where each line starts from a suburban node, goes through the centre of the city, where it first makes a semicircular route, and then gets to another suburban node. Parma3 is formed by 1092 nodes, 2892 arcs and 459 stops. Each one of the considered bus networks has 99 centroids and 685 pedestrian nodes which allow to complete the two-level representation given in the previous section. What we have done is to create four initial chromosomes having lensth 80. being the tota
M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 geometrical structures. Parma? is formed by 20 circular lines, involving 1130 nodes, 3006 arcs and 459 stops. Parma3 is constituted by 20 semicircular lines, where each line starts from a suburban node, goes through the centre of the city, where it first makes a semicircular route, and then gets to another suburban node. Parma3 is formed by 1092 nodes, 2892 arcs and 459 stops. Each one of the considered bus networks has 99 centroids and 685 pedestrian nodes which allow to complete the two-level representation given in the previous section. What we have done is to create four initial chromosomes having lensth 80. being the tota
Fig. 17. Fitness function values for each generation. M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 1.0, and a mutation probability 0.0, 0.1, and 0.2. Results show that the best ff is obtained in correspondence to a 0.8 crossover probability and a 0.1 mutation probability. We remark that our computation was conducted on 100 generations and the best ff value was obtained in corre- spondence to the 66th generation. Moreover, the best initial ff value, i.e., the best ff value among the four initial bus networks, was 0.47. In Fig. 17. we renort the granhic representing the trend of the f# with resnect to the number of
Fig. 17. Fitness function values for each generation. M. Bielli et al. | Transportation Research Part C 10 (2002) 19-34 1.0, and a mutation probability 0.0, 0.1, and 0.2. Results show that the best ff is obtained in correspondence to a 0.8 crossover probability and a 0.1 mutation probability. We remark that our computation was conducted on 100 generations and the best ff value was obtained in corre- spondence to the 66th generation. Moreover, the best initial ff value, i.e., the best ff value among the four initial bus networks, was 0.47. In Fig. 17. we renort the granhic representing the trend of the f# with resnect to the number of
Related topics:
EngineeringIterative MethodsTransportationNetwork optimizationMulticriteria Decision Analysis
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved