5.2. Comparison of Different Algorithms
In this section, a transportation network including highway and railway transportation modes is used to verify the effectiveness of the FAGA algorithm. There are 1–2 modes of transportation in railway transportation and highway transportation between each two urban nodes. In this paper, MATLAB is used to solve the case model. The path optimization effects of general GA, adaptive genetic algorithm (AGA), and the elite genetic algorithm used in [
10] are compared with those of this algorithm.
The crossover probability is 0.2, and the mutation probability is 0.8 in GA. Given the maximum genetic algebra gen = 400, the AGA algorithm adaptively adjusts the crossover and mutation parameters according to the fitness of all individuals in each iteration. The FAGA algorithm uses the fuzzy reference system as the mechanism to adaptively select the crossover probability and mutation probability, ensure the diversity of the population, and finally obtain the best route from Nanchang Station to Berlin using the different parameters set above.
Figure 7 shows the optimization path of the ordinary GA algorithm. Nanchang is the starting city, and Berlin is the destination city. It successively passes through 23 cities, including Wuhan, Zhengzhou, Chongqing, Huaihua, Guiyang, Nanning, Beihai, Kunming, Guangzhou, Shanghai, Manzhouli, Erenhot, Alataw Pass, Kashgar, Gwadar, Yangon, Bangkok, Ho Chi Minh, Singapore, Rotterdam, Hamburg, Warsaw, and Duisburg. According to
Table 7, a multimodal transportation scheme from Nanchang to Berlin is obtained by switching the mode of transport to highway transport from Nanchang to Wuhan, switching the mode of transport to highway transport from Alashan pass to Kashgar, switching the mode of transport to highway transport from Gwadar to Yangon, switching the mode of transport to highway transport from Ho Chi Minh to Singapore, and finally by highway transport from Duisburg to Berlin. Other modes of transportation are railway transportation.
Figure 8,
Figure 9 and
Figure 10 show the convergence curves of the iterative process of the three objective values of the ordinary genetic algorithm optimization, from which it can be seen that the cost objective reaches its optimum at around CNY 121,000 in 310 iterations. Similarly, the time objective converges to its optimum at around 660 h in 370 iterations, and the carbon emission objective reaches its optimum at around 92,500 kg in 330 iterations.
Figure 11 shows the path optimized by the AGA algorithm, with Nanchang as the starting city and Berlin as the destination city, through Wuhan, Zhengzhou, Xian, Huaihua, Guiyang, Nanning, Beihai, Kunming, Guangzhou, Shanghai, Manzhouli, Erenhot, Alataw Pass, Kashgar, Gwadar, Yangon, Bangkok, Ho Chi Minh, Singapore, Rotterdam, Hamburg, Warsaw, and Duisburg, a total of 23 cities. According to
Table 8, it is concluded that in the scheme of using the AGA algorithm for the multimodal transport from Nanchang to Berlin, the mode of transport is switched to highway transport from Nanchang to Wuhan, from Beihai to Kunming, from Kunming to Guangzhou, from Manzhouli to Erenhot, from Kashgar to Gwadar, from Rotterdam to Hamburg, from Warsaw to Duisburg, and finally highway transportation is used from Duisburg to Berlin. Other modes of transportation are railway transportation.
Figure 12,
Figure 13 and
Figure 14 show the convergence curves of the iterative process of the three objective values of the AGA genetic algorithm optimization, from which it can be seen that the cost objective reaches its optimum around CNY 114,000 in 300 iterations. Similarly, the time objective converges to its optimum around 660 h in 320 iterations, and the carbon emission objective reaches its optimum around 89,000 kg in 300 iterations.
Figure 15 shows the optimization path of the algorithm in [
10]. Nanchang is the starting city, and Berlin is the destination city. It passes through Wuhan, Zhengzhou, Xi’an, Huaihua, Nanning, Beihai, Kunming, Guangzhou, Shanghai, Manchuria, Erenhot, Alataw Pass, Kashgar, Gwadar, Yangon, Bangkok, Singapore, Rotterdam, Hamburg, Warsaw, and Duisburg. According to
Table 9, it is concluded that in the scheme of using the elite genetic algorithm for multimodal transport from Nanchang to Berlin, the conversion of transport mode to highway transport occurs from from Erenhot to Allah Pass, and highway transport is used from Warsaw to Duisburg. Other modes of transport are rail transport.
Figure 16,
Figure 17 and
Figure 18 shows the convergence curve of the iterative process of cost, time, and carbon emission target values. It can be seen that the cost target is optimal at about CNY 92,394 in 260 iterations. Similarly, the time target is optimal at about 780 h in 325 iterations, and the carbon emissions target is optimal at about 99,105 kg in 250 iterations.
Figure 19 shows the path optimized by the FAGA algorithm, with Nanchang as the starting city and Berlin as the destination city, through Wuhan, Zhengzhou, Chongqing, Huaihua, Nanning, Beihai, Kunming, Guangzhou, Shanghai, Manzhouli, Erenhot, Alataw pass, Kashgar, Gwadar, Yangon, Bangkok, Singapore, Rotterdam, Hamburg, Warsaw, and Duisburg, a total of 21 cities. According to
Table 10, it is concluded that in the scheme of using the FAGA algorithm for the multimodal transport from Nanchang to Berlin, the mode of transport is switched to highway transport from Guangzhou to Shanghai, from Manzhouli to Erenhot, from Erlianhot to Alashankou, and from Singapore to Rotterdam, and finally, highway transportation is used from Warsaw to Duisburg. Other modes of transportation are railway transportation.
Figure 20,
Figure 21 and
Figure 22 show the convergence curves of the iterative process of the three target values for the optimization of the FAGA algorithm, from which it can be seen that the cost target reaches its optimum at about 260 iterations of CNY 102,000. Similarly, the time target converges to its optimum at about 290 iterations of 630 h, and the carbon emission target reaches its optimum at about 300 iterations of 60,100 kg.
Figure 23 shows the fitness curves of the ordinary GA, AGA, EGA, and FAGA. By comparing the figures, it can be concluded that the fitness function of the FAGA algorithm converges in 6713 iteration over 150 generations, while the GA algorithm converges in 6755 iteration over 325 generations. The EGA algorithm converges in 6730 iterations over 200 generations, and the AGA algorithm converges in 6730 iterations over 160 generations. It can be seen that the FAGA algorithm has a fast convergence speed, good convergence effect, and good optimization quality. In the literature [
10], the elite genetic algorithm is designed with the cost as the objective function to solve a given problem. The elite fragment retention strategy is introduced to enhance the robustness of the algorithm. The elite fragment retention strategy is introduced in the process of gene mutation, and the elite fragment retention is based on the coding of transportation nodes. We apply the model and algorithm in [
10] to our example to analyze the optimization results. From the comparison results, our proposed method is superior to the elite genetic algorithm in the improvement of the genetic algorithm. The introduction of the elite genetic algorithm has the advantages of fast convergence speed, a stable optimal solution, and good stability. In order to prevent the optimal solution generated in the evolution process from being destroyed by crossover and mutation, the optimal solution in each generation can be copied to the next generation. The overall convergence speed can be controlled by introducing the proportion of the number of elites. The greater the number, the faster the convergence, but too many elites may cause local convergence of the algorithm, thus obtaining poor results.
Therefore, the Highway-Railway intermodal transportation using the FAGA algorithm saves transportation costs compared with the ordinary GA, AGA and EGA algorithms in this transportation task and can deliver the goods to the destination in advance, reduce carbon emissions, improve customer satisfaction, and truly complete the transportation task at a low cost and quickly. The comparison between the multimodal transport path solved in this section and the single railway transport effect in the previous section can be obtained as shown in
Table 6 and
Table 11. The three target values of multimodal transport have been significantly improved because no matter how far the freight transport distance is, it is completed by several modes of transport together, which can shorten the delivery time of goods, reduce inventory, and improve freight quality. It fundamentally ensures the safe, agile, accurate and timely delivery of goods to the destination.
Finally, this paper compares the improved results of the multiple genetic algorithms involved above and selects the following statistical indicators after 30 runs: fitness function value, success rate, average running time, etc., as shown in
Table 12.
Through the comparison of data indicators for four improved algorithms based on genetic algorithm, it can be seen that FAGA has achieved good performance based on the genetic algorithm. Because the fuzzy rules used in this study are based on the variance of population fitness value, the three target values of the population will be adjusted in real time during the operation of the algorithm to affect the size of the variance so as to ensure that the variance and the average fitness between individuals are kept within a reasonable range. Secondly, during the operation of FAGA, the dynamic adjustment of GA parameters or operators is realized, which ensures the reasonable utilization and exploratory optimization of GA performance in the whole GA search process to improve the success rate of operation optimization. Although the complexity of the algorithm is high, the optimization process is effective, and the population quality is high. The automatic adjustment of the algorithm parameters can minimize the resources required for the optimization process, thus reducing the running time and achieving optimization in the fastest time. Based on the EGA algorithm, the optimal individual is directly copied to the next generation without pairing, and the population size is not too large. The success rate, running time, and population standard deviation are significantly improved, and the complexity of the algorithm is low. The adaptive genetic algorithm improves the convergence accuracy of the genetic algorithm by adjusting the parameters of the real-time state of the population, and it does not easily become trapped in the dead cycle phenomenon. The convergence speed is accelerated, so the four indexes are higher than the GA algorithm.