Post-Earthquake Emergency Logistics Location-Routing Optimization Considering Vehicle Three-Dimensional Loading Constraints
Abstract
:1. Introduction
- (1)
- A multi-objective location-routing problem with a three-dimensional loading constraints optimization model is formulated. This model is unique in that it optimizes distribution centers, vehicle scheduling, and loading plans while considering three-dimensional loading constraints, facility disruptions, capacity limitations and expansions, and time window constraints while balancing social costs (logistical and deprivation costs) and risk to the logistics network. By integrating these two goals, the model not only enhances resource allocation efficiency but also strengthens the reliability of the ELN.
- (2)
- A multi-objective mixed genetic algorithm (MOGA) based on adaptive large neighborhood search (ALNS) is proposed. This MOGA-ALNS employs ALNS for neighborhood search, with five removal and insertion operators designed to enhance the diversity and flexibility of the search process, effectively preventing convergence to local optima. Simultaneously, it leverages the global search capability of genetic algorithms to ensure the diversity and comprehensiveness of the solutions.
2. Literature Review
2.1. Emergency Logistics Network
2.2. Integrating Research on Delivery Route Optimization and Three-Dimensional Packing Constraints (VRPTDLCs)
2.3. Compartmentalization Strategies for Vehicles
3. Model Formulation
3.1. Problem Description
3.2. Symbols
3.3. Emergency Logistics Network Risk Measurement Formula
3.4. Mathematical Model
4. Solution Method
4.1. Main Framework of the Algorithm
4.2. Representation of Solutions
4.3. Population Initialization
- (1)
- When considering the distance between demand points and distribution centers, the probability function [60] for assigning all demand points to distribution centers is given by Equation (37), where represents the Euclidean distance between the distribution center and demand point , signifies the average distance from demand point to all distribution centers, with representing the total count of demand points. The probability of assigning demand point to distribution center is calculated as follows:
- (2)
- After assigning demand points and distribution centers, we must determine the relationship between vehicles and demand points. In this paper, we use the greedy insertion operator for this initialization, as follows:Step 1: Arrange all demand points in ascending order of their earliest allowable arrival time within the time window.Step 2: Iterate through each vehicle to check if the supplies for each demand point can be inserted into that vehicle. This includes checking if there is enough capacity to carry the items in the task. If the quantity of any item in the task, when added to the quantity of supplies already in the vehicle, exceeds the limit, then that vehicle cannot be used for that demand point.Step 3: For each vehicle, calculate the score (objective function value) of inserting a certain node into it, and record the index of the insertion point, evaluating the effectiveness of different insertion strategies.Step 4: Among all available vehicles, select the one that results in the lowest insertion score. A lower score indicates that inserting this task contributes least to the growth of the objective function, which means it is a better insertion point.
4.4. Selection, Crossover, and Mutation
4.5. Neighborhood Search
- Shaw Removal Operator. Calculate the similarity based on the distance between nodes and the required service time, and remove the top tasks with the highest similarity.
- Random Removal Operator. Randomly remove task nodes from the vehicle’s delivery route.
- Worst Removal Operator. Remove the task nodes that result in the largest increase in total cost.
- Greedy Insertion Operator. Sort the task nodes to be inserted in ascending order of their left time windows and insert them to minimize the delivery time as much as possible.
- Regret Insertion Operator. For each unallocated task node, the algorithm calculates the score after inserting it at a certain position, sorts the scores, and selects the top scores as candidate insertion positions. It computes the sum of the absolute differences between the highest score and the scores of other candidate insertion positions as the regret value for that candidate insertion position. This operator iterates through the list of unallocated tasks, finding the insertion position with the highest regret value for each task.
Algorithm 1. Procedure of the Neighborhood Search | |
1: | input: a feasible solution |
2: | ; ; ; |
3: | repeat |
4: | select removal and insertion operations and |
5: | using and ; |
6: | ; |
7: | if (any of five conditions is satisfied) then |
8: | |
9: | end if |
10: | if < then |
11: | |
12: | end if |
13: | update and ; |
14: | until stop criterion is met |
15: | return |
5. Numerical Experiments
- (1)
- SPEA-II adopts the solution representation method similar to the MOGA-ALNS, as detailed in Section 4.2. It begins with the generation of a random population using the method described in the same section. The selection and population update mechanisms adhere to the foundational structure of the SPEA-II, as outlined in the literature [62]. For genetic operations, SPEA-II incorporates the same crossover and mutation techniques as found in the MOGA-ALNS, ensuring consistency in the approach to evolving solutions.
- (2)
- Aligning with the MOGA-ALNS for solution representation, the MOEA/D leverages the Tchebycheff approach to create a series of subproblems targeting different parts of the objective space [63]. The processes for constructing neighborhoods, selecting individuals, and updating individual solutions are all based on the core principles of the MOEA/D [63]. Furthermore, the algorithm applies identical crossover and mutation strategies as the MOGA-ALNS, facilitating a uniform method of introducing genetic diversity and exploring the solution space.
5.1. Test Case
5.2. Performance Metrics
- (1)
- The C-metric, a tool for evaluating the comparative performance of two different algorithms through their solution sets and , quantifies the extent to which one set dominates another. Specifically, represents the proportion of solutions in set that are dominated by at least one solution in set . The formula for calculating this metric is as follows:
- (2)
- The IGD-metric calculates the minimum Euclidean distance between the approximate solution set and the Pareto-optimal front. A smaller IGD value indicates that the solution set generated by the algorithm is closer to the true front. Let and represent the optimal solution set and the approximate solution set, respectively. Formula (41) for IGD measurement is as follows:
- (3)
- The hypervolume-metric measures the coverage range size of the approximate set in the objective space. A higher hypervolume value indicates a broader coverage range of the approximate set in the objective space, which typically implies the higher quality of the obtained non-dominated solution set. Let be the reference point in the objective space dominated by all optimal solutions. Then, the hypervolume value of the solution set represents the volume of a region where all solutions are dominated by the solution set and dominate . When calculating the hypervolume-metric, a reference point needs to be selected. In this paper, (1, 1) is used as the reference point, and all objective values in the approximate solution set are normalized, mapping them into the range [0, 1].
5.3. Parameter Configuration
5.4. Effectiveness of Neighborhood Search
- (1)
- In the Friedman test, we organize the MOGA-ALNS and MOGA-ALNS-w/o-NS by descending average values of the hypervolume-metric and ascending average values for the IGD-metric, assigning them ranks of 1 and 2, respectively. We then calculate the average ranks across all instances as depicted in Table 5. For the hypervolume-metric, the average ranks are 1.05 for the MOGA-ALNS and 1.95 for MOGA-ALNS-w/o-NS. Similarly, for the IGD-metric, the average ranks stand at 1.1000 for the MOGA-ALNS and 1.9000 for MOGA-ALNS-w/o-NS. This differentiation in average ranks allows us to deduce a statistically significant disparity in performance between the MOGA-ALNS and MOGA-ALNS-w/o-NS according to the Friedman test.
- (2)
- To delve deeper into the distinctions between the MOGA-ALNS and MOGA-ALNS-w/o-NS, we employ the Nemenyi post-hoc test at a significance level of 0.05 to ascertain the critical discrepancy in their average rank values. The gap in average ranks for the hypervolume-metric is 0.9000, surpassing the critical threshold of 0.4382. Similarly, for the IGD metric, the difference in average ranks is 0.8000, also exceeding the critical value. These findings underscore the MOGA-ALNS’s notable superiority over MOGA-ALNS-w/o-NS across both evaluated metrics.
5.5. Experimental Results
5.5.1. Analysis of the C-Metric
5.5.2. Analysis of the IGD-Metric
5.5.3. Analysis of Hypervolume-Metric
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Notation | Description |
---|---|
Indices | |
Set of candidate distribution centers; indicates the number of candidate distribution centers. | |
Set of demand points; represents the number of demand points. | |
Set of distribution centers and demand points; . | |
Set of segments in the distribution network; , and represent nodes in the network. | |
Set of distribution vehicles; represents the total count of vehicles. | |
Set of scenarios; where represents the number of scenarios, each of which has a set of distribution centers experiencing a simultaneous disruption. | |
Set of demand points for vehicle services; . | |
Set of goods types needed across all demand points; where denotes the type of goods. | |
Set of spaces in the distribution vehicle compartment of vehicle , and is the overall count of spaces. | |
Set of goods placed in the same space of the same vehicle with good and overlapping with the under-plane projection of goods in scenario . | |
Set of goods placed in the same space of the same vehicle with good and the bottom surface of good is at the same height in scenario . | |
Parameters | |
Distance between the depot or demand point i and demand point j, . | |
The base capacity of the distribution center . | |
The maximum capacity of the distribution center can be expanded, . | |
The cost of constructing the distribution center . | |
The unit expansion cost of the distribution center . | |
Fixed operating cost of the vehicle. | |
The cost per unit distance traveled by the vehicle. | |
The speed of vehicles. | |
The maximum loading volume of the vehicle. | |
The maximum load capacity of the vehicle. | |
The actual count of layers of goods loaded in the space of vehicle . | |
The actual count of rows of goods loaded in the space of vehicle . | |
The actual count of columns of goods loaded in the space of vehicle . | |
The count of goods placed within the space of vehicle in scenario . | |
The number of goods loaded at demand point within region by delivery vehicle in scenario . | |
The individual quality of the goods loaded in region by delivery vehicle . | |
The overall quality of goods placed in the space of vehicle . | |
The overall size of goods placed in the space of vehicle . | |
The overall number of goods placed in the space of vehicle . | |
The dimensions of the carriage, including its length, width, and height.. | |
The length, width, and height of the space of vehicle . | |
The length, width, and height of the goods loaded in the space of vehicle . | |
The coordinate at the upper-right corner of the front side of the carriage of the point in the space of vehicle . | |
The coordinate at the lower-left corner of the back side of the carriage of the point in the space of vehicle . | |
The probability of scenario occurring, . | |
The probability of secondary disasters such as aftershocks occurring at the distribution center . | |
The probability of huge losses caused by disasters such as aftershocks affecting the distribution center in scenario . | |
The cost of losses incurred by distribution center due to disaster risks such as aftershocks in scenario . | |
The probability of transportation risk associated with the route section in scenario . | |
The probability of significant loss of goods due to transportation risk occurring along route segment in scenario . | |
The cost of loss due to transportation risk when goods are transported from to in scenario . | |
The cargo load of vehicle when transporting from to in scenario | |
The time for vehicle to reach point in scenario . | |
The time vehicle requires to serve demand point in scenario . | |
The penalty coefficient for vehicles arriving at demand point ahead of schedule, . | |
The penalty coefficient for vehicles arriving at demand point behind schedule, . | |
The earliest acceptable service time for demand point . | |
The latest acceptable service time for demand point . | |
The value is 1 if distribution center fails in scenario ; otherwise, it is 0, . | |
The value is 1 if vehicle is loaded with class goods within region ; otherwise, it is 0, . | |
Decision variable | |
The value is 1 if a distribution center is established at location in scenario ; otherwise, it is 0, . | |
The value is 1 if vehicle travels from node to node in scenario ; otherwise, it is 0, . | |
The value is 1 if demand point is serviced by distribution center in scenario ; otherwise, it is 0, | |
The value is 1 if vehicle carries the goods of demand point within region ; otherwise, it is 0, k.. | |
The value is 1 if vehicle departs from distribution center to provide delivery services in scenario ; otherwise, it is 0, . | |
The capacity expansion amount of distribution center in scenario . |
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Reference | Location | Allocation | Objective | Vulnerable Section | Key Constraints | Solution | ||||
---|---|---|---|---|---|---|---|---|---|---|
Facility | Link | Fac. Cap | Fac. Exp | TWs | 3D Loading | |||||
Mohammadi et al. (2020) [40] | Total cost Makespan Transport cost bounds variation | Exa | ||||||||
Wei et al. (2020) [41] | Total cost Demand satisfaction | Met | ||||||||
Li et al. (2020) [42] | Total cost | Exa | ||||||||
Sun et al. (2021) [43] | Total cost Injury severity score | Exa | ||||||||
Gao et al. (2021) [44] | Fairness Makespan | Exa | ||||||||
Abazari et al. (2021) [45] | Total cost Makespan | Met | ||||||||
Cheng et al. (2021) [46] | Fairness | Exa | ||||||||
Alem et al. (2021) [47] | Effectiveness | Exa | ||||||||
Peng et al. (2022) [48] | Total cost Demand satisfaction | Met | ||||||||
Ghasemi et al. (2022) [49] | Total costs Maximum number of unsatisfied demands | Met | ||||||||
Vosooghi et al. (2022) [50] | Total cost Response time | Met | ||||||||
Bayraktar et al. (2022) [51] | Total cost | Met | ||||||||
Wang et al. (2023) [52] | Total cost Makespan | Exa | ||||||||
Meng et al. (2023) [10] | Total cost Makespan | Exa | ||||||||
Yang et al. (2023) [19] | Total cost Fairness | Exa | ||||||||
Wang et al. (2023) [9] | Time cost Quantity of short supplies | Heu | ||||||||
Sheikholeslami et al. (2023) [53] | Total cost Coverage of the network | Met | ||||||||
Li et al. (2023) [54] | Total cost in the worst case | Heu | ||||||||
Zhang et al. (2023) [11] | Total cost | Meta | ||||||||
Yang et al. (2024) [55] | Total cost | Exa | ||||||||
This study | Total cost Risk of network | Met |
|
|
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|
No | ARV | |||
---|---|---|---|---|
1 | 50 | 0.3 | 30 | 0.7555 |
2 | 50 | 0.5 | 60 | 0.7659 |
3 | 50 | 0.7 | 90 | 0.8319 |
4 | 50 | 0.9 | 120 | 0.8440 |
5 | 75 | 0.3 | 60 | 0.8035 |
6 | 75 | 0.5 | 30 | 0.8853 |
7 | 75 | 0.7 | 120 | 0.8059 |
8 | 75 | 0.9 | 90 | 0.9506 |
9 | 100 | 0.3 | 90 | 0.9447 |
10 | 100 | 0.5 | 120 | 0.8874 |
11 | 100 | 0.7 | 30 | 0.8825 |
12 | 100 | 0.9 | 60 | 0.8303 |
13 | 125 | 0.3 | 120 | 0.8796 |
14 | 125 | 0.5 | 90 | 0.9341 |
15 | 125 | 0.7 | 60 | 0.8624 |
16 | 125 | 0.9 | 30 | 0.9682 |
Level | |||
---|---|---|---|
1 | 0.7993 | 0.8458 | 0.8729 |
2 | 0.8613 | 0.8682 | 0.8155 |
3 | 0.8862 | 0.8456 | 0.9153 |
4 | 0.9111 | 0.8983 | 0.8542 |
Delta | 0.1117 | 0.0526 | 0.0998 |
Rank | 1 | 3 | 2 |
Instance | Hypervolume-Metric | IGD-Metric | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
MOGA-ALNS | MOGA-ALNS-w/o-NS | MOGA-ALNS | MOGA-ALNS-w/o-NS | |||||||||
Mean | Var | Rank | Mean | Var | Rank | Mean | Var | Rank | Mean | Var | Rank | |
5-40-a | 0.8442 | 0.0083 | 1 | 0.7442 | 0.0161 | 2 | 0.2064 | 0.0015 | 1 | 0.2679 | 0.0016 | 2 |
5-40-b | 0.7867 | 0.0101 | 1 | 0.7589 | 0.0108 | 2 | 0.0726 | 0.0005 | 1 | 0.2746 | 0.0009 | 2 |
5-40-c | 0.8359 | 0.0104 | 1 | 0.7537 | 0.0105 | 2 | 0.1721 | 0.0011 | 1 | 0.2642 | 0.0014 | 2 |
5-40-d | 0.8119 | 0.0131 | 1 | 0.7894 | 0.0086 | 2 | 0.1621 | 0.0017 | 1 | 0.2222 | 0.0018 | 2 |
5-40-e | 0.8217 | 0.0097 | 1 | 0.7670 | 0.0093 | 2 | 0.1329 | 0.0005 | 1 | 0.2541 | 0.0013 | 2 |
5-60-a | 0.7867 | 0.0106 | 2 | 0.7936 | 0.0103 | 1 | 0.1708 | 0.0018 | 1 | 0.2468 | 0.0022 | 2 |
5-60-b | 0.7986 | 0.0182 | 1 | 0.7274 | 0.0203 | 2 | 0.1739 | 0.0013 | 1 | 0.2630 | 0.0016 | 2 |
5-60-c | 0.8148 | 0.0190 | 1 | 0.7952 | 0.0152 | 2 | 0.1500 | 0.0009 | 1 | 0.2173 | 0.0014 | 2 |
5-60-d | 0.7829 | 0.0180 | 1 | 0.7577 | 0.0153 | 2 | 0.1308 | 0.0008 | 1 | 0.2500 | 0.0014 | 2 |
5-60-e | 0.8466 | 0.0060 | 1 | 0.7323 | 0.0146 | 2 | 0.1713 | 0.0013 | 1 | 0.2790 | 0.0023 | 2 |
5-80-a | 0.8939 | 0.0089 | 1 | 0.7733 | 0.0140 | 2 | 0.1714 | 0.0022 | 1 | 0.2062 | 0.0012 | 2 |
5-80-b | 0.8251 | 0.0148 | 1 | 0.7641 | 0.0195 | 2 | 0.1803 | 0.0016 | 1 | 0.2119 | 0.0011 | 2 |
5-80-c | 0.8641 | 0.0043 | 1 | 0.7670 | 0.0184 | 2 | 0.1966 | 0.0009 | 1 | 0.2035 | 0.0013 | 2 |
5-80-d | 0.8354 | 0.0030 | 1 | 0.7626 | 0.0076 | 2 | 0.1580 | 0.0017 | 1 | 0.2647 | 0.0015 | 2 |
5-80-e | 0.8456 | 0.0043 | 1 | 0.7557 | 0.0125 | 2 | 0.2485 | 0.0027 | 2 | 0.2094 | 0.0013 | 1 |
5-100-a | 0.8317 | 0.0024 | 1 | 0.7618 | 0.0104 | 2 | 0.1700 | 0.0016 | 1 | 0.3164 | 0.0010 | 2 |
5-100-b | 0.7985 | 0.0098 | 1 | 0.7070 | 0.0054 | 2 | 0.1795 | 0.0007 | 1 | 0.2278 | 0.0010 | 2 |
5-100-c | 0.8173 | 0.0056 | 1 | 0.8095 | 0.0154 | 2 | 0.0988 | 0.0007 | 1 | 0.1916 | 0.0010 | 2 |
5-100-d | 0.9211 | 0.0015 | 1 | 0.7455 | 0.0178 | 2 | 0.1797 | 0.0007 | 2 | 0.1587 | 0.0013 | 1 |
5-100-e | 0.8750 | 0.0024 | 1 | 0.7647 | 0.0105 | 2 | 0.1401 | 0.0007 | 1 | 0.1633 | 0.0006 | 2 |
Average | 0.8319 | 0.0090 | 1.0500 | 0.7605 | 0.0131 | 1.9500 | 0.1632 | 0.0012 | 1.1000 | 0.2346 | 0.0013 | 1.9000 |
Instance | C (GA, EAD) | C (EAD, GA) | t-Test | C (GA, SPEA) | C (SPEA, GA) | t-Test | C (GA, DRA) | C (DRA, GA) | t-Test |
---|---|---|---|---|---|---|---|---|---|
5-40-a | 0.7589 | 0.0807 | 0.7267 | 0.0863 | 0.5183 | 0.0923 | |||
5-40-b | 0.8063 | 0.0208 | 0.8110 | 0.0513 | 0.7292 | 0.0618 | |||
5-40-c | 0.8481 | 0.0310 | 0.6696 | 0.0575 | 0.6801 | 0.0836 | |||
5-40-d | 0.7870 | 0.0518 | 0.8489 | 0.0499 | 0.6589 | 0.0731 | |||
5-40-e | 0.8945 | 0.0146 | 0.8588 | 0.0208 | 0.7427 | 0.0427 | |||
5-60-a | 0.7667 | 0.0458 | 0.7828 | 0.0739 | 0.2857 | 0.1631 | |||
5-60-b | 0.7624 | 0.0000 | 0.7983 | 0.0405 | 0.6721 | 0.1010 | |||
5-60-c | 0.8135 | 0.0467 | 0.8265 | 0.0351 | 0.6653 | 0.0494 | |||
5-60-d | 0.8787 | 0.0000 | 0.8546 | 0.0310 | 0.6967 | 0.1147 | |||
5-60-e | 0.8237 | 0.0208 | 0.8574 | 0.0296 | 0.5813 | 0.1120 | |||
5-80-a | 0.6475 | 0.0143 | 0.6276 | 0.0482 | 0.4677 | 0.0488 | |||
5-80-b | 0.6470 | 0.0250 | 0.8523 | 0.0350 | 0.4133 | 0.0417 | |||
5-80-c | 0.8275 | 0.0333 | 0.7361 | 0.0393 | 0.6665 | 0.0714 | |||
5-80-d | 0.8558 | 0.0458 | 0.6980 | 0.1244 | 0.7835 | 0.0796 | |||
5-80-e | 0.7614 | 0.0125 | 0.8023 | 0.0000 | 0.6322 | 0.0333 | |||
5-100-a | 0.9483 | 0.0083 | 0.9217 | 0.0167 | 0.7924 | 0.0917 | |||
5-100-b | 0.7964 | 0.0283 | 0.7343 | 0.0767 | 0.5742 | 0.1233 | |||
5-100-c | 0.5983 | 0.0444 | 0.7663 | 0.1409 | 0.6745 | 0.1937 | |||
5-100-d | 0.8598 | 0.0100 | 0.7638 | 0.0267 | 0.4888 | 0.1600 | |||
Average | 0.7902 | 0.0284 | 0.7848 | 0.0495 | 0.5218 | 0.0429 |
Instance | MOGA-ALNS | SPEA-II | MOEA/D | MOEA/D-DRA | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Mean | Var | Mean | Var | t-Test | Mean | Var | t-Test | Mean | Var | t-Test | |
5-40-a | 0.2065 | 0.0030 | 0.2411 | 0.0011 | 0.3199 | 0.0019 | 0.3630 | 0.0022 | |||
5-40-b | 0.0697 | 0.0003 | 0.2794 | 0.0016 | 0.2995 | 0.0024 | 0.2411 | 0.0011 | |||
5-40-c | 0.1722 | 0.0012 | 0.2538 | 0.0014 | 0.2764 | 0.0015 | 0.2674 | 0.0011 | |||
5-40-d | 0.1572 | 0.0008 | 0.2361 | 0.0020 | 0.2110 | 0.0016 | 0.2097 | 0.0006 | |||
5-40-e | 0.1315 | 0.0004 | 0.2647 | 0.0014 | 0.2763 | 0.0007 | 0.2065 | 0.0005 | |||
5-60-a | 0.1708 | 0.0018 | 0.2783 | 0.0017 | 0.2598 | 0.0020 | 0.1805 | 0.0009 | |||
5-60-b | 0.1740 | 0.0013 | 0.2698 | 0.0016 | 0.2881 | 0.0019 | 0.2234 | 0.0022 | |||
5-60-c | 0.1501 | 0.0009 | 0.2499 | 0.0014 | 0.2499 | 0.0009 | 0.1951 | 0.0015 | |||
5-60-d | 0.1309 | 0.0009 | 0.2195 | 0.0006 | 0.2787 | 0.0013 | 0.2235 | 0.0018 | |||
5-60-e | 0.1714 | 0.0013 | 0.2898 | 0.0009 | 0.2954 | 0.0017 | 0.2907 | 0.0009 | |||
5-80-a | 0.1799 | 0.0002 | 0.2267 | 0.0011 | 0.2392 | 0.0007 | 0.1949 | 0.0011 | |||
5-80-b | 0.1808 | 0.0001 | 0.2345 | 0.0015 | 0.2353 | 0.0011 | 0.2204 | 0.0009 | |||
5-80-c | 0.1938 | 0.0001 | 0.2180 | 0.0017 | 0.2328 | 0.0016 | 0.2175 | 0.0010 | |||
5-80-d | 0.1642 | 0.0002 | 0.2260 | 0.0021 | 0.2528 | 0.0007 | 0.2670 | 0.0008 | |||
5-80-e | 0.2110 | 0.0002 | 0.2102 | 0.0012 | 0.2255 | 0.0013 | 0.2129 | 0.0008 | |||
5-100-a | 0.1658 | 0.0019 | 0.2771 | 0.0019 | 0.3093 | 0.0026 | 0.2875 | 0.0021 | |||
5-100-b | 0.1806 | 0.0003 | 0.2027 | 0.0008 | 0.2371 | 0.0007 | 0.1808 | 0.0007 | |||
5-100-c | 0.1023 | 0.0002 | 0.1886 | 0.0012 | 0.2019 | 0.0014 | 0.1830 | 0.0008 | |||
5-100-d | 0.1649 | 0.0002 | 0.1840 | 0.0010 | 0.1856 | 0.0003 | 0.1356 | 0.0008 | |||
5-100-e | 0.1434 | 0.0002 | 0.1929 | 0.0011 | 0.1814 | 0.0010 | 0.1717 | 0.0005 | |||
Average | 0.1610 | 0.0008 | 0.2372 | 0.0014 | 0.2528 | 0.0014 | 0.2236 | 0.0011 |
Instance | MOGA-ALNS | SPEA-II | MOEA/D | MOEA/D-DRA | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Mean | Var | Rank | Mean | Var | Rank | t-Test | Mean | Var | Rank | t-Test | Mean | Var | Rank | t-Test | |
5-40-a | 0.8442 | 0.0083 | 1 | 0.8029 | 0.0079 | 3 | 0.7315 | 0.0153 | 4 | 0.8139 | 0.0087 | 2 | |||
5-40-b | 0.7867 | 0.0101 | 2 | 0.6933 | 0.0140 | 4 | 0.6990 | 0.0211 | 3 | 0.8072 | 0.0061 | 1 | |||
5-40-c | 0.8438 | 0.0022 | 1 | 0.7788 | 0.0145 | 2 | 0.7765 | 0.0131 | 3 | 0.7543 | 0.0064 | 4 | |||
5-40-d | 0.8119 | 0.0131 | 1 | 0.6793 | 0.0120 | 4 | 0.7678 | 0.0248 | 2 | 0.7413 | 0.0057 | 3 | |||
5-40-e | 0.8217 | 0.0097 | 1 | 0.7861 | 0.0135 | 2 | 0.7499 | 0.0129 | 3 | 0.6809 | 0.0079 | 4 | |||
5-60-a | 0.7867 | 0.0106 | 2 | 0.7191 | 0.0195 | 3 | 0.8342 | 0.0084 | 1 | 0.6746 | 0.0028 | 4 | |||
5-60-b | 0.8196 | 0.0027 | 1 | 0.8064 | 0.0086 | 2 | 0.7689 | 0.0089 | 3 | 0.7410 | 0.0083 | 4 | |||
5-60-c | 0.8232 | 0.0024 | 1 | 0.7793 | 0.0153 | 2 | 0.7480 | 0.0259 | 3 | 0.7100 | 0.0063 | 4 | |||
5-60-d | 0.8006 | 0.0021 | 1 | 0.7486 | 0.0157 | 4 | 0.7565 | 0.0145 | 3 | 0.7781 | 0.0083 | 2 | |||
5-60-e | 0.8466 | 0.0060 | 1 | 0.7180 | 0.0094 | 4 | 0.7361 | 0.0147 | 3 | 0.8044 | 0.0088 | 2 | |||
5-80-a | 0.8939 | 0.0089 | 1 | 0.7364 | 0.0074 | 4 | 0.7963 | 0.0087 | 2 | 0.7631 | 0.0106 | 3 | |||
5-80-b | 0.8198 | 0.0023 | 1 | 0.7488 | 0.0064 | 4 | 0.8016 | 0.0110 | 3 | 0.8182 | 0.0116 | 2 | |||
5-80-c | 0.8641 | 0.0043 | 1 | 0.7834 | 0.0199 | 3 | 0.8006 | 0.0127 | 2 | 0.6968 | 0.0075 | 4 | |||
5-80-d | 0.8354 | 0.0030 | 1 | 0.7983 | 0.0084 | 3 | 0.8183 | 0.0189 | 2 | 0.7729 | 0.0092 | 4 | |||
5-80-e | 0.8456 | 0.0043 | 1 | 0.7583 | 0.0112 | 3 | 0.7937 | 0.0145 | 2 | 0.7237 | 0.0083 | 4 | |||
5-100-a | 0.8317 | 0.0024 | 1 | 0.6763 | 0.0324 | 4 | 0.7940 | 0.0120 | 3 | 0.8087 | 0.0119 | 2 | |||
5-100-b | 0.7985 | 0.0098 | 1 | 0.6820 | 0.0434 | 4 | 0.7718 | 0.0163 | 3 | 0.7810 | 0.0143 | 2 | |||
5-100-c | 0.8173 | 0.0056 | 1 | 0.7787 | 0.0042 | 2 | 0.7697 | 0.0102 | 3 | 0.6957 | 0.0127 | 4 | |||
5-100-d | 0.9211 | 0.0015 | 1 | 0.6818 | 0.0192 | 4 | 0.8211 | 0.0156 | 2 | 0.7957 | 0.0091 | 3 | |||
5-100-e | 0.8750 | 0.0024 | 1 | 0.6833 | 0.0231 | 3 | 0.7831 | 0.0171 | 2 | 0.6674 | 0.0222 | 4 | |||
Average | 0.8343 | 0.0055 | 1.1000 | 0.7419 | 0.0153 | 3.2000 | 0.7759 | 0.0148 | 2.6000 | 0.7514 | 0.0093 | 3.1000 |
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Pu, X.; Zhao, X. Post-Earthquake Emergency Logistics Location-Routing Optimization Considering Vehicle Three-Dimensional Loading Constraints. Symmetry 2024, 16, 1080. https://doi.org/10.3390/sym16081080
Pu X, Zhao X. Post-Earthquake Emergency Logistics Location-Routing Optimization Considering Vehicle Three-Dimensional Loading Constraints. Symmetry. 2024; 16(8):1080. https://doi.org/10.3390/sym16081080
Chicago/Turabian StylePu, Xujin, and Xu Zhao. 2024. "Post-Earthquake Emergency Logistics Location-Routing Optimization Considering Vehicle Three-Dimensional Loading Constraints" Symmetry 16, no. 8: 1080. https://doi.org/10.3390/sym16081080