# Integrated Scheduling of Picking and Distribution of Fresh Agricultural Products for Community Supported Agriculture Mode

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## Abstract

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## 1. Introduction

- (1)
- An integrated scheduling problem of the picking and distribution of fresh agricultural products with the consideration of minimizing picking and distribution costs as well as maximizing the freshness of the order is explored in this work. At the picking stage, a variety of agricultural products need to be assigned among multiple picking groups with different picking abilities. Then the orders are delivered to customers without unnecessary delay. A nonlinear mixed-integer programming model is constructed to formulate the problem.
- (2)
- A multi-objective multi-population genetic algorithm with local search (MOPGA-LS) is designed. The designed algorithm is compared with three multi-objective optimization algorithms in the literature: the non-dominated sorted genetic algorithm-II (NSGA-Ⅱ) [9], the multi-objective evolutionary algorithm based on decomposition (MOEA/D) [10], and the multi-objective evolutionary algorithm based on decomposition that is combined with the bee algorithm (MOEA/D-BA) [11]. The comparison results demonstrate that the designed algorithm is a superior optimizer for tackling the integrated picking and distribution problem for agricultural products.

## 2. Literature Review

## 3. Problem Statement

## 4. Proposed Algorithm

#### 4.1. Solution Representation

#### 4.2. Population Initialization

#### 4.3. Multi-Population Construction

#### 4.4. Selection, Improved Crossover, and Mutation

#### 4.5. Local Search

#### 4.6. Procedure of MOPGA-LS

## 5. Computational Experiments

#### 5.1. Test Instance Generation

#### 5.2. Performance Metrics

#### 5.3. Parameter Setting

#### 5.4. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Savarese, M.; Chamberlain, K.; Graffigna, G. Co-creating value in sustainable and alternative food networks: The case of community supported agriculture in New Zealand. Sustainability
**2020**, 12, 1252. [Google Scholar] [CrossRef] [Green Version] - Yu, Z.; Rehman Khan, S.A. Evolutionary game analysis of green agricultural product supply chain financing system: COVID-19 pandemic. Int. J. Logist. Res. Appl.
**2021**, 25, 1115–1135. [Google Scholar] [CrossRef] - Pulighe, G.; Lupia, F. Food First: COVID-19 Outbreak and Cities Lockdown a Booster for a Wider Vision on Urban Agriculture. Sustainability
**2020**, 12, 5012. [Google Scholar] [CrossRef] - Medici, M.; Canavari, M.; Castellini, A. Exploring the economic, social, and environmental dimensions of community-supported agriculture in Italy. J. Clean. Prod.
**2021**, 316, 128233. [Google Scholar] [CrossRef] - Zhu, A.; Bian, B.; Jiang, Y.; Hu, J. Integrated Tomato Picking and Distribution Scheduling Based on Maturity. Sustainability
**2020**, 12, 7934. [Google Scholar] [CrossRef] - Wang, Z.; Yao, D.-Q.; Yue, X. E-business system investment for fresh agricultural food industry in China. Ann. Oper. Res.
**2017**, 257, 379–394. [Google Scholar] [CrossRef] - Yan, B.; Chen, X.; Cai, C.; Guan, S. Supply chain coordination of fresh agricultural products based on consumer behavior. Comput. Oper. Res.
**2020**, 123, 105038. [Google Scholar] [CrossRef] - Liang, Y.; Liu, F.; Lim, A.; Zhang, D. An integrated route, temperature and humidity planning problem for the distribution of perishable products. Comput. Ind. Eng.
**2020**, 147, 106623. [Google Scholar] [CrossRef] - Deb, K.; Pratap, A.; Agarwal, S.; Meyarivan, T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput.
**2002**, 6, 182–197. [Google Scholar] [CrossRef] [Green Version] - Qingfu, Z.; Hui, L. MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. Evol. Comput.
**2007**, 11, 712–731. [Google Scholar] [CrossRef] - Gharaei, A.; Jolai, F. A multi-agent approach to the integrated production scheduling and distribution problem in multi-factory supply chain. Appl. Soft Comput.
**2018**, 65, 577–589. [Google Scholar] [CrossRef] - Ahumada, O.; Villalobos, J.R. Application of planning models in the agri-food supply chain: A review. Eur. J. Oper. Res.
**2009**, 196, 1–20. [Google Scholar] [CrossRef] - Ferrer, J.-C.; Mac Cawley, A.; Maturana, S.; Toloza, S.; Vera, J. An optimization approach for scheduling wine grape harvest operations. Int. J. Product. Econ.
**2008**, 112, 985–999. [Google Scholar] [CrossRef] - Bohle, C.; Maturana, S.; Vera, J. A robust optimization approach to wine grape harvesting scheduling. Eur. J. Oper. Res.
**2010**, 200, 245–252. [Google Scholar] [CrossRef] - González-Araya, M.C.; Soto-Silva, W.E.; Espejo, L.G.A. Harvest Planning in Apple Orchards Using an Optimization Model. In Handbook of Operations Research in Agriculture and the Agri-Food Industry; Plà-Aragonés, L.M., Ed.; Springer: New York, NY, USA, 2015; pp. 79–105. [Google Scholar] [CrossRef]
- Kusumastuti, R.D.; Donk, D.P.v.; Teunter, R. Crop-related harvesting and processing planning: A review. Int. J. Product. Econ.
**2016**, 174, 76–92. [Google Scholar] [CrossRef] - Gómez-Lagos, J.E.; González-Araya, M.C.; Soto-Silva, W.E.; Rivera-Moraga, M.M. Optimizing tactical harvest planning for multiple fruit orchards using a metaheuristic modeling approach. Eur. J. Oper. Res.
**2021**, 290, 297–312. [Google Scholar] [CrossRef] - Augerat, P.; Belenguer, J.M.; Benavent, E.; Corberán, A.; Naddef, D. Separating capacity constraints in the CVRP using tabu search. Eur. J. Oper. Res.
**1998**, 106, 546–557. [Google Scholar] [CrossRef] - Osvald, A.; Stirn, L.Z. A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food. J. Food Eng.
**2008**, 85, 285–295. [Google Scholar] [CrossRef] - Chen, H.-K.; Hsueh, C.-F.; Chang, M.-S. Production scheduling and vehicle routing with time windows for perishable food products. Comput. Oper. Res.
**2009**, 36, 2311–2319. [Google Scholar] [CrossRef] - International Journal of Lower Extremity WoundsSong, B.D.; Ko, Y.D. A vehicle routing problem of both refrigerated- and general-type vehicles for perishable food products delivery. J. Food Eng.
**2016**, 169, 61–71. [Google Scholar] [CrossRef] - Wang, H.; Xu, Y.; Wang, Z.; Zhou, T.; Tian, D. Distribution Routing Optimization of Fresh Agricultural Products Based on Road Conditions. J. Syst. Simul.
**2019**, 31, 126. [Google Scholar] [CrossRef] - Amorim, P.; Almada-Lobo, B. The impact of food perishability issues in the vehicle routing problem. Comput. Ind. Eng.
**2014**, 67, 223–233. [Google Scholar] [CrossRef] - Geismar, H.N.; Laporte, G.; Lei, L.; Sriskandarajah, C. The integrated production and transportation scheduling problem for a product with a short lifespan. INFORMS J. Comput.
**2008**, 20, 21–33. [Google Scholar] [CrossRef] - Devapriya, P.; Ferrell, W.; Geismar, N. Integrated production and distribution scheduling with a perishable product. Eur. J. Oper. Res.
**2017**, 259, 906–916. [Google Scholar] [CrossRef] - Belo-Filho, M.A.F.; Amorim, P.; Almada-Lobo, B. An adaptive large neighbourhood search for the operational integrated production and distribution problem of perishable products. Int. J. Prod. Res.
**2015**, 53, 6040–6058. [Google Scholar] [CrossRef] [Green Version] - Kergosien, Y.; Gendreau, M.; Billaut, J.C. A Benders decomposition-based heuristic for a production and outbound distribution scheduling problem with strict delivery constraints. Eur. J. Oper. Res.
**2017**, 262, 287–298. [Google Scholar] [CrossRef] - Lacomme, P.; Moukrim, A.; Quilliot, A.; Vinot, M. Supply chain optimisation with both production and transportation integration: Multiple vehicles for a single perishable product. Int. J. Prod. Res.
**2018**, 56, 4313–4336. [Google Scholar] [CrossRef] [Green Version] - Neves-Moreira, F.; Almada-Lobo, B.; Cordeau, J.-F.; Guimarães, L.; Jans, R. Solving a large multi-product production-routing problem with delivery time windows. Omega
**2019**, 86, 154–172. [Google Scholar] [CrossRef] - Marandi, F.; Fatemi Ghomi, S.M.T. Integrated multi-factory production and distribution scheduling applying vehicle routing approach. Int. J. Prod. Res.
**2018**, 57, 722–748. [Google Scholar] [CrossRef] - Mohammadi, S.; Al-e-Hashem, S.M.J.M.; Rekik, Y. An integrated production scheduling and delivery route planning with multi-purpose machines: A case study from a furniture manufacturing company. Int. J. Product. Econ.
**2020**, 219, 347–359. [Google Scholar] [CrossRef] - Qin, C.; Gu, X. Improved PSO Algorithm Based on Exponential Center Symmetric Inertia Weight Function and Its Application in Infrared Image Enhancement. Symmetry
**2020**, 12, 248. [Google Scholar] [CrossRef] [Green Version] - Tefek, M.F. Artificial bee colony algorithm based on a new local search approach for parameter estimation of photovoltaic systems. J. Comput. Electron.
**2021**, 20, 2530–2562. [Google Scholar] [CrossRef] - Ul Hassan, N.; Bangyal, W.H.; Ali Khan, M.S.; Nisar, K.; Ag Ibrahim, A.A.; Rawat, D.B. Improved Opposition-Based Particle Swarm Optimization Algorithm for Global Optimization. Symmetry
**2021**, 13, 2280. [Google Scholar] [CrossRef] - Saad, A.; Khan, S.A.; Mahmood, A. A multi-objective evolutionary artificial bee colony algorithm for optimizing network topology design. Swarm Evol. Comput.
**2018**, 38, 187–201. [Google Scholar] [CrossRef] - Liu, L.; Liu, X.; Wang, N.; Zou, P. Modified cuckoo search algorithm with variational parameters and logistic map. Algorithms
**2018**, 11, 30. [Google Scholar] [CrossRef] [Green Version] - Fu, Y.; Tian, G.; Fathollahi-Fard, A.M.; Ahmadi, A.; Zhang, C. Stochastic multi-objective modelling and optimization of an energy-conscious distributed permutation flow shop scheduling problem with the total tardiness constraint. J. Clean. Prod.
**2019**, 226, 515–525. [Google Scholar] [CrossRef] - Fu, Y.; Zhou, M.; Guo, X.; Qi, L.; Sedraoui, K. Multiverse optimization algorithm for stochastic biobjective disassembly sequence planning subject to operation failures. IEEE Trans. Syst. Man Cybern. Syst.
**2021**, 52, 1041–1051. [Google Scholar] [CrossRef] - Chan, F.T.S.; Wang, Z.X.; Goswami, A.; Singhania, A.; Tiwari, M.K. Multi-objective particle swarm optimisation based integrated production inventory routing planning for efficient perishable food logistics operations. Int. J. Prod. Res.
**2020**, 58, 5155–5174. [Google Scholar] [CrossRef] - Fan, T.; Xu, C.; Tao, F. Dynamic pricing and replenishment policy for fresh produce. Comput. Ind. Eng.
**2020**, 139, 106127. [Google Scholar] [CrossRef] - Yang, Y.; Liu, J.; Tan, S.; Wang, H. A multi-objective differential evolutionary algorithm for constrained multi-objective optimization problems with low feasible ratio. Appl. Soft Comput.
**2019**, 80, 42–56. [Google Scholar] [CrossRef] - Ojsteršek, R.; Brezocnik, M.; Buchmeister, B. Multi-objective optimization of production scheduling with evolutionary computation: A review. Int. J. Ind. Eng. Comput.
**2020**, 11, 359–376. [Google Scholar] [CrossRef] - Xuping, W.; Jun, Z.; Caiyu, Y. An Integrated Production and Delivery Scheduling Model and Algorithm for Online Meal Ordering. J. Syst. Manag.
**2020**, 29, 158. [Google Scholar] [CrossRef] - Guo, F.; Huang, Z.; Huang, W. Integrated sustainable planning of fast-pick area network and vehicle routing with simultaneous delivery and pick-up. Syst. Eng. Theory Pract.
**2021**, 41, 962–978. [Google Scholar] [CrossRef] - Lin, S.-W.; Ying, K.-C. Minimizing makespan and total flowtime in permutation flowshops by a bi-objective multi-start simulated-annealing algorithm. Comput. Oper. Res.
**2013**, 40, 1625–1647. [Google Scholar] [CrossRef] - Fatemi Ghomi, S.; Karimi, B.; Behnamian, J.; Firoozbakht, J. A multi-objective particle swarm optimization based on pareto archive for integrated production and distribution planning in A Green supply chain. Appl. Artif. Intell.
**2021**, 35, 133–153. [Google Scholar] [CrossRef] - Jiang, E.-d.; Wang, L. An improved multi-objective evolutionary algorithm based on decomposition for energy-efficient permutation flow shop scheduling problem with sequence-dependent setup time. Int. J. Prod. Res.
**2019**, 57, 1756–1771. [Google Scholar] [CrossRef] - Riquelme, N.; Von Lücken, C.; Baran, B. Performance metrics in multi-objective optimization. In Proceedings of the 2015 Latin American Computing Conference (CLEI), Arequipa, Peru, 19–23 October 2015; pp. 1–11. [Google Scholar] [CrossRef]
- Majumder, S.; Barma, P.S.; Biswas, A.; Banerjee, P.; Mandal, B.K.; Kar, S.; Ziemba, P. On multi-objective minimum spanning tree problem under uncertain paradigm. Symmetry
**2022**, 14, 106. [Google Scholar] [CrossRef] - Fu, Y.; Hou, Y.; Chen, Z.; Pu, X.; Gao, K.; Sadollah, A. Modelling and scheduling integration of distributed production and distribution problems via black widow optimization. Swarm Evol. Comput.
**2022**, 68, 101015. [Google Scholar] [CrossRef]

Notations | Descriptions |
---|---|

Indices | |

$M$ | Set of groups, $M=\left\{1,2,\dots ,\mathsf{\gamma}\right\},$ where $\mathsf{\gamma}$ is the number of groups. The group is indexed by the symbol $l\in M$. |

$J$ | Set of agricultural product varieties, $J=\left\{0,1,2,\dots ,\omega \right\},$ where $\omega $ is the total number of agricultural product varieties and 0 is a dummy product. The products are indexed by symbols $i,j\in J$. |

${J}_{1m}$ | Set of agricultural product varieties with decay rate ${\beta}_{1}$ required by customer $m$. |

${J}_{2m}$ | Set of agricultural product varieties with decay rate ${\beta}_{2}$ required by customer $m$. |

$D$ | Set of customers, $D=\left\{1,2,\dots ,\phi \right\},$where$$ is the total number of customers. The customers are indexed by symbols $m,n\in D$. |

$N$ | Set of the farm and customers, $N=\left\{0\right\}\cup D$, where 0 denotes the farm. |

$K$ | Set of vehicles, $K=\left\{1,2,\dots ,\delta \right\},$ where $\delta $ is the number of vehicles, which are indexed by symbols $k\in K$. |

Parameters | |

${q}_{mj}$ | Demand for product $j$ of customer $m$. |

${G}_{j}$ | Total demand for product $j$$,{G}_{j}={\displaystyle \sum}_{m\in D}{q}_{mj},\forall j\in J$. |

${U}_{mj}$ | Customer-product matrix, which takes value 1 if customer $m$ requires product $j$, and 0 otherwise. |

${t}_{jl}$ | Picking time of product $j$ with group $l$. |

${p}_{jl}$ | Unit picking cost of product $j$ with group $l$. |

${d}_{mn}$ | Distance between customers $m$ and $n$. |

$\lambda $ | Variable cost of the vehicle per unit of time. |

$v$ | Speed of a vehicle. |

$F$ | Fixed cost of a vehicle. |

$Q$ | Capacity of a vehicle. |

$B$ | An infinite constant. |

Decision variables | |

${X}_{ijl}$ | A binary variable that takes 1 if product $j$ is picked immediately after product $i$ by group $l$, and 0 otherwise. |

${W}_{mk}$ | A binary variable that takes 1 if customer $m$ is delivered by vehicle $k$, and 0 otherwise. |

${Z}_{mnk}$ | A binary variable that takes 1 if customer $n$ is delivered after customer $m$ by vehicle $k$, and 0 otherwise. |

${r}_{i}$ | Auxiliary variable that is employed to eliminate sub-tour in picking. |

${u}_{m}$ | Auxiliary variable that is employed to eliminate sub-tour in distribution. |

${c}_{j}$ | Picking completion time of product $j$. |

${a}_{mk}$ | Visiting time of customer $m$ by vehicle $k$. |

Groups | Unit Picking Speed of Groups | Unit Picking Cost of Groups |
---|---|---|

1 | $U\left[0.001,0.005\right]$ | 100 |

2 | $U\left[0.006,0.01\right]$ | 90 |

3 | $U\left[0.011,0.015\right]$ | 80 |

4 | $U\left[0.016,0.02\right]$ | 70 |

5 | $U\left[0.021,0.025\right]$ | 60 |

Groups | Products with Decay Rate ${\mathit{\beta}}_{1}$ | Products with Decay Rate ${\mathit{\beta}}_{2}$ | Customers | |
---|---|---|---|---|

$\mathrm{M}2\text{-}\mathrm{J}20\text{-}\mathrm{D}20$ | 2 | 10 | 10 | 20 |

$\mathrm{M}2\text{-}\mathrm{J}30\text{-}\mathrm{D}40$ | 2 | 15 | 15 | 40 |

$\mathrm{M}3\text{-}\mathrm{J}30\text{-}\mathrm{D}40$ | 3 | 15 | 15 | 40 |

$\mathrm{M}3\text{-}\mathrm{J}40\text{-}\mathrm{D}60$ | 3 | 20 | 20 | 60 |

$\mathrm{M}4\text{-}\mathrm{J}40\text{-}\mathrm{D}60$ | 4 | 20 | 20 | 60 |

$\mathrm{M}4\text{-}\mathrm{J}50\text{-}\mathrm{D}80$ | 4 | 25 | 25 | 80 |

$\mathrm{M}5\text{-}\mathrm{J}50\text{-}\mathrm{D}80$ | 5 | 25 | 25 | 80 |

$\mathrm{M}5\text{-}\mathrm{J}60\text{-}\mathrm{D}100$ | 5 | 30 | 30 | 100 |

ID | Q | S | α | Z | RV |
---|---|---|---|---|---|

1 | 50 | 3 | 0.2 | 5 | 0.7743 |

2 | 50 | 6 | 0.4 | 10 | 0.7668 |

3 | 50 | 9 | 0.6 | 15 | 0.7512 |

4 | 50 | 12 | 0.8 | 20 | 0.7531 |

5 | 75 | 3 | 0.4 | 15 | 0.7704 |

6 | 75 | 6 | 0.2 | 20 | 0.7598 |

7 | 75 | 9 | 0.8 | 5 | 0.7775 |

8 | 75 | 12 | 0.6 | 10 | 0.7710 |

9 | 100 | 3 | 0.6 | 20 | 0.7420 |

10 | 100 | 6 | 0.8 | 15 | 0.7391 |

11 | 100 | 9 | 0.2 | 10 | 0.7332 |

12 | 100 | 12 | 0.4 | 5 | 0.7117 |

13 | 125 | 3 | 0.8 | 10 | 0.7205 |

14 | 125 | 6 | 0.6 | 5 | 0.6420 |

15 | 125 | 9 | 0.4 | 20 | 0.7093 |

16 | 125 | 12 | 0.2 | 15 | 0.6814 |

Level | $\mathit{Q}$ | $\mathit{S}$ | $\mathit{\alpha}$ | $\mathit{Z}$ |
---|---|---|---|---|

1 | 0.7613 | 0.7518 | 0.7372 | 0.7264 |

2 | 0.7697 | 0.7269 | 0.7396 | 0.7479 |

3 | 0.7315 | 0.7428 | 0.7265 | 0.7355 |

4 | 0.6883 | 0.7293 | 0.7475 | 0.7411 |

Delta | 0.0814 | 0.0249 | 0.0210 | 0.0215 |

rank | 1 | 2 | 4 | 3 |

Set Name | Ins. | MOPGA-LS | NSGA—II | MOEA/D | MOEA/D-BA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Average | Average | t-Test | U-Test | Average | t-Test | U-Test | Average | t-Test | U-Test | ||

M2-J20-D20 | 1 | 0.9025 | 0.8671 | + | + | 0.7092 | + | + | 0.1965 | + | + |

2 | 0.8963 | 0.8455 | + | + | 0.7260 | + | + | 0.2107 | + | + | |

3 | 0.8962 | 0.7470 | + | + | 0.6230 | + | + | 0.2050 | + | + | |

4 | 0.9289 | 0.7911 | + | + | 0.6358 | + | + | 0.1965 | + | + | |

M2-J30-D40 | 1 | 0.8981 | 0.7857 | + | + | 0.6746 | + | + | 0.2172 | + | + |

2 | 0.8974 | 0.7503 | + | + | 0.6192 | + | + | 0.1759 | + | + | |

3 | 0.9550 | 0.8075 | + | + | 0.7168 | + | + | 0.1845 | + | + | |

4 | 0.8881 | 0.7648 | + | + | 0.6271 | + | + | 0.2136 | + | + | |

M3-J30-D40 | 1 | 0.9558 | 0.8978 | + | + | 0.8235 | + | + | 0.3552 | + | + |

2 | 0.9423 | 0.9018 | + | + | 0.8410 | + | + | 0.3850 | + | + | |

3 | 0.9284 | 0.8929 | + | + | 0.8311 | + | + | 0.1566 | + | + | |

4 | 0.9258 | 0.8638 | + | + | 0.8026 | + | + | 0.1772 | + | + | |

M3-J40-D60 | 1 | 0.9451 | 0.9093 | + | + | 0.8689 | + | + | 0.1746 | + | + |

2 | 0.9514 | 0.9287 | + | + | 0.8948 | + | + | 0.3135 | + | + | |

3 | 0.9653 | 0.9399 | + | + | 0.9072 | + | + | 0.1848 | + | + | |

4 | 0.9569 | 0.9336 | + | + | 0.8963 | + | + | 0.3169 | + | + | |

M4-J40-D60 | 1 | 0.9842 | 0.9590 | + | + | 0.9339 | + | + | 0.1181 | + | + |

2 | 0.9808 | 0.9678 | + | + | 0.9463 | + | + | 0.2780 | + | + | |

3 | 0.9835 | 0.9679 | + | + | 0.9478 | + | + | 0.1179 | + | + | |

4 | 0.9816 | 0.9613 | + | + | 0.9358 | + | + | 0.2762 | + | + | |

M4-J50-D80 | 1 | 0.9904 | 0.9842 | + | + | 0.9725 | + | + | 0.1804 | + | + |

2 | 0.9923 | 0.9884 | + | + | 0.9793 | + | + | 0.1857 | + | + | |

3 | 0.9917 | 0.9860 | + | + | 0.9762 | + | + | 0.1116 | + | + | |

4 | 0.9910 | 0.9851 | + | + | 0.9746 | + | + | 0.1121 | + | + | |

M5-J50-D80 | 1 | 0.9944 | 0.9883 | + | + | 0.9799 | + | + | 0.1994 | + | + |

2 | 0.9938 | 0.9867 | + | + | 0.9801 | + | + | 0.1083 | + | + | |

3 | 0.9949 | 0.9936 | ~ | ~ | 0.9889 | + | + | 0.1119 | + | + | |

4 | 0.9944 | 0.9863 | + | + | 0.9844 | + | + | 0.1092 | + | + | |

M5-J60-D100 | 1 | 0.9920 | 0.9885 | + | ~ | 0.9845 | + | + | 0.1279 | + | + |

2 | 0.9951 | 0.9944 | ~ | ~ | 0.9908 | + | + | 0.1268 | + | + | |

3 | 0.9956 | 0.9947 | ~ | ~ | 0.9915 | + | + | 0.1270 | + | + | |

4 | 0.9943 | 0.9936 | ~ | ~ | 0.9901 | + | + | 0.2052 | + | + |

Set Name | Ins. | MOPGA-LS | NSGA—II | MOEA/D | MOEA/D-BA | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Average | Average | t-Test | U-Test | Average | t-Test | U-Test | Average | t-Test | U-Test | ||

M2-J20-D20 | 1 | 0.1113 | 0.1931 | + | + | 0.7035 | + | + | 0.4493 | + | + |

2 | 0.1231 | 0.3256 | + | + | 0.8105 | + | + | 0.6037 | + | + | |

3 | 0.1835 | 0.9014 | + | + | 1.6756 | + | + | 1.1924 | + | + | |

4 | 0.2830 | 0.3093 | + | + | 0.6614 | + | + | 0.5101 | + | + | |

M2-J30-D40 | 1 | 0.1541 | 0.4488 | + | + | 0.9139 | + | + | 0.7899 | + | + |

2 | 0.1511 | 0.6358 | + | + | 1.2209 | + | + | 0.9799 | + | + | |

3 | 0.1354 | 0.4292 | + | + | 0.6814 | + | + | 0.7185 | + | + | |

4 | 0.3099 | 0.7114 | + | + | 1.0881 | + | + | 1.1647 | + | + | |

M3-J30-D40 | 1 | 0.0678 | 0.2347 | + | + | 0.5242 | + | + | 0.4527 | + | + |

2 | 0.1557 | 0.3364 | + | + | 0.6253 | + | + | 0.6201 | + | + | |

3 | 0.0775 | 0.1632 | + | + | 0.3281 | + | + | 0.3093 | + | + | |

4 | 0.1423 | 0.4104 | + | + | 0.7467 | + | + | 0.7239 | + | + | |

M3-J40-D60 | 1 | 0.0604 | 0.1639 | + | + | 0.3129 | + | + | 0.3109 | + | + |

2 | 0.1706 | 0.4405 | + | + | 0.8525 | + | + | 0.8265 | + | + | |

3 | 0.1034 | 0.3151 | + | + | 0.6426 | + | + | 0.6259 | + | + | |

4 | 0.0628 | 0.1331 | + | + | 0.2711 | + | + | 0.2797 | + | + | |

M4-J40-D60 | 1 | 0.0284 | 0.1204 | + | + | 0.2581 | + | + | 0.2600 | + | + |

2 | 0.0534 | 0.1184 | + | + | 0.2507 | + | + | 0.3003 | + | + | |

3 | 0.0424 | 0.1405 | + | + | 0.2848 | + | + | 0.2868 | + | + | |

4 | 0.0402 | 0.1116 | + | + | 0.2227 | + | + | 0.2289 | + | + | |

M4-J50-D80 | 1 | 0.0304 | 0.0721 | + | + | 0.1745 | + | + | 0.1806 | + | + |

2 | 0.0299 | 0.0711 | + | + | 0.1826 | + | + | 0.1791 | + | + | |

3 | 0.0246 | 0.0653 | + | + | 0.1563 | + | + | 0.1605 | + | + | |

4 | 0.0454 | 0.1140 | + | + | 0.2444 | + | + | 0.2924 | + | + | |

M5-J50-D80 | 1 | 0.0205 | 0.0594 | + | + | 0.1647 | + | + | 0.1594 | + | + |

2 | 0.0278 | 0.0652 | + | + | 0.2020 | + | + | 0.2071 | + | + | |

3 | 0.0320 | 0.0649 | + | + | 0.1962 | + | + | 0.2043 | + | + | |

4 | 0.0370 | 0.0782 | + | + | 0.2372 | + | + | 0.2260 | + | + | |

M5-J60-D100 | 1 | 0.0179 | 0.0488 | + | + | 0.1304 | + | + | 0.1461 | + | + |

2 | 0.0339 | 0.0614 | + | + | 0.2236 | + | + | 0.2091 | + | + | |

3 | 0.0190 | 0.0370 | + | + | 0.1379 | + | + | 0.1412 | + | + | |

4 | 0.0183 | 0.0355 | + | + | 0.1116 | + | + | 0.1191 | + | + |

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**MDPI and ACS Style**

Pu, X.; Xu, Y.; Fu, Y.
Integrated Scheduling of Picking and Distribution of Fresh Agricultural Products for Community Supported Agriculture Mode. *Symmetry* **2022**, *14*, 2530.
https://doi.org/10.3390/sym14122530

**AMA Style**

Pu X, Xu Y, Fu Y.
Integrated Scheduling of Picking and Distribution of Fresh Agricultural Products for Community Supported Agriculture Mode. *Symmetry*. 2022; 14(12):2530.
https://doi.org/10.3390/sym14122530

**Chicago/Turabian Style**

Pu, Xujin, Yuchen Xu, and Yaping Fu.
2022. "Integrated Scheduling of Picking and Distribution of Fresh Agricultural Products for Community Supported Agriculture Mode" *Symmetry* 14, no. 12: 2530.
https://doi.org/10.3390/sym14122530