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REVIEW 5 major objections 5 minor 34 references

When to use simulated annealing for solving CVRP? A case study of fuel deliveries in Poland

T0 review · 5 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper claims that a Monte Carlo plus simulated annealing heuristic returns shorter fuel-delivery routes than a Gurobi-powered MIP model for computation times up to about five seconds, after which the MIP solver catches up.

desk verdict A routine MC+SA case study whose central Gurobi comparison is undermined by a flawed written MIP baseline; clear exposition and public code, but the headline claim is not established. read the letter →

arxiv 2412.09293 v1 pith:PDYGV4LQ submitted 2024-12-12 math.OC

Vitalii Naumov This is my paper · ORCID
classification math.OC MSC 90C5990B0690C11
keywords fueldeliveryCVRPsimulatedannealingMonteCarlosimulationGurobivehicleroutingtimewindows
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Fuel dispatchers often need to rebuild delivery routes within seconds when demand shifts, but commercial mixed-integer solvers can take many seconds to return a good solution. The paper claims that a simple two-stage heuristic — random route construction by Monte Carlo, then route-by-route simulated annealing — consistently gives shorter total distances than a Gurobi-powered MIP model when the planning budget is about five seconds or less. In the reported instance, the heuristic finds a 2381-km plan in roughly one second, while Gurobi needs about five seconds to match that quality. The practical answer to the title question is: use simulated annealing when time is short, and switch to an exact solver when the planner can wait longer.

What carries the argument

The mechanism is a two-stage stochastic local search. The first stage runs R Monte Carlo constructions: each route randomly adds stations while respecting the 39,000-liter vehicle capacity and the latest-arrival time windows, and the shortest complete plan is kept. The second stage applies simulated annealing independently to each route, generating a candidate by reversing a randomly chosen fragment between two non-neighbor stations (a 2-opt-style move) and accepting it with probability governed by the temperature schedule $T_i = T_0/(i+1)$, with $T_0 = 1$ and $T_{\mathrm{end}} = 0.001$. The SA stage is what extracts the additional distance reduction at almost no computational cost, about 0.06 seconds per run.

What would settle it

A direct check is to take the demand matrix from the reported instance and sum the demands along each Gurobi-generated route; any route whose total demand exceeds the 39,000-liter capacity shows the baseline solutions are infeasible and the runtime comparison collapses. A stronger test is to re-run the comparison with a corrected MIP model that enforces flow conservation at the first and last stops of every route and bounds total route demand above by capacity, then see whether Gurobi still trails the heuristic in the first five seconds.

Watch

Extended reading notes

Core claim

The paper's central discovery is an empirical answer to when simulated annealing should be used for capacitated fuel-delivery routing. With 1000 Monte Carlo route constructions, the two-stage heuristic averages 2381 km of total route distance in about 1.09 seconds, while the Gurobi solver reaches that same distance only after about five seconds; the paper states that the heuristic consistently outperforms the Gurobi-powered model for up to five seconds of computation time. Beyond that threshold the solver overtakes it: with 10,000 Monte Carlo trials the heuristic takes about ten seconds and yields 2326 km, whereas Gurobi at ten seconds yields 2287 km. The paper therefore positions simulated annealing as the right tool for the seconds-scale replanning window of real dispatch operations, not as a replacement for exact methods when longer computation is available.

Load-bearing premise

The load-bearing premise is that the Gurobi MIP model is a correct and feasible formulation of the same routing problem, so the measured runtime gap is a fair head-to-head comparison.

Editorial extensions

If this is right

  • A dispatcher with a five-second replanning budget gets shorter routes from the MC-SA heuristic than from a commercial MIP solver.
  • The SA stage costs only about 0.06 seconds per run, so almost all of the heuristic's compute budget goes to the Monte Carlo construction phase.
  • For planning budgets beyond roughly five seconds, the paper's data show the MIP solver producing shorter routes, so the heuristic is not a general replacement for exact methods.
  • Because the heuristic runs in Python and needs no commercial solver license, it lowers the software cost of short-window route replanning.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the five-second crossover is almost certainly instance- and hardware-specific; on denser networks or with tighter time windows, the relative advantage of the stochastic heuristic could shift, so the decision rule should be re-estimated on each deployment.
  • A testable extension is to hand the heuristic's solution to an exact solver as a warm start after the first few seconds, which would combine the rapid initial improvement with the solver's longer-horizon convergence.
  • Because the paper's gains come almost entirely from the 0.06-second SA stage rather than from more Monte Carlo trials, tuning the annealing schedule (end temperature and cooling rate) is likely to yield more improvement per compute second than increasing R.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes a two-stage heuristic for the capacitated vehicle routing problem (CVRP) in fuel delivery: a Monte Carlo stage generates many candidate route sets, and a simulated annealing stage improves the best of them. The method is compared against a mixed-integer programming model solved with Gurobi on a single instance built from Polish fuel-delivery data. The central claim is that the simulated-annealing heuristic consistently produces shorter routes than the Gurobi-based model for computation times up to about five seconds, after which Gurobi tends to catch up or surpass it.

Significance. If the comparison were valid, the paper would provide a practically useful result: for short planning budgets, a simple open-source heuristic may beat a commercial MIP solver on a real-world fuel-delivery instance. The authors deserve credit for making source code publicly available and for averaging the stochastic heuristic over 100 repetitions. However, the central claim is not currently established. The written MIP model has serious correctness defects, the presented heuristic algorithm contains a non-terminating loop in its pseudocode, and the quantitative evidence is drawn from one of the 300 claimed instances. The significance of the work is therefore conditional on substantial correction and re-evaluation.

major comments (5)
  1. [Section 3.3, Eq. (5)] Eq. (5) does not enforce flow conservation for the first and last stations of a route. It writes sum_{j=1..G} x_{n,j,i} - sum_{j=1..G} x_{n,i,j} = 0 for each station i, using only station-to-station arcs. For a route of the form 0 -> a -> ... -> b -> G+1, station a has no incoming station-to-station arc, so the balance is -1, and station b has no outgoing station-to-station arc, so the balance is +1. Thus the constraint is violated by every route with at least two stations. If the implemented Gurobi model reflects this equation, the reported baseline solutions cannot be valid routes; if it does not, the written model does not match the experiment.
  2. [Section 3.3, Eqs. (10)-(11)] The capacity constraints do not bound total route demand above by C. Eq. (10) only bounds the demand delivered before the last station by C, while Eq. (11) only requires that the total demand of the route be at least C. A route that delivers 39,000 liters before its final stop and 15,500 liters at the final stop has total demand 54,500 liters, exceeding the stated 39,000-liter capacity, yet it satisfies both inequalities. The Gurobi model as written therefore admits infeasible routes, which invalidates the runtime-quality comparison in Section 5.
  3. [Section 3.3, Eqs. (3)-(6)] Even if Eq. (5) were corrected to include depot arcs, the constraint set does not eliminate disconnected subtours. For a fixed route index n, the constraints allow a cycle b -> c -> b among stations to coexist with the path 0 -> a -> G+1, because station-level inflow-outflow balance does not enforce route connectivity. A correct CVRP formulation needs explicit subtour-elimination constraints or an equivalent connected-flow structure. This is a further load-bearing defect in the baseline model.
  4. [Section 4, Algorithm 2] The inner route-generation loop in Algorithm 2 can fail to terminate. The loop continues while volume < C (line 6), but a station is accepted only when volume + q_j <= C (line 8). Since volume never exceeds C, the loop can exit only if the residual capacity is filled exactly; if no remaining station fits in the residual capacity, the while loop spins forever because no station is removed from Omega. The reported run times therefore imply that the implementation does not match this pseudocode, so the heuristic as presented is not a well-defined algorithm.
  5. [Section 5, Table 2 and Figures 3-5] The paper reports detailed results for only one of the 300 generated instances. The statement that the same regularities were observed in every other instance is not supported by any aggregated data, so the claimed conclusion that the heuristic 'consistently outperforms' Gurobi up to five seconds rests on a single case. In addition, Table 2 gives only means over 100 repetitions, without standard deviations or other variability measures, so the stochastic comparisons are not statistically quantified.
minor comments (5)
  1. [Section 3.3, Eq. (7)] The constraint uses the index k in s_{k,i} and u_{k,j} without specifying which day k corresponds to route n; the mapping between routes and days should be made explicit.
  2. [Section 3.3, notation] Some constraints are written with n = 1,...,N_k and others with n = 1,...,N; since N = sum_k N_k, the intended indexing should be clarified.
  3. [Section 4, Algorithm 3] There is a typo in line 8 of Algorithm 3: 'cadidate' should be 'candidate'.
  4. [Section 5, Figure 2] Reporting the Gurobi MIP optimality gap would help interpret the statement that later improvements yield diminishing returns.
  5. [Table 1] The table header reads 'T able 1'; this formatting error should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the SA-versus-Gurobi comparison is an empirical benchmark with no fitted parameter or self-citation chain doing the work.

full rationale

The paper's central claim is an empirical comparison: the SA-based heuristic and the Gurobi MIP are run on the same real-world instance and their distance-versus-time trade-offs are measured. No parameter of the heuristic is fitted to Gurobi's output or to the comparison outcome: R is varied as an input, and the SA temperature schedule (T0=1, Tend=0.001, Ti=T0/(i+1)) is fixed and stated before the experiments. The objective minimized by the heuristic is the same route-distance objective as in the MIP, but the heuristic does not use the MIP solution or the MIP's equations to construct or calibrate its candidate solutions, so there is no equation that reduces by construction to its own input. The only citation that could be self-related, Kaleta et al. [9], is used as background context for traditional CVRP tools and is not load-bearing for any derived result. The serious concern with the paper is correctness rather than circularity: the written MIP constraints in Section 3.3 appear internally inconsistent (Eq. (5) omits depot arcs in the flow-balance at the first and last stations of a route, and Eqs. (10)-(11) do not impose an upper bound on total route demand). If the implemented Gurobi model matches the written equations, its reported solutions may be infeasible, which would undermine the comparison but would not make the comparison circular. No circular derivation was found.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim rests on hand-chosen algorithm control parameters and on the correctness of the MIP baseline. No new theoretical entities are introduced, but the baseline correctness assumption is both load-bearing and questionable because of the constraint issues identified in the red flags.

free parameters (5)
  • Number of Monte Carlo trials R = 1000, 5000, 10000
    Chosen by the user to trade initial solution quality against runtime; tested at three levels.
  • Initial temperature T0 = 1
    Hand-chosen starting temperature for the simulated annealing acceptance rule.
  • Final temperature Tend = 0.001
    Hand-chosen stop condition for the simulated annealing loop.
  • Cooling schedule = Ti = T0/(i+1)
    Hand-chosen inverse cooling rule with no sensitivity analysis.
  • Big-M constant in Eq (7) = not specified
    Required for the time-window constraint but its numerical value is not stated.
assumptions (4)
  • domain assumption Input demands, service times, and travel times are treated as deterministic expected values.
    Section 3.1 states that stochastic characteristics are replaced by expected values.
  • domain assumption A homogeneous fleet with capacity C=39,000 L is used, and all routes start and end at the fuel hub.
    Section 3.3, constraints (3) and (4), and the capacity discussion.
  • domain assumption Every route must be filled to at least capacity C, as expressed by Eq (11).
    Section 3.3 imposes that the vehicle is emptied upon arrival at the last station, which excludes partial-load routes.
  • ad hoc to paper The Gurobi MIP model as written is a correct representation of the real routing problem.
    Section 3.3, Eqs (5), (10), and (11); the paper treats this model as the baseline, but the equations appear internally inconsistent.

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Pith. "Pith review of When to use simulated annealing for solving CVRP? A case study of fuel deliveries in Poland." pith.science (2026). https://pith.science/paper/PDYGV4LQ

@misc{pith2026241209293,
  author       = {Pith},
  title        = {Pith review of: When to use simulated annealing for solving CVRP? A case study of fuel deliveries in Poland},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PDYGV4LQ}},
  note         = {Machine review of arXiv:2412.09293}
}
read the original abstract

The paper addresses Capacitated Vehicle Routing Problem (CVRP) in the context of fuel delivery to gas stations. The CVRP aims to minimize total travel distance for a fleet with limited capacity. Fuel delivery, however, introduces unique complexities within the CVRP framework. We propose a novel approach that integrates the Simulated Annealing (SA) algorithm with a customized CVRP model specifically designed for gas station networks. This model incorporates real-world constraints like vehicle capacity, fuel demands at each station, and road network distances. The paper outlines the design of SA-based CVRP model for fuel delivery. We detail the objective function (minimizing distance) and the SA's exploration mechanism for generating candidate solutions. To assess its effectiveness, the proposed approach undergoes computational tests in Poland's gas station network serviced by the Samat transportation company. We compare the performance of our SA-based CVRP model with the conventional Mixed Integer Programming model for CVRP powered by Gurobi. The results aim to demonstrate the efficacy of the proposed SA-based heuristic in finding efficient routes for fuel deliveries.

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Works this paper leans on

34 extracted references · 30 canonical work pages

  1. [1]

    European Journal of Operational Research 321(1), 123–146 17 (2025) https://doi.org/10.1016/j.ejor.2024.09.040

    Xiong, X., Han, J., Yin, Y., Cheng, T.: An exact method for the two-echelon split-delivery vehicle routing problem for liquefied natural gas delivery with the boil-off phenomenon. European Journal of Operational Research 321(1), 123–146 17 (2025) https://doi.org/10.1016/j.ejor.2024.09.040

    work page doi:10.1016/j.ejor.2024.09.040 2025

  2. [2]

    Computers and Chem- ical Engineering 192, 108874 (2025) https://doi.org/10.1016/j.compchemeng

    Bonino, S.G., Zeballos, L.J., Moolya, A., La ´ ınez-Aguirre, J.M., Pinto, J.M., Gross- mann, I.E., M´ endez, C.A.: A MILP-based approach to address the production and distribution planning of large industrial gas supply chains. Computers and Chem- ical Engineering 192, 108874 (2025) https://doi.org/10.1016/j.compchemeng. 2024.108874

    arXiv 2025

  3. [3]

    Socio-Economic Planning Sciences 88, 101612 (2023) https://doi.org/10.1016/j.seps.2023.101612

    Edwards, D.R., Idoko, F.O., Vogiatzis, C., Davis, L.B., Mirchandani, P.: Determining optimal fuel delivery strategies under uncertainty. Socio-Economic Planning Sciences 88, 101612 (2023) https://doi.org/10.1016/j.seps.2023.101612

    arXiv 2023

  4. [4]

    Transportation Research Part B: Methodological 126, 45–67 (2019) https://doi.org/10.1016/j.trb.2019.05.014

    Ghiami, Y., Demir, E., Van Woensel, T., Christiansen, M., Laporte, G.: A deteri- orating inventory routing problem for an inland liquefied natural gas distribution network. Transportation Research Part B: Methodological 126, 45–67 (2019) https://doi.org/10.1016/j.trb.2019.05.014

    work page doi:10.1016/j.trb.2019.05.014 2019

  5. [5]

    AIP Conference Proceedings 2772, 070004 (2023) https://doi.org/10.1063/5.0119145

    Baihaqi, M.F., Fitria, L.: The application of sweep algorithm and nearest neighbor algorithm for solving multiple trips heterogeneous fleet vehicle routing problem of subsidized gas distribution. AIP Conference Proceedings 2772, 070004 (2023) https://doi.org/10.1063/5.0119145

    work page doi:10.1063/5.0119145 2023

  6. [6]

    Lecture Notes in Mechanical Engineering, 675–688 (2022) https://doi.org/10.1007/978-3-030-90421-0 58

    Alkan, B., Kikizade, B.D., Karadan, B., Duysak, C., K¨ upeli, E.H., Turan, E.Y., Dilber, T., ¨Oner, E., Ayg¨ un, N.K.: Distribution planning of LPG to gas stations in the Aegean region. Lecture Notes in Mechanical Engineering, 675–688 (2022) https://doi.org/10.1007/978-3-030-90421-0 58

    work page doi:10.1007/978-3-030-90421-0 2022

  7. [7]

    Procedia Computer Science 191, 530–536 (2021) https://doi.org/10.1016/j.procs.2021.07.067

    Assahla, A., Ait Abdelouahid, R., Marzak, A.: Contribution of AI to improve planning gas stations replenishment: Synthetic study. Procedia Computer Science 191, 530–536 (2021) https://doi.org/10.1016/j.procs.2021.07.067

    work page doi:10.1016/j.procs.2021.07.067 2021

  8. [8]

    International Conference on Industrial Engineering and Operations Management (2021)

    Aqidawati, E.F., Anshory, M.I., Dityarini, A., Yuniaristanto, Sutopo, W., Artanto, B.: Application of vehicle routing problem to determine optimal route in fuel distribution: A case study. International Conference on Industrial Engineering and Operations Management (2021)

    work page 2021

Show all 34 references
  1. [9]

    Proceedings CLC2023 – Carpathian Logistics Congress, 64–70 (2023) https://doi.org/10.37904/clc.2023

    Kaleta, J., Karkula, M., Tarczy´ nski, G.: The fuel stations choice flexibility study and its impact on the length of delivery routes. Proceedings CLC2023 – Carpathian Logistics Congress, 64–70 (2023) https://doi.org/10.37904/clc.2023. 4850

    2023 doi

  2. [10]

    Decision Science Letters 13(3), 605–616 (2024) https://doi.org/10.5267/j.dsl.2024.5.002

    Meniz, B., Tiryaki, F.: Genetic algorithm approach to asymmetric capacitated vehicle routing: A case study on bread distribution in Istanbul, T¨ urkiye. Decision Science Letters 13(3), 605–616 (2024) https://doi.org/10.5267/j.dsl.2024.5.002

    2024 doi

  3. [11]

    2024 IEEE 9th International Conference on Computational Intelligence and Applications, ICCIA 2024 (2024)

    Poonpanit, M., Punkong, N., Ratanavilisagul, C., Kosolsombat, S.: An improving 18 genetic algorithm with local search for solving capacitated vehicle routing prob- lem. 2024 IEEE 9th International Conference on Computational Intelligence and Applications, ICCIA 2024 (2024). ht...

    2024

  4. [12]

    Smart Innovation, Systems and Technologies 364, 433–444 (2024) https://doi.org/10

    Kakkar, M.K., Gupta, G., Garg, N., Singla, J.: Solving the capacitated vehi- cle routing problem (cvrp) using clustering and meta-heuristic algorithm. Smart Innovation, Systems and Technologies 364, 433–444 (2024) https://doi.org/10. 1007/978-981-99-5180-2 34

    2024

  5. [13]

    18th IEEE International Conference on Emerging Technologies, ICET 2023 (2023)

    Arshad, U., Ellahie, H.H., Abideen, Z.U., Ali, R.H.: An enhanced genetic algo- rithm framework for efficient solutions to capacitated vehicle routing problems. 18th IEEE International Conference on Emerging Technologies, ICET 2023 (2023). https://doi.org/10.1109/ICET59753.2023...

    2023

  6. [14]

    2023 International Technical Conference on Circuits/Systems, Computers, and Com- munications, ITC-CSCC 2023 (2023)

    Chanachan, C., Sirisethakarn, M., Khapla, P., Povichai, J.: A Comparison of route optimization algorithms on capacitated vehicle routing problem. 2023 International Technical Conference on Circuits/Systems, Computers, and Com- munications, ITC-CSCC 2023 (2023). https://doi.org...

    2023

  7. [15]

    Lecture Notes in Electrical Engineering 888, 479–490 (2022) https://doi.org/10.1007/978-981-19-1520-8 39

    Sharma, V., Varshney, N.: Capacitated vehicle routing problem using genetic algo- rithm and particle swarm optimization. Lecture Notes in Electrical Engineering 888, 479–490 (2022) https://doi.org/10.1007/978-981-19-1520-8 39

    2022 doi

  8. [16]

    6th International Conference on Parallel, Distributed and Grid Computing, PDGC 2020 (2020)

    Sajid, M., Jafar, A., Sharma, S.: Hybrid genetic and simulated annealing algo- rithm for capacitated vehicle routing problem. 6th International Conference on Parallel, Distributed and Grid Computing, PDGC 2020 (2020). https://doi.org/ 10.1109/PDGC50313.2020.9315798

    2020

  9. [17]

    Swarm and Evolutionary Computation 64, 100911 (2021) https://doi.org/10.1016/j.swevo.2021.100911

    Ilhan, I.: An improved simulated annealing algorithm with crossover operator for capacitated vehicle routing problem. Swarm and Evolutionary Computation 64, 100911 (2021) https://doi.org/10.1016/j.swevo.2021.100911

    2021

  10. [18]

    ACM International Conference Proceeding Series, 118–124 (2021) https://doi.org/10

    Arockia, A., Lochbrunner, M., Hanne, T., Dornberger, R.: Benchmarking tabu search and simulated annealing for the capacitated vehicle routing problem. ACM International Conference Proceeding Series, 118–124 (2021) https://doi.org/10. 1145/3450588.3450940

    2021

  11. [19]

    European Transport - Trasporti Europei (78), 8 (2020)

    Kancharla, S.R., Ramadurai, G.: Simulated annealing algorithm for multi depot two-echelon capacitated vehicle routing problem. European Transport - Trasporti Europei (78), 8 (2020)

    2020

  12. [20]

    Journal of Experimental and Theoretical Artificial Intelligence 32(3), 437–452 (2020) https://doi.org/10.1080/ 0952813X.2019.1652356 19

    Rabbouch, B., Saˆ adaoui, F., Mraihi, R.: Empirical-type simulated annealing for solving the capacitated vehicle routing problem. Journal of Experimental and Theoretical Artificial Intelligence 32(3), 437–452 (2020) https://doi.org/10.1080/ 0952813X.2019.1652356 19

    2020

  13. [21]

    WSEAS Transactions on Computer Research 8, 22–25 (2020) https://doi.org/10.37394/232018.2020.8.4

    Davtyan, A., Khachatryan, S.: Simultaneous multi-start simulated annealing for capacitated vehicle routing problem. WSEAS Transactions on Computer Research 8, 22–25 (2020) https://doi.org/10.37394/232018.2020.8.4

    2020

  14. [22]

    Turkish Journal of Electrical Engineering and Computer Sciences 28(3), 1217–1235 (2020) https://doi.org/10.3906/elk-1902-122

    Ilhan, I.: A population based simulated annealing algorithm for capacitated vehi- cle routing problem. Turkish Journal of Electrical Engineering and Computer Sciences 28(3), 1217–1235 (2020) https://doi.org/10.3906/elk-1902-122

    2020 doi

  15. [23]

    Applied Soft Computing Journal 53, 119–132 (2017) https://doi.org/10.1016/j.asoc.2016.12.027

    Yu, V.F., Redi, A.A.N.P., Hidayat, Y.A., Wibowo, O.J.: A simulated annealing heuristic for the hybrid vehicle routing problem. Applied Soft Computing Journal 53, 119–132 (2017) https://doi.org/10.1016/j.asoc.2016.12.027

    2017 doi

  16. [24]

    Lec- ture Notes on Data Engineering and Communications Technologies 189, 294–304 (2024) https://doi.org/10.1007/978-3-031-46970-1 28

    Mexicano, A., Carmona, J.C., Alvarez, D.Y., Montes, P.N., Cervantes, S.: A tool for solving the cvrp problem by applying the tabu search algorithm. Lec- ture Notes on Data Engineering and Communications Technologies 189, 294–304 (2024) https://doi.org/10.1007/978-3-031-46970-1 28

    2024 doi

  17. [25]

    Journal of Physics: Conference Series 1581(1), 012008 (2020) https://doi.org/10.1088/1742-6596/1581/1/012008

    Wati, E., Fauzan, M.: Implementation tabu search algorithm for optimization distribution LPG. Journal of Physics: Conference Series 1581(1), 012008 (2020) https://doi.org/10.1088/1742-6596/1581/1/012008

    2020 doi

  18. [26]

    tabu search

    Masudin, I., Sa’Diyah, R.F., Utama, D.M., Restuputri, D.P., Jie, F.: Capacitated vehicle routing problems: Nearest neighbour vs. tabu search. International Journal of Computer Theory and Engineering 11(4), 76–79 (2019) https://doi.org/10. 7763/IJCTE.2019.V11.1246

    2019

  19. [27]

    Journal of Industrial Engineering International 13(3), 323–330 (2017) https://doi.org/10.1007/s40092-017-0187-9

    Kır, S., Yazgan, H.R., T¨ uncel, E.: A novel heuristic algorithm for capacitated vehicle routing problem. Journal of Industrial Engineering International 13(3), 323–330 (2017) https://doi.org/10.1007/s40092-017-0187-9

    2017 doi

  20. [28]

    Computers and Industrial Engineering 107, 211–222 (2017) https://doi.org/10

    Soto, M., Sevaux, M., Rossi, A., Reinholz, A.: Multiple neighborhood search, tabu search and ejection chains for the multi-depot open vehicle routing problem. Computers and Industrial Engineering 107, 211–222 (2017) https://doi.org/10. 1016/j.cie.2017.03.022

    2017

  21. [29]

    Advanced Materials Research859, 395–398 (2014) https: //doi.org/10.4028/www.scientific.net/AMR.859.395

    Ren, C.Y.: New tabu search algorithm with applied technology for capacitated vehicle routing problem. Advanced Materials Research859, 395–398 (2014) https: //doi.org/10.4028/www.scientific.net/AMR.859.395

    2014 doi

  22. [30]

    Symmetry 15(11), 2020 (2023) https://doi.org/10.3390/sym15112020

    Ahmed, Z.H., Hameed, A.S., Mutar, M.L., Haron, H.: An enhanced ant colony system algorithm based on subpaths for solving the capacitated vehicle routing problem. Symmetry 15(11), 2020 (2023) https://doi.org/10.3390/sym15112020

    2023 doi

  23. [31]

    In: Kumar Sagar, A., Nand, P., Kumar, N., Das, S., Sahana, S

    Sajid, M., Singh, J., Rajak, R.: Capacitated vehicle routing problem using algebraic particle swarm optimization with simulated annealing algorithm. In: Kumar Sagar, A., Nand, P., Kumar, N., Das, S., Sahana, S. (eds.) Artificial Intelli- gence in Cyber-Physical Systems: Princi...

    2023 doi

  24. [32]

    International Arab Journal of Information Technology 19(4), 689–694 (2022) https://doi.org/10.34028/iajit/19/4/14

    Mahmood, N.: Solving capacitated vehicle routing problem using meerkat clan algorithm. International Arab Journal of Information Technology 19(4), 689–694 (2022) https://doi.org/10.34028/iajit/19/4/14

    2022 doi

  25. [33]

    Networks 84(4), 465–480 (2024) https://doi.org/10.1002/ net.22244

    As ´ ın-Ach´ a, R., Espinoza, A., Goldschmidt, O., Hochbaum, D.S., Huerta, I.I.: Selecting fast algorithms for the capacitated vehicle routing problem with machine learning techniques. Networks 84(4), 465–480 (2024) https://doi.org/10.1002/ net.22244

    2024

  26. [34]

    AIP Conference Proceedings 2705, 040003 (2023) https://doi.org/10.1063/5.0133810 21

    Sehta, N., Thakar, U.: Capacitated vehicle routing problem: A solution using convex hull based sweep algorithm and genetic algorithm. AIP Conference Proceedings 2705, 040003 (2023) https://doi.org/10.1063/5.0133810 21

    2023 doi

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