Cattaruzza, Diego

Gu, Wenjuan

Ogier, Maxime

Semet, Frédéric

Hal-Diderot

Adaptive large neighborhood search for multicommodity VRP

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HAL Id: hal-01940685https://hal.archives-ouvertes.fr/hal-01940685Submitted on 30 Nov 2018HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Adaptive large neighborhood search for multicommodityVRPWenjuan Gu, Diego Cattaruzza, Maxime Ogier, Frédéric SemetTo cite this version:Wenjuan Gu, Diego Cattaruzza, Maxime Ogier, Frédéric Semet. Adaptive large neighborhood searchfor multicommodity VRP. ROADEF 2018 - 19ème Congrès de la Société Française de RechercheOpérationnelle et d’Aide à la Décision, Feb 2018, Lorient, France. ￿hal-01940685￿Adaptive large neighborhood search for multicommodity VRPWenjuan Gu, Diego Cattaruzza, Maxime Ogier, Frédéric SemetUniv. Lille, CNRS, Centrale Lille, Inria, UMR 9189 - CRIStAL, F-59000 Lille, France{wenjuan.gu, diego.cattaruzza}@inria.fr{maxime.ogier, frederic.semet}@centralelille.frMots-clés : multicommodity VRP, adaptive large neighborhood search, local search.1 IntroductionIn this work we study a vehicle routing problem where customers request multiple com-modities. Different strategies to deliver a set of commodities to customers were presented in[1]. Among these strategies, a new one, the commodity-constrained split-delivery mixed routingproblem (C-SDVRP) is presented and compared with classical ways to deliver multiple prod-ucts (allowing to split a commodity or using vehicles dedicated to each commodity). In theC-SDVRP, the vehicles are flexible and can deliver any set of commodities, and a customerwho requests multiple commodities can be delivered by different vehicles. When a commodityis delivered to a customer, the entire required amount is handed over.This problem arises for example in delivery of fresh fruits and vegetables to catering. Inthis case, products can easily be mixed into the same vehicle, and splitting the delivery of anindividual commodity is not acceptable.The C-SDVRP has first been studied in [1]. The authors proposed a branch-and-cut algo-rithm and a heuristic method. The heuristic consists in (1) making copies of each customer,one for each commodity required by the customer, and (2) using a heuristic for the capacitatedVRP. In [2], the authors proposed an extended formulation for the C-SDVRP and developeda branch-price-and-cut algorithm.This work proposes an adaptive large neighborhood search to solve the C-SDVRP, with theobjective of obtaining very good solutions on small instances, and to be able to efficiently solvelarge instances.2 Problem definitionThe C-SDVRP can be defined based on a directed graph G = (V , A) in which V = {0}⋃VCis the set of vertices, and A is the set of arcs. More precisely, VC = {1, ..., NC} represents theset of customer vertices, and 0 is the depot. A cost cij is associated with each arc (i, j) ∈ Aand represents the non-negative cost of travelling from i to j. Let M be the set of commoditiesthat have to be delivered to the customers. Any customer i ∈ VC may request any set ofcommodities. The depot contains a fleet of identical vehicles with capacity Q, able to deliverany subset of commodities. The objective is to minimize the total travelling cost.The problem involves two decisions : (1) finding a set of vehicle routes serving all customers ;(2) selecting commodities delivered to each customer. The constraints are : (1) each route startsand ends at the depot ; (2) the total quantity of commodities delivered by each vehicle doesnot exceed the vehicle capacity Q ; (3) each commodity requested by each customer must bedelivered by a single vehicle ; (4) the demands of all customers need to be satisfied.To solve the C-SDVRP, it is possible to duplicate the node associated with each customerby the number of commodities requested by the customer [1]. To each duplicated node, wethen associate the demand of the customer for the corresponding commodity. For the sake ofclarity, in the following we will call the duplicated nodes customer commodity.3 Adaptive large neighborhood searchIn order to solve the C-SDVRP for large instances, we propose a heuristic method based onthe ALNS framework of [3]. Local search moves are also used in order to improve the solutions.A solution is represented as a set of routes. In order to take into account the specific features ofC-SDVRP, a route can be represented : (1) as a sequence of customers, each customer havinga set of commodities, or (2) as a sequence of customer commodities. In the first case, removinga customer from a route implies to remove the customer with the set of commodities deliveredin this route, while in the second case it is possible to remove only one commodity.ALNS relies on a set of removal and insertion heuristics which iteratively destroy and repairsolutions. The probability to select a heuristic at a given iteration is influenced by its perfor-mance during past iterations. An initial solution is constructed as follows : (1) give a randomsequence of customers commodities to construct a giant tour, (2) apply a split procedure [4] toget a solution, (3) apply local search to improve this solution. At each iteration, a simulatedannealing criterion is used to accept a new solution.Classical removal and insertion heuristics [3] have been implemented. Removal heuristicsare : random removal, worst removal and Shaw removal with a relatedness measure basedon distance. Insertion heuristics are : greedy insertion and regret insertion. Worst removaland Shaw removal work with customers, while random removal can be applied either withcustomers or customer commodities. Insertion heuristics work with customer commodities.In order to improve a solution, seven different local search moves are implemented. In thefirst three moves routes are considered as a set of customers. These moves are : (1) insertcustomer, (2) swap customers, (3) 2-opt of customers. Then, we propose two other classicalmoves adapted for customer commodities : (4) insert customer commodity, and (5) swap cus-tomer commodities. We also propose two other moves : (6) erase route : from a given route,remove the customer commodities until no other route has capacity to accept another cus-tomer commodity ; and (7) reassign commodities : for a given customer we propose a MixedInteger Program to optimally assign all the commodities of this customer to the routes of thesolution. Given a feasible solution, all 7 moves are iteratively applied one after the other, untilno one improves the solution. Then, routes of the current solution are concatenated and splitalgorithm is applied. If this gives a better solution, the procedure is repeated.4 Conclusions and perspectivesWe test the efficiency of our ALNS on the instances proposed in [1]. Computational resultsshow that our algorithm can solve to optimality 62 out of 64 small instances, and we pro-vide some new best known values on mid-sized instances in reasonable computing time. Theprospects are to implement other specific removal and insertion heuristics. Moreover, the pro-posed method can then be extended to other versions of the problems, like multi-depot versionwith a limited capacity of each commodity at each depot.Références[1] C. Archetti, A. M. Campbell, and M. G. Speranza, “Multicommodity vs. single-commodityrouting”, Transportation Science 50(2), 461-472, 2014.[2] C. Archetti, N. Bianchessi, and M. G. Speranza, “A branch-price-and-cut algorithm for thecommodity constrained split delivery vehicle routing problem”, Computers & OperationsResearch 64, 1-10, 2015.[3] S. Ropke, and D. Pisinger, “An adaptive large neighborhood search heuristic for the pickupand delivery problem with time windows”, Transportation Science, 40(4), 455-472, 2006.[4] C. Prins, “A simple and effective evolutionary algorithm for the vehicle routing problem”,Computers & Operations Research 31(12),1985-2002, 2004.

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HAL Id: hal-01951948https://hal.archives-ouvertes.fr/hal-01951948Submitted on 11 Dec 2018HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Adaptive large neighborhood search for multicommodityVRPWenjuan Gu, Diego Cattaruzza, Maxime Ogier, Frédéric SemetTo cite this version:Wenjuan Gu, Diego Cattaruzza, Maxime Ogier, Frédéric Semet. Adaptive large neighborhood searchfor multicommodity VRP. Odysseus 2018 - the Seventh International Workshop on Freight Trans-portation and Logistics, Jun 2018, Cagliari, Italy. ￿hal-01951948￿Adaptive large neighborhood search formulticommodity VRPWenjuan Gu, Diego Cattaruzza, Maxime Ogier, Frédéric SemetUniv. Lille, CNRS, Centrale Lille, Inria, UMR 9189 - CRIStALF-59000 Lille, FranceEmail: maxime.ogier@centralelille.fr1 IntroductionIn this work we study a vehicle routing problem where customers request multiple com-modities. Different strategies to deliver a set of commodities to customers were presentedin [1]. Among these strategies, a new one, the commodity-constrained split-delivery mixedrouting problem (C-SDVRP) is presented and compared with classical ways to delivermultiple products (allowing to split a commodity or using vehicles dedicated to each com-modity). In the C-SDVRP, the vehicles are flexible and can deliver any set of commodities,and a customer who requests multiple commodities can be delivered by different vehicles.When a commodity is delivered to a customer, the entire required amount is handed over.This, if the customer is visited more than once, the different vehicles will deliver differentsets of commodities.This problem arises for example in delivery of fresh fruits and vegetables to catering.In this case, products can easily be mixed into the same vehicle, and splitting the deliveryof an individual commodity is not acceptable. This is also very relevant in the multi-depotcase, where each each depot has a limited quantity of each commodity. A customer canthen be delivered by vehicles coming from different depots.The C-SDVRP has first been studied in [1]. The authors proposed a branch-and-cutalgorithm able to solve 25 out of 64 small instances (15 customers) to optimality within30 minutes, and a heuristic method. The heuristic consists in (1) making copies of eachcustomer, one for each commodity required by the customer, and (2) using a heuristicfor the capacitated VRP. In [2], the authors proposed an extended formulation for theC-SDVRP and developed a branch-price-and-cut algorithm. They solved to optimalityinstances with up to 40 customers and 3 commodities per customer within 2 hours.This work proposes an adaptive large neighborhood search to solve the C-SDVRP,with the objective of obtaining very good solutions on small instances, and to be able toefficiently solve large instances.2 Problem definitionThe C-SDVRP can be defined based on a directed graphG = (V,A) in which V = {0}⋃VCis the set of vertices, and A is the set of arcs. More precisely, VC = {1, ..., NC} representsthe set of customer vertices, and 0 is the depot. A cost cij is associated with each arc(i, j) ∈ A and represents the non-negative cost of travelling from i to j. Let M be theset of commodities that have to be delivered to the customers. Any customer i ∈ VCmay request any set of commodities. The depot contains a fleet of identical vehicles withcapacity Q, able to deliver any subset of commodities. The objective is to minimize thetotal travelling cost.The problem involves two related decisions: (1) finding a set of vehicle routes servingall customers; (2) selecting commodities delivered to each customer. The constraints are:(1) each route starts and ends at the depot; (2) the total quantity of commodities deliveredby each vehicle does not exceed the vehicle capacity Q; (3) each commodity requested byeach customer must be delivered by a single vehicle; (4) the demands of all customers needto be satisfied.To solve the C-SDVRP, it is possible to duplicate the node associated with each cus-tomer by the number of commodities requested by the customer [1]. To each duplicatednode, we then associate the demand of the customer for the corresponding commodity. Forthe sake of clarity, in the following we will call the duplicated nodes customer commodity.3 Adaptive large neighborhood searchIn order to solve the C-SDVRP for large instances, we propose a heuristic method basedon the ALNS framework of [3]. Local search moves are also used in order to improve thesolutions. A solution is represented as a set of routes. In order to take into account thespecific features of C-SDVRP, a route can be represented: (1) as a sequence of customers,each customer having a set of commodities, or (2) as a sequence of customer commodities.In the first case, removing a customer from a route implies to remove the customer withthe set of commodities delivered in this route, while in the second case it is possible toremove only one commodity.3.1 General frameworkALNS relies on a set of removal and insertion heuristics which iteratively destroy andrepair solutions. The probability to select a heuristic at a given iteration is influenced byits performance during past iterations. A sketch of the method is outlined in Algorithm 1.An initial solution is constructed as follows: (1) give a random sequence of customerscommodities to construct a giant tour, (2) apply a split procedure [4] to get a solution,(3) apply local search to improve this solution.Algorithm 1 Adaptive large neighborhood search1: generate an initial solution s ∈ {solutions}, ρ← 1, sbest ← s2: repeat3: Roulette wheel: select a removal heuristic hrem and an insertion heuristic hins4: Destroy: srem ← remove ρ customer commodities from s applying hrem5: Repair: sins ← insert removed customer commodities into srem applying hins6: Improve: s′ ← improve solution sins with local search7: if f(s′) < f(sbest) then sbest ← s′ end if8: if accept(s′, s) then s← s′, ρ← 1 else ρ← ρ+ 1, or ρmin if ρ = ρmax end if9: until stopping criterion is met10: return sbestAt each iteration, a simulated annealing criterion is used to determine if the newsolution s′ is accepted. The number ρ of customer commodities to remove from the currentsolution s follows the scheme proposed in [5], with the aim of applying small moves whena new solution has just been accepted, while applying large move when no new solutionshas been accepted in the most recent iterations.3.2 Removal and insertion heuristicsClassical removal and insertion heuristics ([3]) have been implemented. Removal heuristicsare: random removal, worst removal and Shaw removal with a relatedness measure basedon distance. Insertion heuristics are: greedy insertion and regret insertion. Worst removaland Shaw removal work with customers, while random removal can be applied either withcustomers or customer commodities. Insertion heuristics work with customer commodities.3.3 Local search movesIn order to improve a solution, we apply a set of local search moves. Seven differentmoves are implemented. In the first three moves routes are considered as a set of cus-tomers. These moves are: (1) insert customer, (2) swap customers, (3) 2-opt of customers.Then, we propose two other classical moves adapted for customer commodities: (4) insertcustomer commodity, and (5) swap customer commodities. We also propose two othermoves: (6) erase route: from a given route, remove the customer commodities until noother route has capacity to accept another customer commodity; and (7) reassign com-modities: for a given customer we propose a Mixed Integer Program to optimally assignall the commodities of this customer to the routes of the solution.Given a feasible solution, all 7 moves are iteratively applied one after the other, untilno one improves the solution. Then, routes of the current solution are concatenated andsplit algorithm is applied. If this gives a better solution, the procedure is repeated.4 Preliminary resultsThe algorithm is implemented in C++ and run on a Intel (R) Core(TM) i7-6500U,2.50GHz and 8GB of RAM. The instances are the ones proposed in [1], based on theR101 and C101 Solomon instances for the VRP. We consider 3 sets of instances with up to3 commodities: small instances with 15 customers, mid-sized instances with 20 customersor 80 customers.Global results are reported in Table 1. We report the average, minimum and maximumgap (gap%) between the value we obtained and the best known solution in literature [2],the number of optimal values we obtained and the average computational time in seconds.Table 1: Global results.|NC | nb instances av.gap (%) min gap(%) max gap(%) nb optimal av.time(s)15 64 0.12 0.00 4.20 61 5820 20 0.18 0.00 1.8 12 9780 20 0.77 -0.88 6.69 - 1767From Table 1, we can see that our algorithm can solve to optimality 61 out of 64 smallinstances in reasonable computing time. On mid-sized instances, we obtain very goodquality results on a reasonable amount of time, and we provide 10 new best known valuesfor mi-sized instances with 80 customers.The prospects are to implement specific removal and insertion heuristics. Moreover,the proposed method can then be extended to other versions of the problems, like multi-depot version with a limited capacity of each commodity at the each depot.References[1] C. Archetti, A. M. Campbell, and M. G. Speranza, “Multicommodity vs. single-commodity routing”, Transportation Science 50(2), 461-472, 2014.[2] C. Archetti, N. Bianchessi, and M. G. Speranza, “A branch-price-and-cut algorithmfor the commodity constrained split delivery vehicle routing problem”, Computers &Operations Research 64, 1-10, 2015.[3] S. Ropke, and D. Pisinger, “An adaptive large neighborhood search heuristic forthe pickup and delivery problem with time windows”, Transportation Science, 40(4),455-472, 2006.[4] C. Prins, “A simple and effective evolutionary algorithm for the vehicle routing prob-lem”, Computers & Operations Research 31(12),1985-2002, 2004.[5] V. François, Y. Arda, Y. Crama, G. Laporte, “Large neighborhood search for multi-trip vehicle routing”, European Journal of Operational Research, 255(2), 422-441,2016.

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Adaptive large neighborhood search for multicommodity VRP

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