ALNS destroy: Random, WorstDistance, WorstTime, Route, Shaw, ProximityBased, TimeBased, DemandBased, HistoricalKnowledge, Neighborhood, Zone, NodeNeighborhood ALNS repair: Greedy, Regret, GreedyWithNoise, RegretWithNoise, Zone Speed opt.: first optimal speeds are computed to find violations if any, and then in the second part the current speeds are revised to optimize the fuel consumption
Push forward insertion heuristic + LP optimization of charges
Heuristics for feasible upper bound, TS
SA
MATLAB, CPLEX - small, DP
Adapted Solomon
Compare three procedures for small instances: Master LP: three different relaxations by applying cutting plane algorithm + CPLEX for MIP subproblem; ( Best Lagrangian bound + heuristic ( CPLEX TS neighborhood operators: - interchange (, DP for determining optimal route cost
( Determine the set of optimal routes ( Assignment of routes over the planning horizon ( Charge scheduling + rerouting to CSs Mutation: OR, XOR between individuals Crossover: random -point
Solution: a two-dimensional binary array of routes and CSs After assigning CS to routes the TSP route is determined Initial: no charging, battery constrained SPP Crossover: 2-point, the second parent is chosen to reduce the concurrency at CSs Selection: random or based on the fitness Mutation: random - remove/insert CS, Exchange LS: removing/inserting vertices (Relocate)
ALNS of Demir et al. [32] + speed optimization - to generate non-dominated Pareto optimal solutions Heuristic: adaptive weighting with -constraint method for bi-objective solutions
VNS - 15 neighborhood structures based on the cyclic exchange move TS - operators: 2-opt∗, Relocate, Exchange, StationInRe Diversification mechanism based on the attributes frequency
LS: Relocate, Exchange Neighborhood search: replace located and unlocated BSS
X
Modified sweep + greedy
SIGALNS
SA
Remove all BSSs and then apply the iterated greedy procedure to insert best BSSs ALNS destroy: Random, Worst, Related, RequestGraph, SinglePoint, TwoPoint, Binary, StationBased ALNS repair: Greedy, Regret-k, AdvanceGreedy, AdvanceRegret-k Improvement: try to remove BSSs
Initial route is driven in combustion mode + LS - 2-Opt hill-climbing 4:1 ratio - four arcs have to be driven in charging mode in order to drive the last one in electric mode LS: -mode change () - changes only the mode, -Opt with mode change () - changes the route configuration and the mode ITS: Search: 2-opt with mode change + arcs in tabu list, Hill-climbing - mode change (first or best), Diversification: -Opt with the mode change
Improved MIP formulation of GVRP SA improvement operators: Merge routes, Swap, station Add/Drop Branch-and-cut is applied to the initial solution On optimal fractional solution, the heuristic is applied to obtain a feasible solution which is further improved by SA
( random NNH, random nearest insertion, random best insertion) + split
Modified multi-space sampling heuristic + set partitioning
Gurobi - set partitioning
GVRP
Build the TSP route constructed by applying one of the construction procedures ( Split TSP route and repair (CSPP) - pulse algorithm ( Set partitioning over a set of routes
ALNS destroy: Random, TimeRelated, NeighboringSchedule (problem specific) ALNS repair: regret-2,3,4 (deterministic and stochastic version) Post-optimization: a set of feasible solutions are used in set partitioning model
Multigraph - arc represents possible paths between customers with inserted CS Set partitioning formulation + subset row inequalities and -path cuts (Chvatal–Gomory (CG) cuts of rank one) - MILP formulation of separation + cut-and-column algorithm
First stage without CS capacity constraint: ILS - giant TSP route + perturbation (random double bridge) + split procedure on acyclic graph with heuristic for CSs + LS: 2-Opt, Relocate and MILP model for charging decisions; local optimum solutions are stored in a pool of solutions Second stage: solutions are assembled using Benders’ like decomposition into route selection master problem, and CS capacity management sub-problem Three strategies for CS capacity management: ( no revision (only feasibility check), delay the charging operations to satisfy CS capacity constraints, and revise the charging amount The set partitioning model is solved using the branch-and-bound algorithm and cuts for CS capacity management
AVNS - Schneider et al. [55] - 32 neighborhood structures - (24) + ( new one based on the facility-removal and facility-replacement ) LS: 2-Opt, Or-Opt, Relocate, Exchange, FacilityInsertion, FacilityReplacement, FacilityExchange
Sequencing first, charging (FRVCP) second VND: Relocate, 2-Opt and GlobalChargingImprovement Perturbation: build TSP route, perturb and split Heuristic concentration: set partitioning over a set of routes FRVCP- Gurobi and a greedy heuristic
Dynamic Dijkstra algorithm for time-dependent SPP, single string encoding, each individual after the crossover or mutation needs to satisfy all the constraints - if not run the procedure again, elitism
Origin-destination, Optimal a priori policy - CSPP + searching for policies with a lower costs (2.1) Two-stage heuristic: select the EV path to follow and select adaptive recharging policy for the fixed path (2.2) Adjusting vehicle trajectory - find optimal policy between a priori stop locations and permit adaptive decision making for both routing and recharging
ALNS of Keskin and Çatay [28] with modf.: Station destroy procedures: Random, WorstDistance, LeastUsedStation, ExpensiveStation; Customer insertion procedures - only fastest recharging option; modified station insertions algorithms which start from the cheapest and go to the more expensive charging options Post optimization of charging decisions (location, amount and type)
Markov decision process - approximated DP solution The Benders-based branch-and-cut algorithm to solve the decomposition Integration of static policies into dynamic lookahead policies: pre-decision, post-decision, and one-step rollouts Exact labeling for FRVCP with time-dependent waiting times and discrete charging decisions Nonlinear information penalties that tighten the perfect information bound of the optimal policy
Case study, new life additional benefit costs method for the replacement of vehicles (CPLEX); two routing methods: single/multi-period approach for solving the recharging problem
Multi-layer taxi-flow time-space network Network decomposition by vehicles: first MTFSP sub-model for EVs is solved and then the MTFSP for the rest of ICEVs Network composition by time: in each slice of the time-sliced network to each request the nearest vehicles are assigned and then the recharging of EV is performed
EVO - chromosome encoded as a sequence of vehicles and pickup/drop off vertices: (1a) population is divided in groups (1b) solutions are selected from each group (roulette wheel), and if the best solution was not improved for the last three iterations, merge crossover (MX1) is applied between one solution from and one from the rest of the solutions in the groups that were not selected ( VNS - neighborhood operators: Swap, RemoveSequence, CrossExchange; three versions: : in each iteration roulette wheel selection of routes in neighborhood structures and order of LS operators with the first improvement strategy, CA acceptance function : after new solution additional iterations of LS with only one operator in each iteration, RR acceptance function : for applying each neighborhood structure, LS, acceptance of only better solutions LS: 2-Opt∗, RemoveTwoInsertOne, Relocate, 4-Opt, Remove/Insert BatteryStation ( Insert new solutions in the population, the rest of the solutions are generated based on the destroy and repair heuristic (-regret)
Particle encoding: customer sequence only which is converted to solution by inserting depots and refueling stations Personal and global best particles + velocity update Time-varying inertia and acceleration coefficients Decoding: rank of value to convert the route to the particle position GMO and archive of Pareto optimal solutions
E-LRPTWPR (old and new), BSS-EV-LRP, E-VRPTW, E-VRPTWPR
Penalty terms evaluation - corridor-based approach - a range of possible refueling times + concatenation operators ALNS and LS: Schiffer et al. [11] DP - optimal place of recharging visits - solve resource constrained SPP for each route by extending the given routes only for facility vertices + resource extension functions for feasibility and dominance checks
Parallelized ALNS of Schiffer and Walther [88]: LS, DP and customer configuration performed in parallel for fixed CS configuration, while CSs configuration, adaptive evaluations and stopping criterion are executed within a critical section of the code Adversarial approach for robust formulation
Fuzzy programming and fuzzy preference relations are applied to transform the objective function into a single objective function GA: chromosome genes - CSs
Initial: TSP - construction based on the savings and intensity trail value, VRP - insertion of depots, E-VRP - insertion of CSs ILS perturbation: random removal of customers and CSs, and then the best insertion procedure LS: 2-Opt∗, Exchange, Relocate, StationInRe Elitism ALNS of Goeke and Schneider [30] with modf.: no cluster removal operator
LNS destroy: RelatedRemoval, Random, CloseSatellite, OpenSatellite, RemoveSingleCustomerRoutes LNS repair: (i) the reinsertion of customers in the second echelon with Greedy (random or demand quantity) operators; (ii) greedy insertion on the first echelon routes (iii) DP for CSs insertions LS on second echelon: 2-Opt, 2-Opt∗, Relocate, Swap, Swap2-1
Path-based approach - the route is a composition of paths for a subset of customers without station visits: ( All feasible paths are generated, removing from set of the dominated ones ( MILP formulation is used to combine paths in routes
The sequence of customers and vehicle types without CS ( GA - assignment and sequencing of customer visits - populations: feasible and infeasible ( DP - sequencing of CS: resource CSPP - labeling algorithm for CSs insertions ( Greedy extension policy - known sequence, partial recharging, mode selection Route evaluation: (&, extension functions GA crossover: binary tournament selection, each parent forms giant TSP tour, OX crossover, split procedure GA mutation: LNS - random selection of destroy operators: Random, RandomRoutes, Similar, Target; uniform selection of repair operators: Greedy, Regret-2 LS (only promising edges): 2-opt, 2-opt∗, Swap, Relocate (single and pairs), VehicleSwap Set partitioning over a pool of routes during the search The cache memory of move evaluations for unchanged route sequences
Initial: CPLEX to find an initial feasible solution Random order of destroy and repair operators and tabu list to forbid the removal of recently removed customers and reinsertion into routes from which they were removed Destroy: Random, WorstDistance, WorstTime, Route Insertion: Greedy, GreedyAndCS, GreedyNewRoute, GRASP
Initial: two clusters of customers for EV and ICEV routes - ICEV routes, EV routes - all customers from EV cluster and all un-routed customers from ICEV cluster LS with/without penalty function and perturbation operators: relocate-only EV, ICEV or both
Random neighborhood structures: Swap, Insertion, station Insert/Delete
Reference: referenced paper; Problem name: the name of the analyzed problem; NF: allowing infeasible solutions during the search process; Initial: procedure used for the creation of the initial solution if any; Hybrid heuristics: heuristics, metaheuristics, and hybrid combinations applied for solving the problem; A: the acceptance criteria; Exact & Software: the exact procedure or software applied on the analyzed problem or subproblem; Instances: instances used for testing of the applied procedures where Real denotes the real case-study instances, Generated denotes the artificially created instances which are not benchmark instances, and other denotes the benchmark instances of the problem; Description: short description of procedure used to solve the analyzed problem.
