Table 1: Related Works.

AlgorithmProblemContribution

Multiphase heuristic [72]Multiperiod petrol station replenishment problemA heuristic with a route construction and truck loading procedures, a route packing procedure, and two procedures enabling the anticipation or the postponement of deliveries for the MPSRP.

Exact algorithm [45]Petrol station replenishment problemThe algorithm decomposes the problem into truck loading problem and a routing problem.

Genetic algorithm [73]Air transportation scheduling problemThe Taguchi experimental design method is applied to set and estimate the proper values of gas parameters.

Simulated annealing based heuristic algorithms [74]Air transportationThe problem is formulated as a parallel machine scheduling problem with earliness penalties.

Simulated annealing algorithm [75]Arrival flight delays problemBased on the characteristic of the flights and the thinking of system optimization, this paper builds up dynamic optimizing models of the flight delays scheduling with the objective function of delay cost.

Greedy algorithm [76]Single-airport ground-holding problem (SAGHP)A dynamic programming formulation with a corresponding backward solution algorithm.

Coevolutionay genetic algorithm [14, 15]Multiairport ground-holding problemSurvey model with dynamic capacity in details.

Column generation based heuristic algorithm [77]Helicopter routing problemA MIP based heuristic with an add column generation procedures that improve the solution quality for the Brazilian State Oil Company (Petrobras).

Heuristic algorithm [42]Cash transportation vehicle routing problemA solution algorithm based on a problem decomposition/collapsing technique, coupled with the use of a mathematical programming software.

Tabu search [78]Helicopter routing problemThree routing policies are considered: a direct routing policy, a Hamiltonian routing policy, and a general routing policy.

Hub-and-spoke configuration [79]Helicopter routing problemMathematical model and theoretical results for route planning with a safety-based objective for helicopter routing in the Norwegian oil industry.

Genetic algorithm [80]Multiobjective helicopter routing problemA variation of the cluster-first route-second method for routing helicopters.

Transgenic algorithm [81]Vehicle routing problem with time windowsHorizontal gene transfer based on the transformation mechanism and an intelligent mutation operator called Symbion operator.

Vertical transfer algorithm [82]School bus routing problemA computer algorithm based on the mechanism of vertical gene transfer.

Particle swarm optimisation [83]Vehicle routing problem with time windowsAn improved hybrid particle swarm optimisation (IHPSO) method with some postoptimisation procedures.

Genetic algorithm [84]Vehicle routing problem with time windowsPopulation preselection operators.

Genetic algorithm [85]Vehicle routing problem with time windowsA physical parallelisation of a distributed real-coded genetic algorithm and a set of eight subpopulations residing in a cube topology.

Tabu search [86]Vehicle routing problem with time windows and multidepot (VRPTW)A unified Tabu search heuristic.

Simulated annealing [87]Vehicle routing problem with time windowsA two-phase system (global neighbourhoods and local neighbourhood) of a parallel simulated annealing.

Simulated Annealing [88]Vehicle routing problem with time windows2 interchanges with the best-accept-strategy.

Evolutionary Algorithm [89]Vehicle routing problem with time windowsAn individual representative called the strategy parameter used in the recombination and mutation operators.

Tabu Search [90]Vehicle routing problem with time windowsThe Tabu search with a neighbourhood of the current solution created through an exchange procedure that swaps sequences of consecutive customers.

Genetic Algorithm [91]Vehicle routing problem with time windowsA genetic routing system or GENEROUS based on the natural evolution paradigm.

GRASP [92]Vehicle routing problem with time windowsA two-phase greedy randomised adaptive search to solve VRPTW.

Branch-and-Bound method [93]Vehicle routing problem with time windowsA Branch-and-Bound method to solve VRPTW.

A rural routing heuristic [94]School bus routing problemConstructing the initial route and then improving it by using a fixed tenure Tabu search algorithm.

GRASP [95]School bus routing problemThe solution method starts with a GRASP-like saving algorithm, after which a variable neighbourhood search algorithm is used to improve the initial solution. A modified version of the well-known transportation problem helps the metaheuristic to quickly assign students to stops.

Genetic algorithm [96]School bus routing problemUse the GENROUTER system to route school buses for two school districts. The routes obtained by GENROUTER system were superior to those obtained by the CHOOSE school bus routing system and the current routes in use by the two school districts.

Simulated annealing [97]Train formation problemTo explore the solution space, where the revised simplex method evaluates, selects, and implements the moves. The neighbourhood structure is based on the pivoting rules of the simplex method that provides an efficient method to reach the neighbours of the current solution.

Genetic algorithm [98]Train formation problemThe calibration and validation of the GA model are carried out for three different complexity levels of objective functions.

Neural networks [99]Train formation problemA training process for neural network development is conducted, followed by a testing process that indicates that the neural network model will probably be both sufficiently fast and accurate, in producing train formation plans.

Column generation based heuristic [54]Generalized location routing problem with space exploration or generalized location routing problem with profits (GLRPPs)The problem arises in exploration of planetary bodies where strategies correspond to different technologies. A description of the generalized location routing problem with profits and its mathematical formulation as an integer program are provided. Two solution methodologies to solve the problem—branch-and-price and a three-phase heuristic method combined with a generalized randomized adaptive search procedure—are proposed.

Memetic algorithm [100]Helicopter routing problemThe personnel transportation within a set of oil platforms by one helicopter that may have to undertake several routes in sequence.

Genetic algorithm [101]Locomotive routing problemA cluster-first, the route-second approach is used to inform the multidepot locomotive assignment of a set of single depot problems and after that we solve each problem independently. Each single depot problem is solved heuristically by a hybrid genetic algorithm that in which push forward insertion heuristic (PFIH) is used to determine the initial solution and λ-interchange mechanism is used for neighbourhood search and improving the method.

Genetic algorithm [102]Locomotive routing problemThe proposed solution approach is tested with real-world data from the Korean railway.

Branch-and-bound method [103]Locomotive routing problemBacktracking mechanism that can be added to this heuristic branch-and-price approach.

Heuristic algorithm [50]Tour planning problemA heuristic method based on local search ideas.

Heuristic algorithm [104]Team orienteering problemBilevel filter-and-fan method for solving the capacitated team orienteering problem. Given a set of potential customers, each associated with a known profit and a predefined demand, and the objective of the problem is to select the subset of customers as well as to determine the visiting sequence and assignment to vehicle routes such that the total collected profit is maximized and route duration and capacity restrictions are satisfied.

Memetic algorithm [105]Team orienteering problemThe memetic algorithm is a hybrid genetic algorithm using new algorithms.

Branch-and- price algorithm [106]Team orienteering problemIncludes branching rules specifically devoted to orienteering problems and adapts acceleration techniques in this context.

Tabu search algorithm [107]Team orienteering problemA variable neighbourhood search algorithm turned out to be more efficient and effective for this problem than two Tabu search algorithms.

Ant colony optimization [108]Team orienteering problemThe sequential, deterministic-concurrent and random-concurrent,and simultaneous methods are proposed to construct candidate solutions in the framework of ACO.

Iterated local search heuristic [109]Team orienteering problemAn algorithm that solves the team orienteering problem with time windows (TOPTW)

Simulated annealing [110]Team orienteering problemTwo versions of the proposed SA heuristic are developed and compared with existing approaches

GRASP [111]Team orienteering problemA greedy randomised adaptive search Procedure for solving the Team orienteering problem.

GLS, VNS, ILS [112]Tourist trip design problemsGuided local search (GLS) and variable neighbourhood search (VNS) are applied to efficiently solve the TOP. Iterated local search (ILS) is implemented to solve the TOPTW.

Tabu search [113]Team orienteering problemThe Tabu search heuristic is embedded in an adaptive memory procedure that alternates between small and large neighbourhood stages during the solution improvement phase. Both random and greedy procedures for neighbourhood solution generation are employed and infeasible, as well as feasible, solutions are explored in the process.

Tabu search [114]Truck and trailer routing problemA solution construction method and a Tabu search improvement heuristic coupled with the deviation concept found in deterministic annealing is developed.

Simulated annealing [115, 116]Truck and trailer routing problemThe combination of a two-level solution representation with the use of dummy depots/roots, and the random neighbourhood structure which utilizes three different types of moves.

GRASP [117]Truck and trailer routing problemA hybrid meta-heuristic based on GRASP, VNS and path relinking.

Branch-and-cut [118]Maritime inventory routing problemA case study of a practical maritime inventory routing problem (MIRP) shows that the proposed neighbour and algorithmic framework are flexible and effective enough to be a choice of model and solution method for practical inventory routing problems

Branch-and-cut [119]Inventory routing problemThe algorithms could solve the instances with 45 and 50 customers, 3 periods and 3 vehicles.

Branch-and-cut [120]Inventory routing problemThe algorithm solves the IRP with several vehicles and with many products, each with a specific demand, but sharing inventory and vehicle capacities.

Branch-and-cut [121]Inventory routing problemThey implement a branch-and-cut algorithm to solve the model optimally.

Branch-and-price [122]Inventory routing problemA new branching strategy to accommodate the unique degeneracy characteristics of the master problem, and a new procedure for handling symmetry. A novel column generation heuristic and a rounding heuristic were also implemented to improve algorithmic efficiency.

Local search [123]Inventory routing problemOur model takes into account pickups, time windows, drivers’ safety regulations, orders, and many other real-life constraints. This generalization of the vehicle-routing problem was often handled in two stages in the past: inventory first, routing second.

Genetic algorithm [124]Inventory-distribution problemThe delivery schedule represented in the form of a 2-dimensional matrix and two random neighbourhood search mechanisms are designed.

Genetic algorithm [125]Bus Terminal Location ProblemA new crossover and mutation for the BTLP.

Branch-and-price method [126]Maritime inventory routing problemThe method is tested on instances inspired from real-world problems faced by a major energy company.

Variable neighbourhood search [127]Inventory routing problemA variable neighbourhood search (VNS) heuristic for solving a multiproduct multiperiod IRP in fuel delivery with multi-compartment homogeneous vehicles, and deterministic consumption that varies with each petrol station and each fuel type.

Branch-and-cut [128]Airline crew scheduling problemsThe branch-and-cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree-search algorithm that uses automatic reformulation procedures, heuristics and linear programming technology to assist in the solution.

Simulated annealing [129]Airline crew scheduling problemsComputational results are reported for some real-world short-to medium-haul test problems with up to 4600 flights per month.

Simulated annealing [130]Airline crew scheduling problemsThe first step uses the “pilot-by-pilot” heuristic algorithm to generate an initial feasible solution. The second step uses the Simulated Annealing technique for multi-objective optimization problems to improve the solution obtained in the first step.

Genetic algorithms [131]Airline crew scheduling problemsThe development and application of a hybrid genetic algorithm to airline crew scheduling problems. The hybrid algorithm consists of a steady-state genetic algorithm and a local search heuristic. The hybrid algorithm was tested on a set of 40 real-world problems.

Simulated annealing [132]Train scheduling problemThey integrated the train routing the train routing problem and the train scheduling problem. They used simulated annealing to solve the problem. The objective is to minimize operational costs (fuel, crew, capital, and freight car rental costs) without missing cars.

Genetic algorithm [133]Train scheduling problemThey applied GA for solving the freight train scheduling problem in a single track railway system.

Genetic algorithm [134]Train scheduling problemThey solved the passenger train scheduling problem by attempting to minimize the waiting time for passengers changing trains. They proposed a GA with a greedy algorithm to obtain the sub-optimal solutions.

Genetic algorithm [135]Train dispatching problemA model for train dispatching on lines with double tracks. The model can optimize train dispatching by adjusting the order and times of train departures from stations, and then the efficiency of the method is demonstrated by simulation of the Guangzhou to Shenzhen high-speed railway.

Genetic algorithm [136]Train timetable problemTo obtain the optimal train timetables to minimize delay and changes of gates, they divided the railway network into multiple block, used the branch-and-bound method to determine the train sequence for each block, and calculate the train times. They applied GA to improve the solutions.

ACO [137]Railroad blocking problemAn ant colony optimization algorithm for solving RBP. The solution method is applied to build a car blocking plan in the Islamic Republic of Iran Railways.

Very large-scale neighbourhood [71]Railroad blocking problemAn algorithm using a technique known as very large-scale neighbourhood (VLSN) search that is able to solve the problem to near optimality using one to two hours of computer time on a standard workstation computer.

ACO [138]Railroad blocking problemA new formulation for RBP in coal heavy haul rail network in north China. An improved ACO to solve a new formulation for RBP in coal heavy haul rail network in north China. They discussed the problem with direct train routing and frequencies and they did not consider the terminal capacity in handling classification process and maximum available blocks constraints.

Multiobjective evolutionary algorithms [139]Aeronautical and aerospace design problemsA taxonomy and a comprehensive review of applications of MOEAs in aeronautical and aerospace design problems. They provide a set of general guidelines for using and designing MOEAs for aeronautical and aerospace engineering problems.

Genetic algorithms [140]Aerospace problemsThe paper uses GA to solve H-2 and H-infinity norm model reduction problems and helps obtain globally optimized nominal models.

Genetic algorithms [44]Military transport planning (MTP)They study a logistics problem arising in military transport planning. A Niche genetic algorithm, together with a hybridized variant, is applied to the problem.

GRASP [141]School bus routing problemA matheuristic that uses a GRASP construction phase followed by a variable neighbourhood descent (VND) improvement phase to solve 112 instances with 5 stops and 25 students to 80 stops and 800 students of the SBRP.

ACO [142]School bus routing problemA hybrid evolutionary computation based on an artificial ant colony with a variable neighbourhood local search algorithm to solve the urban bus routing problem in the Tunisian case.

Hybrid algorithm [143]School bus routing problemA mixed load improvement algorithm to solve 48 test instances for the SBRP with a number of schools 6, 12, 25, 50, and 100 and bus stops 250, 500, 1000, and 2000.

Tabu search [144]School bus routing problemIn addition to the min-max vehicle routing problem criterion imposed on the time it takes to complete the longest route, school districts are concerned with the minimization of the total distance travelled and they develop a solution procedure for this problem by applying Tabu search within the framework of Multiobjective Adaptive Memory Programming and compare it to an implementation of the Non-dominated Sorting Genetic Algorithm— a well-known approach to multiobjective optimization.

Hybrid algorithm [145]School Bus Routing ProblemFor a school bus routing problem, called the MV-TPP-RC, which combines a bus stop selection and bus route generation with additional constraints on certain resources, we have developed a BCP algorithm as an implementation of a set partitioning formulation proposed for that problem. This formulation has been obtained from a Dantzig-Wolfe decomposition of a three-index variables model that describes the MV-TPP-RC.