It has been considered a simple decay coefficient i. The weight of 25 the solution goodness is the makespan i. A constant of pheromone updating i. The algorithm works as follow. It is evaluated and 30 laid, according to the disjunctive graph representation of the instance in issue, the amount of 31 pheromone on each arc evaporation coefficient is applied to design the environment at the 32 next step.
An objective function value is optimised accordingly to partial good 5 solution. Bees Algorithm BA approach 9 A colony of bees exploits, in multiple directions simultaneously, food sources in the form of 10 antera with plentiful amounts of nectar or pollen. They are able to cover kilometric distances 11 for good foraging fields [50].
Flower paths are covered based on a stigmergic approach — 12 more nectar places should be visited by more bees [51]. They wave randomly from one patch to another. Returning at the hive, those 15 scout bees deposit their nectar or polled and start a recruiting mechanism rated above a 16 certain quality threshold on nectar stored [52]. The recruiting mechanism is properly a 17 launching into a wild dance over the honeycomb.
Bees, stirring up for discovery, flutter in a number from one to one hundred 19 circuits with a waving and returning phase. The waving phase contains information about 20 direction and distance of flower patches. Waving phases in ascending order on vertical 21 honeycomb suggest flower patches on straightforward line with sunbeams. This 22 information is passed using a kind of dance, that is possible to be developed on right or on 23 left.
So through this dance, it is possible to understand the distance from the flower, the 24 presence of nectar and the sunbeam side to choose [54]. After waggle dancing on the dance floor, the dancer 27 i. A squadron moves forward into the patches. More follower bees are sent to more 29 promising patches, while harvest paths are explored but they are not carried out in the long 30 term.
A swarm intelligent approach is constituted [55]. This allows the colony to gather food 31 quickly and efficiently with a recursive recruiting mechanism [56].
In its basic version, the algorithm performs a kind of neighbourhood search 34 combined with random search. Advanced mechanisms could be guided by genetics [57] or 35 taboo operators [58].
The standard Bees Algorithm first developed in Pham and Karaboga in 36 [59, 60] requires a set of parameters: no. The standard BA starts with random search. For each solution, a complete schedule of operations in JSP is 6 produced. The makespan of the solution is analogous to the profitability of the food source 7 in terms of distance and sweetness of the nectar.
Bees, n scouts, explore patches, m sites - 8 initially a scout bee for each path could be set, over total ways, ngh, accordingly to the 9 disjunctive graph of fig. Once a 12 feasible solution is found, each bee will return to the hive to perform a waggle dance.
Researches of patches are conducted, other nsp bees, in the neighbourhood of the 16 selected sites, m-e sites. System maintains, step repetition: imax, where each bee of the colony 17 of bees will traverse a potential solution. Electromagnetism like Method EM 21 The Electromagnetic Like Algorithm is a population based meta-heuristics proposed by 22 Birbil and Fang [61] to tackle with combinatorial optimisation problems.
EM 2 simulates electromagnetic interaction [63]. The algorithm evaluates fitness of solutions 3 considering charge of particles. Each particle represents a solution. Two points into the 4 space had different charges in relation to what electromagnetic field acts on them [64]. An 5 electrostatic force, in repulsion or attraction, manifests between two points charges.
The 6 electrostatic force is directly proportional to the magnitudes of each charge and inversely 7 proportional to the square of the distance between the charges.
Points xi could be 14 evaluated as a task into the graph representation fig. The generic pseudo-code for the EM is 21 reported in figure 6. Each particle is initially located into a source node see disjunctive 22 graph of figure 2.
While moving, 24 particle jumps in a node based on its attraction force, defined in module and direction and 25 way. If the force from starting line to arrival is in relation of positive inequality, the particles 26 will be located in a plane position in linear dependence with force intensity.
A selection 27 mechanism could be set in order to decide where particle is directed, based on node force 28 intensity. Force is therefore the resultant of particles acting in node. A solution for the JS is 29 obtained only after a complete path from the source to the sink and the resulting force is 30 updated according to the normalized makespan of different solutions.
This optimization method is based on works of Metropolis et al. It is a generic probabilistic metaheuristic used to find a good 6 approximation to the global optimum of a given objective function.
Mostly it is used with 7 discrete problems such as the main part of the operations management problems. The technique 11 deals with the minimization of the global energy E inside the material, using a control 12 parameter called temperature, to evaluate the probability of accepting an uphill move inside 13 the crystals structure.
The procedure starts with an initial level of temperature T and a new 14 random solution is generated at each iteration, if this solution improves the objective 15 function, i.
Afterwards a new iteration of the procedure is implemented. The acceptance probability can be measured as following:! Tabu Search TS 2 Tabu search Glover, is an iterative search approach characterised by the use of a 3 flexible memory [69]. The process with which tabu search overcomes local optimality is 4 based on the evaluation function that chooses the highest evaluation solution at each 5 iteration. The evaluation function selects the move, in the neighbourhood of the current 6 solution, that produces the most improvement or the least deterioration in the objective 7 function.
Since, movement are accepted based on a probability function, a tabu list is 8 employed to store characteristics of accepted moves so to classify them as taboo i. This is used to dodge cycling movements. A strategy called 10 forbidding is employed to control and update the tabu list.
This method was formalized by 11 Glover [69]. An algorithm based on tabu search requires some elements: i the move, ii the 12 neighbourhood, iii an initial solution, iv a search strategy, v a memory, vi an objective 13 function and vii a stop criterion. The of TS is based on the definition of a first feasible 14 solution S, which is stored as the current seed and the best solution, at each iteration, after 15 the set of the neighbours is selected between the possible solutions deriving from the 16 application of a movement.
The value of the objective function is evaluated for all the 17 possible movements, and the best one is chosen. The new solution is accepted even if its 18 value is worse than the previous one, and the movement is recorded in a list, named taboo 19 list. Some rules of movements can be defined as the crossover of 23 some jobs to different machines and so on, defining new solutions and generating new 24 values of the objective functions.
The best solution between the new solutions is chosen and 25 the movement is recorded in a specific file named taboo list. The stopping criterion can be 26 defined in many ways, but simplest way is to define a maximum number of iterations [71]. Neural networks NNs 2 Neural networks are a technique based on models of biological brain structure.
Artificial 3 Neural Networks NN , firstly developed by McCulloch and Pitts in , are a 4 mathematical model which wants to reproduce the learning process of human brain [72]. An algorithm processes data through its interconnected network of processing 7 units compared to neurons. NNs are an adaptive system, constituted by 11 several artificial neurons interconnected to form a complex network, those change their 12 structure depending on internal or external information.
This data record, called training set, is 3 constituted by inputs with their corresponding outputs. This process reproduces almost 4 exactly the behaviour of human brain that learns from previous experience.
After having built a training set of 14 examples coming from historical data and having chosen the kind of architecture to use 15 among feed-forward networks, recurrent networks , the most important step of the 16 implementation of NNs is the learning process.
This means that, from a very large number of extremely simple 19 processing units neurons , each of them performing a weighted sum of its inputs and then 20 firing a binary signal if the total input exceeds a certain level activation threshold , the 21 network manages to perform extremely complex tasks. It is important to note that different 22 categories of learning algorithms exists: i supervised learning, with which the network 23 learns the connection between input and output thank to known examples coming from 24 historical data; ii unsupervised learning, in which only input values are known and similar 25 stimulations activate close neurons otherwise different stimulations activate distant 26 neurons; and iii reinforcement learning, which is a retro-activated algorithm capable to 27 define new values of the connection weights starting from the observation of the changes in 28 the environment.
Supervised learning by back error propagation BEP algorithm has 29 become the most popular method of training NNs.
The Hopfield Network a content addressable 34 memory systems with weighted threshold nodes dominates, however, neural network 35 based scheduling systems [77]. They are the only structure that reaches any adequate result 36 with benchmark problems [78]. It is also the best NN method for other machine scheduling 37 problems [79]. In Storer et al. The values of the function are determined by 41 the precedence and resource constraints which violation increases a penalty value.
The 42 Multi Layer Perceptron i. The black 44 box has a great no. Discussion and Conclusions 5 In this chapter, it was faced the most intricate problem i. The job shop scheduling is one of the most 7 formidable issues in the domain of optimization and operational research. Many methods 8 were proposed, but only application of approximate methods metaheuristics allowed to 9 efficiently solve large scheduling instances.
Most of the best performing metaheuristics for 10 JSSP were described and illustrated. The acyclic graph representation is a quite good way to 13 model alternatives in scheduling.
How to fit approaches with problem domain industrial 14 manufacturing system is generally a case in issue. A common rule is: less 16 parameters generate more stable performances but local optimum solutions. All the proposed approaches use probabilistic transition rules and 3 fitness information function of payoff i.
They do not need a coding system. GAs surpasses their cousins in the request for robustness. The 8 matching between genotype and phenotype across the schemata must be investigated in 9 GAs in order to obtain promising results. The difficult of GA is to translate a correct 10 phenotype from a starting genotype.
A right balancing between crossover and mutation 11 effect can control the performance of this algorithm. The EM approach is generally affected 12 by local stability that avoid global exploration and global performance. It is, moreover, 13 subject to infeasibility in solutions because of its way to approach at the problem. SA and 14 TS, as quite simpler approaches, dominate the panorama of metaheuristic proposal for JS 15 scheduling. They manifest simplicity in implementation and reduction in computation effort 16 but suffer in local optimum falls.
These approaches are generally used to improve 17 performances of previous methodologies and they enhance their initial score. The influence 18 of initial solutions on the results, for overall approaches, is marked.
Performances of NNs 19 are generally affected by the learning process, over fitting. Too much data slow down the 20 learning process without improving in optimal solution.
Neural Network is, moreover, 21 affected by difficulties in including job constraints with network representation. The 22 activating signal needs to be subordinated to the constraints analysis. Measurement of 25 output and cost-justification computational time and complexity are vital to making good 26 decision about which approach has to be implemented.
They are vital for a good scheduling 27 in operations management. In many cases there are not enough data to compare — 28 benchmark instances, as from literature for scheduling could be useful - those methods 29 thoroughly.
In most cases it is evident that the efficiency of a given technique is problem 30 dependent. It is possible that the parameters may be set in such way that the results of the 31 algorithms are excellent for those benchmark problems but would be inferior for others.
There is, however, a group of several methods that 34 dominates, both in terms of quality of solutions and computational time. But this definition 35 is case dependent. It is reasonable to expect that humans 39 will intervene in any schedule. Humans are smarter and more adaptable than computers. So it makes sense to see what optimal configuration is 2 before committing to the final answer.
Heuristic search methods: A review. Johnson and F. The Particle Swarm Optimization Algorithm: convergence analysis and parameter selection. Information Processing Letters ; 85 6 : —; [4] Garey M. Production Inventory Management in the computer Age.
Blackstone, Jr. Factory Physics. Foundations of manufacturing Management. Industrial Scheduling. Prentice-Hall, Englewood Cliffs, N. A computational study of local search algorithms for job shop scheduling. Scheduling Algorithms. Springer-Verlag, Berlin, A survey of scheduling rules. Operations Research, ; 25 1 : 45— An algorithm for solving the job-shop problem.
Management Science, ; 35 2 : — M, The use of workload information to control job lateness in controlled and uncontrolled release production systems, J. Spencer, edt. In Proc. The shifting bottleneck procedure for job shop scheduling. Management Science, ; Vol.
Modern Heuristic Techniques for Combinatorial Problems. Algorithms for solving production scheduling problems. Operations Research, , ;Vol. Science, ; 13 1 : Holthaus, O. A comparative Study of Dispatching rules in dynamics flowshops and job shops, European J. Of Operational Research. D, Vecchi M. Science ; : Journal of Global Optimization.
MIT Press, Tabu Search. Di Caro and L. Ant algorithm for discrete optimization. The Bees Algorithm. IEEE Trans. ICAPS03 ; Aron, J. Deneubourg, and J. Self-organized shortcuts in the Argentine ant. Marques: Ant colony optimization for job shop scheduling. The Ant System: Optimization by a colony of cooperating agents. Dorigo, and F. Glover, editors. This topic provides information about operations scheduling.
You can use operations scheduling to provide a general estimate of the production process over time. You can schedule production at the operation level and the job level. Unlike job scheduling, operations scheduling doesn't explode the operations for the production route into jobs.
If you want to include more detail in the scheduling, such as information about current capacity, you can run job scheduling after you run operations scheduling. You can also run job scheduling only. Job scheduling is typically used to schedule individual jobs on the shop floor for an immediate or short-term time frame. The main components of operations scheduling are the scheduling direction, the capacity of resources, and materials optimization. By using operations scheduling, you can achieve the following goals:.
You must estimate the cost of a production order before you can run operations scheduling. If you haven't run an estimate, it's automatically run before operations scheduling is started. An operations schedule specifies the following information:. The setup time, process time, and run time are set for operations in the production. After you run operations scheduling, the status of the production order is Scheduled , and all operations are scheduled in the order that is specified by the production route.
However, only the duration of the operation is considered. Start times and end times aren't scheduled. The scheduling direction is fundamental to the scheduling process. Production can be scheduled forward or backward from any date, depending on timing and scheduling requirements.
When you run an operations schedule, each operation in the production route is scheduled for the resource that is specified for the operation.
Additionally, the duration of each operation is specified on the production route. If a resource group is specified for an operation, the scheduling reserves capacity on the group. However, unlike job scheduling, operations scheduling doesn't select the specific resources in the group. If you're working with finite capacity, the schedule depends on the availability of the resources that are required in order to complete production. Operations scheduling follows the sequence of operations that is specified on the production route.
The scheduling reserves capacity on the resource groups, based on the operation times that are defined on the production route. The sum of available capacity on the resources that are involved determines the capacity for the resource group.
Capacity reservations that already exist for the resources are considered unavailable capacity. If there isn't enough available capacity for the production, the production orders can be delayed or even stopped. You can also specify the efficiency that you expect from the resources that are involved in the production.
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