VIETNAM NATIONAL UNIVERSITYHO CHI MINH CITY INTERNATIONAL UNIVERSITYDEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING

SPECIAL STUDY REPORT

MINIMIZE CYCLE TIME/MAKESPAN/FLOWTIME IN SCHEDULING SIMULATION BY HEURISTIC METHODS APPLICATION

Table of ContentsTable of Contents2Abstract4Article 1: An Ant Colony Optimization Algorithm for Shop Scheduling Problems [1]5I.Introduction51.1 New neighborhood structure for GSS51.2 Ant Colony Optimization for GSS by using ND algorithm51.3 Improving the solution by using the black-box local search.5II.Model5III.Result6IV.Conclusion7Article 2: An effective artificial bee colony algorithm for the flexible job-shop scheduling problem [2]7I.Introduction7II.Formulation7III.Solution8IV.Result8V.Limitation9Article 3: An improved artificial bee colony algorithm for the blocking flow-shop scheduling problem [3]9I.Introduction9II.Formulation9III.Solution9IV.Result10V.Limitation10Article 4: A simulated annealing/local search to minimize the makespan and total tardiness on a hybrid flow-shop [4]10I.Introduction10II.Formulation11III.Solution11IV.Result from comparison of SA/LS and genetic algorithm (GA)12V.Limitation12Article 5: Analysis of electric vehicle charge scheduling and effects on electricity demand costs [5]12I.Introduction12II.Formulation13III.Solution133.1 The first available scheduling algorithm (FAS)133.2 The random and first available scheduling algorithm (RFAS)133.3 Greedy local search algorithm with pairwise exchange (GLS)143.4 Simulated annealing algorithm with pairwise exchange (SA)14IV.Result14V.Limitation14Conclusion15References15

AbstractScheduling is a major issue faced every day in manufacturing systems as well as service industry, so it is essential to develop effective and efficient advanced manufacturing and scheduling technologies and approaches. In these articles that we summarize, the authors applied many algorithms as well as methods to improve the constructed solutions and increase the problem size. Here is the structure of all articles that we summary. Firstly, we summarize the problem. Secondly, we restate the problem formulation. Thirdly, we paraphrase the solution and result of experiments. Finally, we conclude and raise the article limitation.

Article 1: An Ant Colony Optimization Algorithm for Shop Scheduling Problems [1]Keywords: ACO, scheduling, group shop, job shop, open shop

I. IntroductionIn this article, Christian Blum and Michael Samples dealt with the Ant Colony Optimization (ACO) applicability to group shop scheduling (GSS). Firstly, they proposed a new neighborhood structure. Secondly, the solutions is constructed and improved by the development of ACO which uses the ND algorithm and employs the black-box local search procedure. Finally, the comparison between ACO and tabu search for GSS.

1.1 New neighborhood structure for GSSBased on the neighborhood structure proposed by Nowicki and Smutnicki for the JSS problem, Christian Blum and Michael Samples defined a neighborhood of a feasible solutions of a GSS instance as an extension of the neighborhood structure. The new neighborhood denoted by N1c,GSS is defined as followed: a feasible solution s is a neighborhood of a feasible solution s if in the critical path P of s for exactly one machine block or exactly one group block B =(o1,o2,...,onk1,onk) on P, the order of o1 and o2 or the order of onk1 and onk is swapped in s.

1.2 Ant Colony Optimization for GSS by using ND algorithmThe ACO for GSS (ACO_GSS) is Max-Min ant system (MMAS) in the hyper-cube framework (HCF). This ACO_GSS is applied the the lower and upper bound, min and max, to the pheromone values. The pheromone model referred to as relation-learning model. A high level description of the algorithm is as followed:- Firstly, all of variables are initialized. The pheromone values are set to the initial value 0.5 by the procedure InitializePheromoneValues(T). Secondly, use the ConstructSolution(T) procedure to construct the solutions. Then, these solutions are improved by the application of ApplyLocalSearch(Siter) procedure. Thirdly, update the value of variables sib , srb and sbs. Fourthly, update the pheromone trail value by application of ApplyPheromoneUpdate(cf,bs_update,T,srb,sbs) procedure. Fifthly, compute the convergence factor. Finally, depend on the variable bs_update, a decision on whether to restart the algorithm or not is made.

1.3 Improving the solution by using the black-box local search.ApplyLocalSearchiter): To every solution sj iter a steepest descent local search is applied. The neighborhood structure for this local search is N1c,GSS as introduced in section 1.1

II. ModelThis ACO approach based on the model of pheromone, reperred to as relation-learning model.In the model:- 2 operations Oi and Oj are either in the same group or processed by the same machine. Thus, Oi and Oj are called related- Ri is the set operations that are related to Oi.- Tij and Tji are denoted for pheromone trail parameter for each pair of operation Oi,Oj- Tij and Tji are the value of Tij and Tji respectively.- T is the set of all pheromone trail parameter- Variable Sib is the best solution generated in the current iteration.- Variable Sbs is the best solution since the start of the algorithm.-Variable Srb is the best solution since the last restart of algorithm.- Variable cf mesures the algorithm's convergence- Variable bs_update becomes true since the algorithm reaches convergence

ALGORITHM 1. ACO for the GSS problem (ACO_GSS)input: A problem instance P of the GSS problemsbs NULL, srb NULL, cf 0, bs_update FALSEna DetermineNumberOfAnts(P )InitializePheromoneValues(T)While termination conditions not satisfied doiter for j=1to na doiter iter ConstructSolution(T) end for ApplyLocalSearch(iter) sib argmin{Cmax(s)|s iter} EliteAction(sib) Update(sib,srb,sbs) ApplyPheromoneUpdate(cf,bs_update,T,srb,sbs) cf ComputeConvergenceFactor(T) if cf > 0.99 then if bs_update = TRUE then ResetPheromoneValues(T) srb NULL bs_update FALSE else bs_update TRUE end if end ifend whileoutput:sbs

III. Result The result of ACO for GSS (ACO_GSS) in compare to tabu search for GSS (TS_GSS) as below:- For GSS instances (ft10, la38, abz7) in 20 long runs of algorithm and time linit are 180s, 1800s and 1800s for ft10, la38 and abz7 respectively. The result shows TS_GSS has advantages for JSS-like instances and ACO_GSS has advantages for more OSS-like instances.- For OSS benchmark instances: ACO_GSS is better in the best solution, in average solution quantities, in standard deviation and in the average time needed to find the best solution. - For JSS instances: TS_GSS is one of the state-of-art algorithm for JSS instances

IV. ConclusionThe article is proposed the ACO approach to deal with the group shop scheduling problems. This ACO_GSS is MMAS in hyper-cube framework. The constructing solutions is used the ND algorithm. Besides, the ACO_GSS employs the black-box local search procedure to improve the constructed solutions. In addition, the experimental is conducted to evaluate the ACO_GSS and compare it with the tabu search approach. The result showed that, ACO_GSS is suitable for the application of OSS instances. Based on the result, we suggest a genetic algorithm approach to those combinatorial optimization problems.

Article 2: An effective artificial bee colony algorithm for the flexible job-shop scheduling problem [2]Keywords: Flexible job-shop scheduling problem. Makespan. Artificial bee colony algorithm. Machine assignment. Operation sequence. Critical path

I. IntroductionFJSP extended from the classical JSP. It is divided into 2 sub-problems routing and scheduling, in which, routing is to assign each operation to machine appropriately, whereas scheduling is to sequence the assigned operations reasonably to get the optimal solution.The ABC algorithm is aimed to the balance between global exploration and local exploitation. First, the decoding rule is employed to achieve an active schedule. Second, generate an initial population with certain quantity and diversity. Whereas the employed bee phase is designed to derive the new neighbor food source, onlooker bee phase is developed to improve the convergence speed and scout bee phase is applied to enrich and avoid the premature convergence. In addition, the simulation results and comparisons between ABC algorithm and some existing algorithms are conducted.

II. FormulationMin Cmax(1)Subject to

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Eq.1 is the objective function. Eq.2 ensures that the operations belonging to the same job satisfy the precedence constraints. Eq.3 ensures that each operation is assigned to only one machine from its candidate machine set. Eq.4 guarantees that each operation should be processed only at one priority on one machine. Eq.5 ensures that each machine processes one operation at a time. Eq.6 and Eq.7 guarantee that each operation should be started only after the previous operation of the same machine and the previous operation of the same job are both completed and L is a number large enough.

III. SolutionThe work process can describe as below: the employed bees bring load of nectar from the food sources and share this information with onlooker bees. By dancing, the onlooker bees can know the status of the currently being exploited. The onlooker bees can choose the food source according to quantity of food source. If the better food source is explored, the scout or onlooker bees can change into an employed bee. Otherwise, employed bees can be change into the scout or onlooker bees if the food source is exploited fully.The procedure of ABC algorithm as below:Step 1: Initialize parameters, including the number of food sources or the number of the employed bees (neb), number of onlooker bees (nob) and number of scout bees (nsb).Step 2: Initialize population of food sources with random solutions.Step 3: Calculate the objective value (si) of each food source si and then determine the best food resource gbest.Step 4 (employed bee phase):Step 4.1: For every employed bee ui,i = 1,2,,neb, generate the new food source from siStep 4.2 (onlooker bee phase):Step 4.2.1: Calculate the probability of selecting food source according to Eq. (10)Step 4.2.2: Calculate the number of onlooker bees Ni = pi * nob to be sent the food source Step 4.2.3: For every onlooker bee vj,j = 1,2,,Ni, generate the Ni new food sources from And let be the best of all the . If () (si) then si = Step 4.3: For i= 1,2,neb: if (si) (gbest), then gbest = siStep 5 (scout bee phase):Step 5.1: Initialize scout bees with random solutions and update gbest if possibleStep 5.2: Determine the worst nsb employed bees and replace them with the scout bees if the scout bees are better.Step 6. If a stopping criterion is met, then output gbest and its objective value; otherwise, go back to Step 4.

IV. ResultWith five Kacem instances, with its range from four jobs five machines to 15 jobs ten machines, the ABC algorithm s performance is tested and compared with some algorithms. The results showed that the ABC algorithm is the best and this algorithm can get the optimal results. Besides, based on the results, its seen that ABC algorithm is the good searching quality and robustness. In addition, its computation time is pretty short.About the BRdata instances, with its range from ten jobs six machines to 20 jobs 15 machines, The results showed that ABC algorithm has more powerful optimization capability and robust on initial conditions. Besides, the best makespan and best solution for whole population convergence are obtained by ABC algorithm.

V. LimitationThis is the first research which work on the application of ABC algorithm for FJSP. Based on the obtained results, it can be concluded that this algorithm is effective, efficient and robust in solving the complex FJSP. However, the purpose of this research is to minimize Cmax only. It need more effort to do research further for multi-objective scheduling problem as well as stochastic problem.

Article 3: An improved artificial bee colony algorithm for the blocking flow-shop scheduling problem [3]Keywords: Blocking flow-shop. Makespan. Artificial bee colony algorithm. Differential evolution

I. IntroductionBlocking flow-shop scheduling problem (BFS) can be defined as follow: each of job from set J = {1,2,,n}has to be processed on m machine from the set M = {1,2,,m}with order that have no intermediate buffer. It means that a job must be blocked if the next machine is unavailable. The Oj,k operation corresponds to the processing of job j on machine k during an uninterrupted processing time Pj,k. The problem is to seek a schedule such that the processing sequence of jobs is the same on each machine and the makespan is minimized.Assumption is each machine can process at most one job and each job can be processed on at most one machine.

II. FormulationOj,k be the job operation j on machine k, where j{1,2,,n} and k{1,2,,m}.Pj,k be j processing time on machine k.Sj,k be starting time of j on machine k. = {(1), (2),..,, (n)} be the job permutation.S1,0= 0 (1)S1,k = Si,k-1 + P1,k where k{1,2,,m} (2)Sj,0 = Sj-1,1 where j = {2,3,, n} (3)Sj,k = max (Sj,k-1 + Pj,k,Sj-1,k+1) where k{1,2,,m-1} and j{2,3,,n} (4)Sj,m = Sj,m-1 + Pj,m where j{2,3,,n} (5)Eq. (4) computes the starting time Sj,k of job j with k{1,2,,m}. Eq. (5) computes the staring time of job j on the last machine m where consider completion time of the previous operation of job j (Sj,m-1 + Pj,m). The makespan of the job permutation = {(1), (2),..,, (n)} is equal the time when the last job in the processing sequence is finished at machine m Cmax() = Sn,m. The BFS problem with the makespan criterion is find a permutation * in the set of all permutation II such that MS(*) MS(n,m) where * II(6)

III. SolutionThe work process of IABC algorithm for the BFS problem with the makespan criterion can be presented briefly as below:Step1: initialize parameters and population P = {1, 2,,SN} and evaluate solution in the population.

Step2: Employed bee phase: generate new solution i* by using swap and insert operator method. Compare and replace the ith employed bee i by the better solution between i*.

Step3: Onlooker bee phase: the solution i* is followed the following method onlooker bee chooses randomly 2 two solutions from population and takes the solution which its minimum makespan. Then, the local search algorithm is performed to find the new solution i*.

Step4: Scout bee phase: Improve the solution with the limited condition in the population by preforming mutation and crossover operator of DDE algorithm.

Step5: Memorize the optimal solution obtained so far.

Step6: if the limited condition in unsatisfied, go to step 2.

IV. ResultIn this article, the researchers made the comparison the presented IABC algorithm with GA, TS, TS+M, HDDE and DABC algorithm.Based on the well-known benchmark set of Taillard about the BFS problem. The benchmark set is divided into 12 same-sized subset from 120 different instances. The subset range is from 20 jobs 5 machines to 500 jobs 20 machines. From the simulated data, we can see the IABC algorithm outperforms the DABC, HDDE, TS, TS+M, and GA algorithm for average PRD, maximum PRD and minimum PRD. Besides, the problem size increases, the superiority of the IABC algorithm over HDDE and DABC algorithm increases. Thus, we can draw the conclusion that IABC algorithm outperforms the HDDE and DABC algorithms for BFS problem with the makespan criterion. In the procedure, the parameters pls, u, c have great effect on performance of IABC algorithm. The experiment result showed that parameter u affects the searching quality of the IABC algorithm. When the parameter c and pls are equal to 0.1 the APRD values are better.

V. LimitationIn this paper, the researchers presented the IABC algorithm application for BFS problem with makespan criterion. The writers developed the IABC-based searching mechanism to perform the exploration the solution within solution space. In the onlooker bee phase, the local search is employed to exploit. In the scout bee phase, the differential evolution algorithm is adopted to obtain the solution. Based on the experiment and comparison result, it showed that IABC algorithm is the superior in terms of solution quality and effectiveness. However, the article is focus on the BFS only with the single criteria only. So, we suggest that the future work is to improve the local search in order to apply the IABC to other optimization problem and extend the ideas to the different objective function or multi-objective.

Article 4: A simulated annealing/local search to minimize the makespan and total tardiness on a hybrid flow-shop [4]Keywords: Bi-objective scheduling. Hybrid flow-shop. Simulated annealing. Makespan.Total tardiness

I. IntroductionIn manufacturing system as well as in the service industry, the analysis of the performance of a schedule often involves more than one aspect and requires a multi-objective treatment. Since these objectives are in conflict of interests, a solution may perform well for one objective, but giving bad results for others. So, scheduling problems have often a multi-objective nature.Hybrid flowshop scheduling problem: The hybrid flowshop scheduling problem involves the sequence of jobs in a flowshop which at least one stage has to consist of several machines. All data in this problem(i.e., processing times of operations, setup times, due date, number of stages, number of machines, and number of jobs) are known and constant and deterministic when scheduling is undertaken. The setup times considered in this problem are classified into two types: sequence-independent setup time and sequence-dependent setup times.Scheduling objective: the objective is assigning jobs to the machines at the corresponding stages and to determine the processing sequences on them in order to minimize a convex combination of makespan and the total tardiness.

II. FormulationFor a solution x, the objective function is followed:(x) = 1*1(x) + 2*2(x).1(x) be makespan; 2(x) be total tardiness; 1+2 = 1. The meaning of 1 is to balance both objectives. For a low value of 1, total tardiness problem will be dominated the makespan problem. Otherwise, the makespan problem will be dominated whereas for a large value of 1.The normalized objective is followed:1(x) = 2(x) =

III. Solution In this paper, the authors proposed the simulated annealing approach with some differences versus the original simulated annealing approach. The SA/LA pseudo code is as belowInitialization The representation of a solution: We apply a scheme using integers which show the number of job(s). Draw a seed sequence x: The seed sequence is generated in a random way from the search space. Evaluate 1(x) and 2(x): Where 1(x) is the makespan, 2(x) is the total tardiness of seed sequence which is generated. Input parameters: Initial temperature (T0); final temperature(T); number of stages for reach of T0 to T (N); maximum number of iterations in each temperature (max_it); the weighting coefficients ( {0:25; 0:5; 0:75}). Set: T = T0; it = 1; q = 1; Archive(q) = {x};

While T > TFor it = 1: max_itStep1: y=Move x;Step2: Calculate SA and E as follow;Min 1 = min (1(x),1(y))Min 2 = min (2(x),2(y))SA(x) = [1*1(x) + 2*2(x)]-1SA(y) = [1*1(y) + 2*2(y)]-1E = SA(y) - SA(x)Step3: Decision making;If E