Developing a Multiobjective Optimization Scheduling ... - IEEE Xplore

Received February 18, 2014, accepted April 16, 2014, date of publication April 23, 2014, date of current version May 2, 2014. Digital Object Identifier 10.1109/ACCESS.2014.2319351

Developing a Multiobjective Optimization Scheduling System for a Screw Manufacturer: A Refined Genetic Algorithm Approach TUNG-KUAN LIU1 , YEH-PENG CHEN2 , AND JYH-HORNG CHOU1,2 , Senior Member, IEEE 1 Institute

of Engineering Science and Technology, National Kaohsiung First University of Science and Technology, Kaohsiung 824, Taiwan of Electrical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan

2 Department

Corresponding author: J.-H. Chou ([email protected]) This work was supported by the National Science Council of Taiwan under Grant NSC 102-2221-E-151-021-MY3.

ABSTRACT Over time, the traditional single-objective job shop scheduling method has grown increasingly incapable of meeting the requirements of contemporary business models; thus, a multiobjective scheduling solution is required. Because of changing orders, understanding the schedule and output is a constant challenge when using a traditional manual schedule, particularly among manufacturers that produce various products. The multiobjective optimization genetic algorithm (MOGA) is a relatively superior method of solving multiobjective optimization problems; therefore, we used a MOGA to solve flexible job-shop problems for a middle-scale screw manufacturer in Taiwan. For solving the problems of incorrect jobs assign and diversity problem of traditional genetic algorithm (GA) caused by encoding method when applying traditional GA in the flexible manufacturing environment, a refined GA was proposed. Two-phase test has performed for proposed approach, using a classical benchmark of distributed and flexible jobs-shop scheduling problem, and 80 set of work orders, the empirical results indicated that the proposed model yielded substantial savings, regardless of the total order completion time, machine retooling rate, and average machine load rate. INDEX TERMS Flexible jobs shop, multiobjective optimization genetic algorithms, screw manufacturer, refined genetic algorithms.

I. INTRODUCTION

Because the life cycle of products has substantially decreased and the price of raw material prices have increased, using of manual scheduling to responds to fluctuations in capacity planning has become increasingly difficult. Therefore, using optimization techniques is increasingly critical to address production scheduling problems, manages available resources, respond to external changes, and enhance the competitiveness of enterprises. Screw manufacturing is a thriving industry in Taiwan; however, this industry faces challenges as the prices of raw materials and electricity continue to increase, and the number of foreign competitors increases. The Screw manufacturing has involved a low margin and numerous products, requiring frequent adjustments to various orders; thus, scheduling effectiveness ensures enterprise competitiveness. Manual scheduling causes numerous problems because of limited resources, Typically, orders that have the earliest delivery deadline are prioritized in the production process; this allows 356

promote shipping, but ignores product losses caused by switching processes or replacing molds (retooling). By contrast, prioritizing orders by process type may cause delays in delivery. Thus, optimizing the allocation of limited resources is a typical problem of FJS scheduling. In this study, an optimization method is proposed to trade-off the delivery date and reduce losses caused by switching processes, using a GA and a multi-objectiveulti-objective design, and optimizing FJS scheduling. In traditional optimization management, a single optimization target is set; however, this does not represents real-life situations, which often require two or more goals to meet the various requirements. This is called multi-objective problem, for example, a problem that combines performance and price optimization. Therefore, multi-objective, multi-attribute or so-called multi-criteria optimization methodologies have been proposed to balance numerous goals. Implementing multi-objective optimization decisions is a challenge, because balancing the weight of multiple objectives is difficult;

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VOLUME 2, 2014

T.-K. Liu et al.: Developing a Multiobjective Optimization Scheduling System

various methods have been proposed to attain this goal, such as the 1) weighting method [7], 2) priority method [10], 3) fuzzy goal programming method [3], and 4) Pareto optimal solution method [6], this study was based on the concept of Pareto optimal solutions which trade-off different goals is suitable to the needs of case study manufacturer, minimizing delivery date and minimizing losses caused by switching processes. Pareto optimal solution has been widely used to solve problems in several manners, such as the multi-objective optimization genetic algorithm (MOGA) [12], multi-objective particle swarm optimization [2], and multi-objective differential evolution algorithms [8]. The related studies using GA based on concept of Pareto optimal solution in engineering field are introduced as follows; most of them focus on schedule problems in different domains. Murata and Ishibuchi [12] used a GA framework to search Pareto optimal solution in multi-objective problem, the weight is generated using a random number, enabling algorithm to search for the Pareto optimal solution in various directions in the solution space. An elite retention policy is used throughout the evolution process and the GAs typically updates and record each generation of evolution. An elite Preservation strategy is randomized to add chromosomes belong to the parent generations; to retain the number of outstanding chromosomes and maintain diversity, thereby preventing the optimal solution from falling into the local optimal area. Three years later, an incorporated local search procedure with MOGA to prevent spending almost all available computation time in flow-shop schedule issue was proposed in [15]. Salinas et al. [16] aimed of minimizing energy consumption cost and maximize a certain utility, developing two evolutionary algorithms to obtain the Pareto-front solutions and the ε-Pareto-front solutions. Yang and Chang [17] proposed an integrated methodology with three functional blocks, to optimize the reliability and maintenance failure costs for composite power systems, the test was carried out on the Roy Billnton test system for proving model capacity, and the results indicate this approach can handle complex systems. The multi-objective optimization method was used in decision making of imperfect preventive maintenance policy by Wang and Pham [18], the goals were maximizing the system asymptotic availability and minimizing the system cost rate for a single-unit system using the fast elitist non-dominated sorting genetic algorithm. Another novel application domain, environmental commitment of power unit, Li et al., [19] proposed an evolutionary algorithm to minimize the operation cost and to minimize the emissions from generation units, the novel non-dominated sorting genetic algorithm combined with local search algorithm was used for discovering optimal schedule. In addition, the weighted-sum lambda-iteration approach was used to resolve power dispatch problem, the results indicate outperform pure non-dominated sorting genetic algorithm. In summary above researches, the Pareto optimal solution which trade-off different goals is well suits to the needs VOLUME 2, 2014

of case study manufacturer, minimizing delivery date and minimizing losses caused by switching processes. Because of advancement of technology, the machine can handle various operations becoming increasingly common; thus, enabling traditional job-shop (JS) schedule approach in which only focus on job routing issue cannot to meet the requirements of practical. With respect to JS schedule, flexible jobs-shop (FJS) can not only handle job routing issue well, but consider machine function and selection; therefore, FJS has drawn a great attention in flow-shop environment. Since Brucker and Schile [1] proposed the concept of FJS scheduling problems, considerable concern has arisen regarding this topic. A solution to solve the FJS by using two neighborhood functions was proposed by Mastrolilli [11]. Gao et al. [4] combined a local search method with GA to solve the FJS problem. Because of the local search is favorable, the search area can be dynamically adjusted using confirmatory experiments, the empirical results indicated that the proposed method was effective. Two algorithms to solve assignments schema problems and job-shop scheduling problems, this approach is meant for searching possible initial combination, and enhances solution quality presented by Kacem et al. [9]. Wang and Chu [14] applied GAs to determine an optimal solution by dividing the chromosome into two components: job operation assignment (OA); and machine selection (MS), the same concept was employed in the current study. Noticed that previous studies mostly aim at a single objective, one study which very closes this topic is Ishibuchi and Murata [15] using a local search procedure in each solution generated by genetic operations, this algorithm can effectively handle a multi-objective optimization problem with a non-convex feasible region in the objective space from two simulation problems. An empirical study was conducted using actual orders from a famous screw manufacturer in Taiwan, yielding satisfactory results. When 80 work orders were evaluated applying the proposed Pareto optimal model decreased the total orders expired time, yielding a significant reduction of exceed 50% savings; the results of total replacement time for molds was insignificant reduction, among −1.8% to 0.9%, and machine workload yielding exceed 4.75%. This paper is organized as follows: In the first section, we introduce the motivation for methods and results of this study. In the second section, we review and discuss related studies on Pareto optimal solution. The third chapter presents the proposed MOGA method, explaining how the model was employed. In the fourth section, we discuss the results of case studies, and compare the results of the proposed and manual factory scheduling methods. The fifth section provides a conclusion and future prospects. II. SYSTEM MODELING

Flexible jobs shop scheduling problem, it is organizes the execution of jobs and machines, where jobs Ji = {J1 , J2 , . . . , Ji }, each job consists of the number of operations 357


Oi ,j = {Oi,1 , Oi,2 , . . . , Oi,j }, index i is the number of job, and index j is the order number of the operations, for each operation Oi,j there is a set of machine Mk = {M1 , M2 , . . . , Mk } can processing it, index k is the number of machine, and for each machine k has a processing set Uk = {Oi,j }, Pi,j,k is denotes processing time unit for operation j of job i on machine k is given. This problem rapidly cause the computing time and solution space to increase to unacceptable levels, because of increasing numbers of jobs and machines; therefore we proposed using the MOGAs to solve practical problems, to reduce company costs, minimized the number of total orders expired time and added the total replacement time for molds in the multi-objective optimization design.

the one is OA and the other is MS. The integer is used in the encoding method [13], [14], In contrast to previous studies, the refined real-parameter encoding operator was adapted in this study. The integer in the gene represents OA, and the decimal in the gene represents the MS. This method is advantageous because the chromosome length is not required to be doubled, thereby saving computing resources. Table 1 is an example in which a chromosome is represented as Table 2, where chromosome length is 20, thereby representing 20 operations. TABLE 2. The encoding representation of a sample chromosome.

A. CHROMOSOME REPRESENTATION

Table 1 for further illustrating the FJS model, where Oi,j represents Job i Operation j, Ti,j,k reports the processing time of Job i Operation j in machine k; O1,1 represents Job 1 Operation 1, T1,1,1 represents the processing time of Job 1 Operation 1 in Machine 1, the corresponding machine processing time is 3 time units, and operation O1,1 cannot be handled by Machines 6 and 8. TABLE 1. Time table for a sample of FJS.

B. INITIAL CHROMOSOME ENCODING

Determining the initial GA populations is critical, because it will affects the speed of convergence and the quality of the final result, a large population size requires a longer computing time than does a small size, in contrast, it has a higher probability to identify an optimal solution. We proposed a refined GA encoding method to encode chromosomes that could solve the conflicts caused by the encoding problem at the crossover step, and did not require designing a mechanism for chromosome repair. The length of a chromosome was equal to the number of genes contained therein, representing the total number of processes in an FJSP problem Chromosomes typically comprise two components: 358

Regarding the encoding of job operations, the Oij index i reports the job number and j reports the processing order of job operations, Job 1 comprises two operations, O11 and O12 , Job 3 comprises three operations, O21 , O22 and O23 , the job processing order for each operation is arranged in increasing order from left to right. Table 2 shows the third gene ‘‘1.4’’ in the chromosome, the integer is 1 and first time appears in chromosome, thus meaning Job 1 first Operation O11 , and in the same way, the Job 1 Operation 2 O12 is located in seventh gene of the chromosome. Next we discuss the decimal components of each gene, the value of decimal represents the probability of MS, each machine has the same probability of being selected and is sequentially allocated to the interval (0–1). When we determined the probability of each machine to jobs operation, then randomly generates a decimal number between 0 and 1, and subsequently assessed which probability value is allocated to which interval. The value of first gene O31 was ‘‘3.43’’; as previously discussed, the integer 3 represents the job number, indicating Job 3, and the decimal represents the probability of a machine being selected, which is similar to the meaning of the roulette law of GA, Table 1 shows that five machines are able to perform job operation O31 , M2 , M4 , M6 , M7 , M8 , respectively, which mapping to the probability intervals of [0 − 0.2), [0.2 − 0.4), [0.4 − 0.6), [0.6 − 0.8), [0.8 − 1], VOLUME 2, 2014


respectively, and 0.43 was allocated at interval [0.4 − 0.6); thus M6 was being selected (Fig. 1 and Fig. 2).

FIGURE 1. Schematic diagram of machine selection for first gene of a sample chromosome in Table 2.

FIGURE 2. Schematic diagram of first gene of a sample chromosome in Table 2 (Using proposed refined encoding operator).

TABLE 3. The molds number of Product A.

C. FITNESS FUNCTIONS

In this study, we applied the total orders expired time and total replacement time of molds as a mainly parameters of the fitness function. • The total orders expired time We retrieved the follows information from the ERP database for scheduling. When scheduling orders, we first considered 1) the feasible order start times, and 2) scheduled order completion times for the assigned machine, and 3) the relationship between these conditions. If the start date of a new order was earlier than the scheduled completion date for an assigned machine, then the new order was scheduled to the next order to be executed. Else if the start date of the new order was scheduled after the completion date for an assigned machine, then confirming whether the start date of new order fell within the plant calendar was necessary, if yes, the job could be initiated at a feasible start time, otherwise, the next available plant calendar date was determine the start date. The total orders expired time was defined as the predefined order completion date minus the order delivery deadline, and the dates were converted into hours. The formula is showed in (3.2). TTOET =

m X

where Teti represents the expired time of order i; Ci represents the predefined completion time for order i; and di represents the delivery date of order i. If the expected completed date of order i does not exceed the delivery date, then take 0. • Total replacement time for molds In screw manufacturing, replacing a mold is a timeconsuming task requiring several hours to a day, or more. The mold set is usually comprises the primary and secondary mold, punches, cutlery and other components. Replacing the primary and secondary molds is a time-consuming, but replacing only the punches or cutlery, requires relatively less time. We used a three- bit string to represent a mold (e.g., 1A0, 5PA, 2D1; Table 3 and 4) and a mold set comprising various molds. We compared the strings for two mold set to determine the difference between a current Product A and the upcoming Product B then calculated the proportion of the number of changed molds to the number of whole mold set, next respectively multiplying the time of total mold set replacement. Finally we added both replacement times, using Formula (3.3), as shown in top of the next page. Tables 3 and 4 represent mold sets for Product A and B, respectively. Assuming that Product A is currently being produced and Product B is scheduled to be product next, the total replacement time for molds was calculated as follows. The retooling (mold replacements) time for Product A was (5/27) * 7 = 1.30 hours, whereas the retooling time for Product B was

TABLE 4. The molds number of Product B.

Tet i

i=1

Teti = VOLUME 2, 2014

Teti = (Ci − di ), 0,

if Ci > di Otherwise

(3.2) 359


TTRTM =

n P i=1

Michange(x) Mioriginal(x) ∗ T(x) +

Michange(x+1) Mioriginal(x+1) ∗ T(x+1)

(3.3)

where Michange(x) represents the number of molds to be changed from the current product x for order i; Mioriginal(x) represents i represents the number of molds the number of total mold sets used to fabricate the current product x for order i; Mchange(x+1) i to be changed to fabricate the subsequent product x + 1 for order i; Moriginal(x+1) represents the number of total mold sets used to fabricate the subsequent product x + 1 for order i; T(x) represents total replacement time for molds for product x; T(x+1) represents total replacement time for molds for product x + 1.

(23/45) * 11 = 5.63 hours. If a process change is required from Product A to B, then 1.30 + 5.63 = 6.93 hours are consumed. D. SELECTION

We used a wheel mechanism to select individual and copied to the offspring, to form a new generation. The fitness values were calculated at the initialization stage Sorting based on the fitness value, each value proportionate to the size of the wheel. The high fitness values occupied a larger area than did the low fitness values, indicating an increased probability of being selected. After repeating the selection and attaining target offspring size, moved to the next stage. E. CROSSOVER

The crossover aim of this mechanism was swapping chromosomes to yield better chromosomes fitness. This contrasts with traditional methods, which require a repair action, to address operations being incorrectly assigned to inappropriate machines. In this research, we used a refined encoding operator to overcome above problem. After crossover, only the operation or processing orders are changed, thereby preventing incorrect assignments from occurring. • Machine selection (two-point crossover) Steps1: Randomly generates two crossover points; these numbers should less than the chromosome size. Steps2: Swap the head and tail within the range of two crossover points of the two chromosomes to form a new chromosome. • Job operation The POX (Precedence preserving order-based crossover) was used for the OA. F. MUTATION

Mutation increases the diversity of chromosomes, in this study; additional modifications increased the population of chromosomes. • Machine selection This process was conducted to select the minimal machine operating time; the mutation MS changes a particular gene on chromosome, through the following process: Step1: A mutation decimal and random number are generated to determine whether to mutate the MS, if the mutation rate is less than the decimal, and then proceed to Step 2. 360

Step2: Choose a machine that exhibits a minimal operating time from the mutation point in the gene that corresponds to the operation. Step3: Ensure the mutation is completed in the operating group; otherwise, return to Step1 and select a new random number to determine which machine to select. • Process assignment Two-point mutation was adapted to OA, as follows: Step1: Randomly generate two mutation points and a decimal number to determine whether the mutation occurred; if the mutation rate is less than the decimal, then proceed to Step 2. Step2: Swap the integer of the two point mutations. Step3: Ensure the mutation is completed in the operating groups; otherwise, return to Step1. • Termination conditions An optimal solution can typically be obtained for traditional scheduling problems; therefore, the termination condition can be either an optimal solution or a fixed number of iterations. In a real scheduling system, determining an optimal solution may be impossible when numerous orders exit; therefore users can choose an appropriate degree of optimization. III. PRACTICAL EXAMPLE AND RESULTS A. PROBLEMS HYPOTHESIS AND DEFINITION

The hypotheses are introduced as follows: Hypothesis 1: a job consists of at least one operation, and each job contains varying number of operations. Hypothesis 2: assigning operation to different machine will result in different processing time and sequence independent. Hypothesis 3: a machine can conduct some particular job operations, but not all. Hypothesis 4: each machine can process at most one operation at a time. Therefore, the FJS problem is a complex problem and numerous factors be considered. According to the needs of the case manufacturer, the following multi-objective optimization problem was considered in formula (4.1): Objective function = Min.(αTTOET + βTTRTM ), Subject to a ≤ TTOET ≤ b;

a, b ∈

a ≤ TTRTM ≤ b;

a, b ∈

(4.1)

where α and β are weight coefficients, TTOET is total orders expired time, xT TRTM is the t otal replacement time for molds, VOLUME 2, 2014


(formulas in 3.2 and 3.3), a and b are the feasible solution space. B. PROBLEM ANALYSIS

The case manufacturer is a medium-scale enterprise in Taiwan (http://www.anchorfast.com.tw/) that mainly produces screw and nut products. In practice, the manufacturer encountered following problems: 1) Comprehending the order delivery schedule is difficult, and delays can cause fines or increased transportation costs. 2) Human and machine dispatching cannot cooperate, resulting in increased overtime labor costs and idle machine consumption. In traditional manual scheduling, jobs are typically scheduled usually based on the delivery date priority, if a new job is added, and its delivery date is soon, it supersedes other orders, causing delay. This can require reparations, substantially increase the shipping costs when shipments must be changed from ocean to air transport, to meet the delivery schedule, or increase employee overtime costs. When jobs are manually scheduled, two similar products that may have distant date are often merged during production to conserve retooling time; this can cause other orders to be delayed, generating scheduling dilemmas for production managers. All of these problems can draw a conclusion of scheduling optimization problems, thus enhances the capability of schedule will helpful of solving above problems. C. SYSTEM ARCHITECTURE

In this study, the Microsoft Visual Studio 2010 C # programming language was employed in the production scheduling system, which comprised three core components: (1) user interfaces, (2) ERP for SYBASE database, and (3) a refined MOGA. Database consists of the SYBASE and SQLite, SYBASE database for the ERP vendor used. The system acquires order data via the ERP database, such as the machine production speed, required molds, and mold replacement times. These data are saved in the local SQLite database for calculation. SQLite is convenient and portable; thus,

FIGURE 3. Job searching display of intelligent scheduling system. VOLUME 2, 2014

intelligent scheduling can be carried out on any computer, allowing managers to simply determine whether to accept orders. In the user interface, a simple chart shows the incomplete orders among the current production orders, a job searching display (Fig. 3), and a Gantt diagram of the scheduled orders (Fig. 4). A button allows users to gather information from the ERP database, and assess the parameters settings such as the factory calendar, and optimization degree settings.

FIGURE 4. The display of Gantt diagram.

D. RESULTS AND DISCUSSION

A two-phase test was performed to evaluate the proposed model. In the first phase, the classical benchmark of distributed and FJS scheduling problem in [5] was performed, to proven the effective of our proposed model, then apply our proposed model to solve the real scheduling problems of a screw manufacturer. The results indicated that the optima makespan for a scheduling problem involving three factories, five jobs, eleven jobs operation, and eight machines was 11 time units. After five iterations, the computing time was approximately 15 seconds, and the solution (answer) is same with original study, rather rapidly, and the convergence is also very strong as shown in Fig. 5. This tested has been proven the effectiveness of the proposed model.

FIGURE 5. Convergence diagram of the sample in [5]. 361


TABLE 5. The comparison of the performance between manual scheduling and intelligent scheduling system for three of Pareto optimal solutions.

In the second phase, three indicators were used to evaluate the our model when applied to a real case, 1) total orders expired time, 2) total replacement time for molds, and 3) machine workload. The results were compared with the historical data obtained using manual scheduling. We used sets of 80 work orders from the screw manufacture to test the proposed model. After several tests, the results show a substantial improvement in the level of schedule performance. Table 5 shows a comparison of the results between manual scheduling and the proposed method when using Pareto optimal solutions. Three of Pareto frontier solutions, solutions 1, 2, and 3 to decrease total order completion time, yielding a substantial reduction (all exceed 50%, −56.6%, −58%, and −54.5%, separately), outperformed traditional manual scheduling method. Regarding total replacement time for molds, the Pareto optimal solutions performance were not insignificant, among −1.8% to 0.9% and the average machine workload were also reduced −4.75%, −5.23%, −5.3%, respectively, substantial savings were yielded, meant increases the available product capacity. A three-dimensional coordinate chart for manual scheduling results and AI scheduling results was displayed in Fig. 6, where square sign represents the projection of three- dimensional coordinate of solutions, the terms of Manual, P1, P2, P3 were represented manual scheduling results, Pareto optimal solution 1, 2, and 3, separately. It clearly indicates the results obtained from three Pareto optimal solutions were all superior to results of manual scheduling. Fig. 7 and Fig. 8 depict the Pareto frontier solutions were obtained from the results of AI scheduling, and 3-D plotting, separately. This section also presents a comparison between manual scheduling and proposed method, which is referred to as the intelligent scheduling system. Manual scheduling yields errors if input incorrect data; by contrast, the intelligent scheduling system is to acquire information through a 362

FIGURE 6. A three-dimensional coordinate chart for manual scheduling results and AI scheduling results.

FIGURE 7. Pareto frontier solutions were obtained from the results of AI scheduling system (The proposed method in this article).

database, thereby avoiding this problem. Manual scheduling often requires conferring with the site master to determine a schedule, this is time-consuming, whereas the intelligent VOLUME 2, 2014


FIGURE 8. 3-D plotting was obtained from the results of AI scheduling system (The proposed method in this article).

scheduling system provides a relatively rapid response to this problem. Regarding effectiveness, when using manual scheduling orders that have distant delivery dates are often prioritized to save retooling time, causing other orders to be delayed; by contrast, he intelligent schedule system is based on delivery dates, and optimizes retooling to attain superior results. Empirical data shows that the proposed method is robust, and outperforms traditional manual scheduling method. IV. CONCLUSION

In this study, we applied FJS and multi-objective optimization techniques using refined GA to solve a practical problem, setting minimal total order completion time and total replacement time for molds values as objectives. The proposed method achieved these goals. The validated results show that the proposed model decreased the total order completion time, total replacement time for molds, and machine workload, although the reduction of total replacement time for molds was insignificant. Decreasing the number of the work hours promotes production efficiency, facilitating increased production capacity and firm competitiveness. The proposed method in this article as a useful tool can also help managers accurately estimate order delivery and decide whether to accept contracts. In addition, an effectively encoding method has been proposed in this article to overcome problems of incorrect jobs assign and diversity problem caused by encoding method. However, in practice, this was inadequate for fulfilling the needs of the case manufacturer. Further improvements are anticipated to enhance the proposed system, and various factors such as machine sequence preference, machine maintenance times should be considered. REFERENCES [1] P. Brucker and R. Schile, ‘‘Job-shop scheduling with multi-purpose machines,’’ Computing, vol. 45, no. 4, pp. 369–375, 1990. [2] C. Coello and M. S. Lechuga, ‘‘MOPSO: A proposal for multiple objective particle swarm optimization,’’ in Proc. 2002 Congr. Evolutionary Computation, Honolulu, HI, USA, pp. 1051–1056. [3] F. Waiel, A. E. Wahed, and S. M. Lee, ‘‘Interactive fuzzy goal programming for multi-objective transportation problems,’’ J. Omega, vol. 34, no. 2, pp. 158–166, 2006. VOLUME 2, 2014

[4] J. Gao, M. Gen, L. Sun, and X. Zhao, ‘‘A hybrid of genetic algorithm and bottleneck shifting for multi-objective flexible job shop scheduling problems,’’ Comput. Ind. Eng., vol. 53, no. 1, pp. 149–162, 2007. [5] L. D. Giovanni and F. Pezzella, ‘‘An improved genetic algorithm for the distributed and flexible job-shop scheduling problem,’’ Eur. J. Oper. Res., vol. 200, no. 2, pp. 395–408, 2010. [6] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA, USA: Addison-Wesley, 1989. [7] K. Graham and F. C. Ismael, ‘‘Weighting method,’’ J. Off. Statist., vol. 19, no. 2, pp. 81–97, 2003. [8] S. Kukkonen and J. Lampinen, ‘‘An extension of generalized differential evolution for multi-objective optimization with constraints,’’ in Parallel Problem Solving From Nature (Lecture Notes in Computer Science), vol. 3242. Berlin, Germany: Springer-Verlag, Jan. 2004, pp. 752–761. [9] I. Kacem, S. Hammadi, and P. Brone, ‘‘Approach by localization and multiobjective evolutionary otimization for flexible job-shop scheduling problems,’’ IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 32, no. 1, pp. 1–13, Feb. 2002. [10] A. Lachlans, ‘‘The priority method I,’’ Math. Logic Quart., vol. 13, nos. 1–2, pp. 1–10, 1967. [11] M. Mastrolilli and L. M. Gambardella, ‘‘Effective neighborhood functions for the flexible job shop problem,’’ J. Scheduling, vol. 3, no. 1, pp. 3–20, 2000. [12] H. Ishibuchi and T. Murata, ‘‘MOGA: Multi-objective genetic algorithms,’’ in Proc. 2nd IEEE Int. Conf. Evolutionary Computation, Osaka, Japan, Dec. 1995, pp. 284–294. [13] J. F. Wang, B. Q. Du, and H. M. Ding, ‘‘A genetic algorithm for the flexible job-shop scheduling problem,’’ Adv. Res. Comput. Sci. Inform. Eng. Commun. Comput. Inform. Sci., vol. 152, pp. 332–339, Jan. 2011. [14] J. F. Wang and K. Y. Chu, ‘‘An application of genetic algorithms for the flexible job-shop scheduling problem,’’ Int. J. Adv. Comput. Technol., vol. 4, pp. 271–278, Feb. 2012. [15] H. Ishibuchi and T. Murata, ‘‘A multi-objective genetic local search algorithm and its application to flowshop scheduling,’’ IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 28, no. 3, pp. 392–403, Aug. 1998. [16] S. Salinas, M. Li, and P. Li, ‘‘Multi-objective optimal energy consumption scheduling in smart grids,’’ IEEE Trans. Smart Grid, vol. 4, no. 3, pp. 341–348, Oct. 2013. [17] F. Yang and C. S. Chang, ‘‘Optimization of maintenance schedules and extents for composite power systems using multi-objective evoluationary algorithm,’’ IET Generat. Transmiss. Distrib., vol. 3, no. 10, pp. 930–940, Oct. 2009. [18] Y. Wang and H. Pham, ‘‘A multi-objective optimization of imperfect preventive maintenance policy for dependent competing risk systems with hidden failure,’’ IEEE Trans. Rel., vol. 60, no. 4, pp. 770–781, Dec. 2011. [19] Y. F. Li, N. Pedroni, and E. Zio, ‘‘A memetic evolutionary multi-objective optimization method for environmental power unit commitment,’’ IEEE Trans. Power Syst., vol. 28, no. 3, pp. 2660–2669, Aug. 2013.

TUNG-KUAN LIU received the B.S. degree in mechanical engineering from National Akita University, Akita, Japan, in 1992, and the M.S. and Ph.D. degrees in mechanical engineering and information science from National Tohoku University, Sendai, Japan, in 1994 and 1997, respectively. He is currently a Professor with the Mechanical and Automation Engineering Department, National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan. From 1997 to 1999, he was a Senior Manager with the Institute of Information Industry, Hsinchu, Taiwan. From 1999 to 2002, he was an Assistant Professor with the Department of Marketing and Distribution Management, National Kaohsiung First University of Science and Technology. His research and teaching interests include artificial intelligence, applications of multiobjective optimization genetic algorithms, and integrated manufacturing and business systems. 363


YEH-PENG CHEN received the B.S. degree in information engineering from I-Shou University, Kaohsiung, Taiwan, in 1996, and the M.S. degrees in information management science from the National Kaohsiung First University of Science and Technology, Kaohsiung, in 2003, where he is currently pursuing the Ph.D. degree with the Institute of Engineering Science and Technology. His research interests include artificial intelligence, applications of multiobjective optimization genetic algorithms, power system, and data mining.

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JYH-HORNG CHOU (SM’04) received the B.S. and M.S. degrees in engineering science from National Cheng Kung University, Tainan, Taiwan, in 1981 and 1983, respectively, and the Ph.D. degree in mechatronic engineering from National Sun Yat-sen University, Kaohsiung, Taiwan, in 1988. He is currently a Chair Professor with the Department of Electrical Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, and a Distinguished Professor with the Institute of Electrical Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung. He has co-authored three books, and authored more than 250 refereed journal papers. He holds five patents. His research and teaching interests include intelligent systems and control, computational intelligence and methods, automation technology, robust control, and quality engineering. He was a recipient of the 2011 Distinguished Research Award at the National Science Council of Taiwan, the 2012 IEEE Outstanding Technical Achievement Award at the IEEE Tainan Section, the Research Award, the Excellent Research Award at the National Science Council of Taiwan 14 times, and the Numerous Academic Awards from various societies.

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