Using Genetic Algorithms to solve scheduling ... - Springer Link

Flex Serv Manuf J (2014) 26:408–431 DOI 10.1007/s10696-012-9143-6

Using Genetic Algorithms to solve scheduling problems on flexible manufacturing systems (FMS): a literature survey, classification and analysis Moacir Godinho Filho • Clarissa Fullin Barco Roberto Fernandes Tavares Neto

•

Published online: 21 March 2012 Springer Science+Business Media, LLC 2012

Abstract This paper reviews the literature regarding Genetic Algorithms (GAs) applied to flexible manufacturing system (FMS) scheduling. On the basis of this literature review, a classification system is proposed that encompasses 6 main dimensions: FMS type, types of resource constraints, job description, scheduling problem, measure of performance and solution approach. The literature review found 40 papers, which were classified according to these criteria. The literature was analyzed using the proposed classification system, which provides the following results regarding the application of GAs to FMS scheduling: (1) combinations of GAs and other methods were relatively important in the reviewed papers; (2) although most studies deal with complex environments concerning both the routing flexibility and the job complexity, only a minority of papers simultaneously consider the variety of possible capacity constraints on an FMS environment, including pallets and automated guided vehicles; (3) local search is rarely used; (4) makespan is the most widely used measure of performance. Keywords Scheduling Flexible manufacturing systems (FMS) Genetic Algorithms Literature review

M. Godinho Filho C. F. Barco (&) R. F. Tavares Neto Department of Industrial Engineering, Federal University of Saõ Carlos, Via Washington Luı´s, Km 235, Saõ Carlos, SP 13565-905, Brazil e-mail: [email protected] M. Godinho Filho e-mail: [email protected] R. F. Tavares Neto e-mail: [email protected]

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1 Introduction Flexible manufacturing systems (FMS) are important because they have the capacity to quickly respond to the dynamics of the market (Chan and Chan 2004). MacCarthy and Liu (1993a, b) state that FMS aim to achieve both high productive flexibility and high productivity to meet present competitive needs. FMS have been broadly studied over the last 25 years. In the last decade, they became important elements in the success of enterprises (Chan and Chan 2004). These manufacturing systems are composed of numeric control (NC) or computer numeric control (CNC) machines connected by an automated material handling system. This system configuration must be operated by an automated computer system and is responsible for the large initial investment required to implement an FMS. However, Balogun and Popplewell (1999) state that this initial investment generates a set of benefits that include lead time reduction, increased throughput, decreased inventory, and other benefits that combine to assure the economic viability of the system. An analysis of those benefits easily shows that only a few of them can be achieved without production scheduling. Morton and Pentico (1993) state that scheduling is the process of organizing, assigning and temporizing available resources to fulfill a set of activities required to process a set of jobs. Scheduling must consider a set of constraints and one or multiple objectives. A large number of studies have devoted attention to the roles of the activities performed during production planning and control. The first approaches to scheduling problems included optimal methods and problem-specific heuristics and were restricted to manufacturing environments with limited complexity. Classical algorithms are inadequate to treating FMS environments, as they respect a set of premises derived from less complex problems. Thus, implementing an FMS requires the development of specific methods that consider all of the assumptions and constraints describing the system. Of the proposed set of solution methods, artificial intelligence techniques (e.g., Specialist Systems, Genetic Algorithms, Neural Networks) have proven to be adequate strategies. Genetic Algorithms (GAs) were proposed by John H (1975). Holland in 1975 and can be understood as a process for optimizing complex functions based on the mechanisms of genetics and natural evolution. According to Goldberg (1989), GAs can be adapted to treat the complexity levels required to provide adaptive search at the required robustness. Ponnambalam et al. (2001) state that GAs are the most popular type of evolutionary algorithms. The good results provided by this class of algorithms have led many researchers to use it to solve scheduling problems, including those in FMS environments. The main objective of this paper is to perform a bibliographic review, classification and analysis of the application of GAs to solving scheduling problems in FMS. The first step was to search the Compendex, Science direct and Google Scholar databases. Then, a classification scheme for the resulting papers found in step 1 was proposed. This classification scheme encompasses six criteria. In a third phase, the papers were read and classified. Finally, the results were analyzed. This paper is structured as follows: Sect. 2 presents the required concepts used in this paper, and Sect. 3 describes the proposed classification scheme. Section 4

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presents the bibliographic survey, structured according to the presented classification scheme. Section 5 contains a general analysis of the reviewed papers’ themes. Section 6 presents the final conclusions and suggestions for future works.

2 An overview of the concepts used in this paper The specialized literature contains several definitions of the term ‘‘FMS’’ (e.g., see Kaltwasser et al. (1986), Byrkett et al. (1988), O’ Keefe and Kasirajan (1992), and others). MacCarthy and Liu (1993a, b) believed that an FMS must be classified according to its operational and control characteristics and proposed that an FMS is a production system composed of some CNC and/or NC machines connected by a material handling system, is capable of producing a set of products with some degree of variability and is operated by an automated computer-controlled system. MacCarthy and Liu (1993a b) state that an FMS is composed of three subsystems: (1) a processing system composed of a set of CNC machines with automatic toolchanging capabilities; (2) a material handling and storage system composed of robots, AGVs (Automated Guided Vehicles) and other systems that allow flexibility in the movement of the processing material; (3) a computer control system that automatically operates the system. According to Balogun and Popplewell (1999), an FMS contains a large number of variables and constraints that change over time, and these characteristics justify the use of dynamic scheduling algorithms. Balogun and Popplewell (1999) note six approaches to solving scheduling problems in FMS: (a) combinatory optimization methods; (b) artificial intelligence; (c) simulation; (d) heuristics; (e) multi-criteria decision making; (f) hybrid solutions. The field of Artificial Intelligence provides other methods including specialist systems, Genetic Algorithms, and Neural Networks. This paper focuses on Genetic Algorithms. According to Haupt and Haupt (1998), a GA is a process to optimize highly complex functions utilizing the mechanisms of natural evolution and genetics. Goldberg (1989) stated that a GA is a stochastic search technique that is based on selection and evolution. Carvalho et al. (2003) define GAs as evolutionary programs that are based on natural selection and heredity theories. These definitions all include the idea that in a given population, individuals with beneficial genetic characteristics have better chances of survival, which promotes the reproduction of the fittest individuals and the extinction of the least fit. When Genetic Algorithms are applied to problems, each individual, or chromosome, represents a viable solution to the problem. The algorithm, according to Zhou et al. (2001), identifies the best solutions and combines them to generate new individuals and renew the population. Carvalho et al. (2003) explain the behavior of GAs as follows: initially, a population of individuals (a set of viable solutions to the problem) is generated. During the evolutionary process, this population is evaluated, and the fitness of each individual is calculated and stored. A subset of the individuals with the highest fitness scores is saved, and more individuals are generated using mutation and crossover operations.

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3 The proposed classification system and the bibliographic survey The system for classifying the literature surrounding the application of Genetic Algorithms to scheduling problems is proposed and presented in this section. The system is based on six criteria: (A) type of fms; (B) type of resources and capacity constraints; (C) job characteristics; (D) scheduling problem approached; (E) measure of performance; (F) utilized approach. The first criterion, Type of FMS, is based on the results found by Maccarthy and Liu (1993a) and classifies the FMS environment into five subtypes: • • •

•

•

SFM (single flexible machine): a single production unit composed of a CNC with tool-changing capabilities and a material handling and storage system; FMC (flexible manufacturing cell): an FMS environment composed of a group of SFMs sharing a single material handling system; MMFMS (multi-machine flexible manufacturing system): contains some SFMs connected by an automatic material handling system composed of two or more material handling sub-systems, allowing it to serve two or more machines simultaneously; MCFMS (multi-cell flexible manufacturing system): an FMS composed of several FMCs and possibly SFMs, all connected by an automatic material handling system. Not available: environments in which the number of machines, system characteristics and/or physical configuration were not specified.

The second criterion refers to the types of resources and constraints on the system. This criterion is based on the work of MacCarthy and Liu (1996), which identifies resource types using the following notation: machines (M), storage buffers (SB), material handling devices (HD), tool-changing devices (TD), fixtures (FX) and pallets (PL). The quantity of each kind of resources limits the system capacity. In this paper these constraints are represented by the notation: lim: resource (quantity of this resource). For example, if a scenario has five machines and only one material handling device system, the second criterion for this environment will be denoted by: lim: M (5); HD (10). It’s important to note that constrains of a system justify the scheduling requirement. According to MacCarthy and Liu (1996), if the capacity of a specific resource is unlimited, then it does not represent a constraint on the studied scheduling problem. The third criterion is also based on the work of MacCarthy and Liu (1996) and classifies the jobs according to complexity. The measure of complexity is based on the number of operations in each job. Two options are possible: • •

JC1 (job complexity = 1): each job contains just one operation; JC? (job complexity [1): some or all jobs contain two or more operations;

The third criterion also classifies the jobs according to routing flexibility, which can assume two values: • •

RF1: there is only one machine enabled to perform a single operation; RF ? : there are two or more machines allowed to perform one or more operations.

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The fourth criterion considers the scheduling problem that the paper focuses on. Because the scheduling literature contains numerous methods for classifying scheduling problems, this paper adopts some aspects of the nomenclature used by Chan and Chan (2004) and by Balogun and Popplewell (1999). Then, in this paper scheduling problems are classifies as follows: (1) (2) (3) (4) (5)

sequencing problem for jobs and operations; positioning and routing problems for the AGVs; loading problem (allocation of operations and tools required for a machine to perform an operation); routing problem (routes used by each job in the FMS); others.

It is important to note that this research analyzed papers that treated sequencing problems in FMS environments, which explains why all of the reviewed papers contain sequencing problems in their scope. The fifth criterion is the measure of performance used in the paper. The present literature review admits that these measures can contain one (mono-criterion) or more criteria (multi-criteria). Following some classical references such as Sipper and Bulfin (1997) and the bibliographic review itself, Table 1 contains all of the criteria used in this paper. Finally, the sixth criterion used in the proposed classification system is the approach used in the paper to solve the FMS scheduling problem. Table 2 presents the approaches found in the reviewed papers. Some authors used only one approach to solving the problem (denoted in this paper by ‘‘pure’’), while others considered hybrid techniques combining two or more approaches (denoted in this paper by ‘‘hybrid’’). Table 1 Criteria and the codification used in this paper

Criteria

Code

Idle time

T idle

Length of the AGVs route

Route length

Number of backtrackings of each AGV

Backtrackings

Total flowtime

F

Mean flow time Makespan

F medium Lma´x Cma´x

Tardiness

T

Maximum tardiness

Tma´x

Maximum lateness

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Due date

Dd

Cost for tardiness and earliness; production cost, penalty cost

Cost

Throughput

T

Work in process

WIP

Machine utilization

U

Maximum utilization of the machines

Uma´x


413

Table 2 Approaches found in the reviewed papers Approach

Description

Genetic Algorithm (GA)

GAs are methods for moving from one population of ‘‘chromosomes’’ (candidate solutions to a problem) to a new population by using a kind of ‘‘natural selection’’ together with the genetically inspired operators of crossover, mutation, and inversion (Mitchell 1998)

Particle swarm optimization (PSO)

PSO is aimed at producing computational intelligence by exploiting simple analogs of social interaction. Problem-solving is a populationwide phenomenon that emerges from the individual behaviors and interactions of particles. Populations are organized according to some sort of communication structure or topology, often thought of as a social network (Poli et al. 2007)

Ant colony optimization (ACO)

ACO is a meta-heuristic approach inspired by the pheromone trail and following behavior of real ants, who use pheromones as a communication medium. The pheromone trails in ACO serve as numerical information that the ants use to probabilistically construct solutions to the problem (Dorigo and Stu¨tzle 2003)

Simulated Annealing (SA)

SA is a stochastic computational technique evolved from statistical mechanics for discovering near-global-minimum-cost solutions to large optimization problems (Kamboj and Sengupta 2009)

Tabu search (TS)

Tabu Search is a meta-heuristic created to tackle large, hard combinatorial optimization problems. It is based on the principle that intelligent search must embrace more efficient and systematic forms of direction, such as memorizing and learning (Kamboj and Sengupta 2009)

Memetic algorithms (MAs)

Memetic algorithms (MAs) are search strategies that use a populationbased approach in which a set of cooperating and competing agents are engaged in periods of individual improvement to the solution while sporadically interacting. MAs denote a family of metaheuristics whose central theme is hybridization and are intrinsically concerned with exploiting all available knowledge about the problem under study (Moscato and Cotta 2003)

Simulation/Petri Nets

Petri Nets allow for the modeling of states, events, conditions, synchronization, parallelism, choice, and iteration and descriptions of real processes that tend to be complex and extremely large

Fuzzy

A fuzzy set is a class of objects with a continuum of membership grades. Such a set is characterized by a membership function that assigns each object a membership grade ranging between zero and one. Fuzzy Logic provides a natural way of dealing with these sets (Zadeh 1965)

Priority rules/dispatching rules

Priority rules are rules used to schedule operations and jobs. The basic idea is to choose the job with the highest priority according to the rule if there is more than one job waiting to be processed by the same machine (Sipper and Bulfin 1997)

Earliest due date (EDD) First come, first served (FCFS) Shortest processing time (SPT) Critical ratio (CR) Neural Networks

A neural network is a massively parallel, distributed processor that has a natural propensity for storing experimental knowledge and making it available for use. Neural Networks resemble the brain in that knowledge is acquired through a learning process and interneuron connection strengths, known as synaptic weights, are used to store the knowledge (Aleksander and Morton 1990)

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Table 2 continued Approach

Description

Deterministic dynamic programming (DDP)

Programming used to solve optimization problems. The main feature of DDP is the decomposition of the original problem into a sequence of smaller and simpler problems (Arenales et al. 2007)

Other heuristics

Heuristics or heuristic algorithms are techniques that often quickly provide a good solution, but not necessarily the optimal solution, i.e., the best solution (Fernandes and Godinho Filho 2010)

Note that, according to the scope of the present work, all of the reviewed papers use the GA technique. This criterion is still useful to differentiate the studies that use only GAs from the ones that combine GAs with other AI techniques. Table 3 presents the 40 reviewed papers classified according to the six proposed criteria.

4 Structuring the literature review using the proposed method This section presents the structure of the review of literature pertaining to Genetic Algorithms applied to FMS scheduling. This structure is based on two of the classification criteria proposed in the previous section: the scheduling problem and the work-focused measure of performance utilized by the authors. Thus, the sections below treat two classes of papers: papers that addressed only the sequencing problem and articles that addressed problems beyond sequencing, which may include the allocation and AGV routing problems, the loading problem, or others. Within these two classes, the 40 papers were sub-classified according to the number of measures of performance used (single-criterion or multi-criteria). 4.1 Papers that address only the sequencing problem In this section, we present the work that addressed the sequence of operations as a single scheduling problem. Of the 40 studies in this literature review, 32 belong to this category. Of the 32 papers presented in this section, 19 used only one measure of performance (single-criterion), and the remaining 13 are classified as multicriteria. 4.1.1 Papers that use only one measure of performance (single-criterion) Jawahar et al. (1998a) propose knowledge-based scheduling schemes (Work cell attribute-oriented dynamic schedulers ‘‘WCAODSs’’) to control the flow of parts in real-time for FMS in which the part-mix varies continually with the planning horizon. The work uses Genetic Algorithms to schedule an FMS with 10–20 machines to minimize the makespan. A comparison made with a GA-based scheduling methodology shows that the proposed approach provides solutions nearer to the optimum.

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Lim:M(5); HD(1)

Lim: M(6); HD(2)

Not available

Not available

Not available

MMFMS

MCFMS

MMFM

FMC

Holsapple et al. (1993)

Rabelo et al. (1994)

Fujimoto et al. (1995)

Chiu and Fu (1997)

Erkmen et al. (1997)

Ulusoy et al. (1997)

Jawahar et al. (1998a)

FMC

FMC

Keung et al. (2003)

MCFMS

Sankar et al. (2003)

Haq et al. (2003)

Not available

Hsu et al. (2002)

Lim: M(3)

Not available

Not available

Yang (2001)

Reyes et al. (2001)

FMC

Not available

Keung et al. (2001)

Saitou et al. (2002)

Lim:M(5)

FMC

Rossi and Dini (2000)

Lim: M(5); HD(1)

Lim: M(3); HD(1)

Lim: M(9); HD(1)

Lim: M(16) HD(11)

Lim: M(6)

Lim: M(10)

Lim: M(4)

Lim: M(4)

Lim: M(2); HD(1)

Lim: M(16); HD(1); B(16)

Lim: M(2–10); HD(1)

MCFMS

FMC

Chung et al. (1998)

Jawahar et al. (1998b)

Lim:M(3); HD (1)

Lim:M(5); HD(1)

Lim: M(3); HD(3)

Lim:M(6)

Not available

Lim: M(3)

Lim: M(5); HD (1); SB (1)

FMC

Rabelo et al. (1993)

Criterion B

Criterion A

Author/publication year

Table 3 Classification and coding of the studied papers

JC1; RF?

JC? ; RF?

JC? ; RF?

JC1; RF?

i, iii

i, ii

i

i

i i

JC? ; RF?

i

i

i

i

i

i

i, ii

i

i

i

i

i

i

Criterion D

JC? ; RF1

JC? ; RF?

Not available

JC? ; RF?

JC? ; RF?

JC? ; RF1

JC? ; RF?

JC? ; RF?

JC? ; RF1

JC? ; RF?

Not available

Not available

JC? ; RF?

JC1; RF1

Criterion C

Multi (costs)

Multi (Cma´x; route length; backtrackings)

GA

hybrid (GA_heuristic) and hybrid (SA_ heuristic)

GA

GA

Hybrid (PN_GA_dispatching rules)

WIP Multi (Cma´x; T idle)

Hybrid (PN_GA)

Cma´x Multi (Cma´x; cost)

GA

GA

Cma´x

Hybrid (GA_DDP)

Hybrid (PN_GA) GA

Multi (Cma´x; Dd; Umax) Cma´x

Multi (costs) Cma´x

Hybrid (GA_dispatching rules_ RN)

GA

Hybrid(Fuzzy_GA)

Hybrid(PN_GA)

Cma´x

Due date Cma´x

Hybrid (PN_simulation_GA) Hybrid (GA_simulation)

Hybrid (GA_heuristic)

Cma´x Multi (Cma´x; F medium) Cma´x

Hybrid (RN_GA)

Multi (F medium; Tma´x)

WIP

Criterion F

Criterion E

Using Genetic Algorithms 415

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MCFMS

MMFMS

Not available

Jerald et al. (2006)

Reddy and Rao (2006)

Kim et al. (2007a)

Not available

Not available

Chan et al. (2005)

Chan et al. (2006b)

MCFMS

Jerald et al. (2005)

MCFMS

FMC

Sankar et al. (2004b)

Not available

Not available

Nearchou (2004)

Sankar et al. (2005)

MCFMS

Sankar et al. (2004a)

Chan et al. (2006a)

Not available

FMC

Chiang and Fu (2004)

Not available

Honghong and Zhiming (2003)

Gang and Wu (2004)

Criterion A


Table 3 continued

Lim: M(5)

Lim: M(6); HD(2)

Lim: M(16); HD(11)

Lim: M(30)

Lim: M(15)

Lim: M(3)

Lim: M(30)

Lim: M(15)

Lim: M(3)

Lim: M(16);HD(2)

Lim: M(33)

Lim: M(3)

Lim: M(16); HD(11)

Lim:M(15); HD(11)

Lim: M(8); HD(11)

Lim: M(4); HD(1)

Lim:M(20)

Lim: M(10)

Lim:M(5)

Lim: M(16); HD (2)

Lim: M(3); B(1)

Lim: M(20)

Lim: M(33); M(6)

Criterion B

JC?; RF?

JC?; RF1

JC?; RF1

JC?; RF?

i

i;ii

i, ii

i

i i

JC?; RF1

i

JC?; RF?

JC?; RF?

i; ii, iv i

JC?; RF1

i

JC?; RF1

JC?; RF1

i

i

i

i

Criterion D

JC?;RF1

JC?; RF1

JC?; RF?

JC?; RF?

Criterion C

Multi (cost; T idle) Multi (Cma´x; F medium; T) Multi (Cma´x, F)

Cma´x

Multi (U; T) Cma´x

Cma´x

Multi (costs; T idle)

Cma´x

Multi (cost; T idle) Cma´x

GA


GA

GA

GA

GA

GA

GA, SA, MA, PSO

Hybrid (GA_Simulation)

Hybrid (GA_SA)

GA

Hybrid (PN_GA)


GA

Multi (cost; Cma´x) Due date Cma´x

Criterion F

Criterion E

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Criterion A

FMC

Not available

Not available

Not available

Not available

FMC

Not available


Tu¨rkcan et al. (2007)

Kim et al. (2007b)

Chan et al. (2008)

Hsu et al. (2008)

Choudhury et al. (2009)

Taghavifard et al. (2009)

MohammadPour et al. (2010)

Table 3 continued

Lim: M(4)

Lim: M(2); HD(1)

Lim: M(4)

Lim: M(6)

Lim:M(10)

Lim:M(33)

Lim:M(3)

Lim: M(10)

Lim:M(2);HD(3)

Criterion B

JC?; RF?

JC?; RF?

JC?; RF?

i

i, iii

i

i

i

JC?; RF?

JC?; RF1

i

i, iii

Criterion D

JC?; RF?

JC?; RF?

Criterion C

Hybrid (PN_GA)

Cma´x

GA and SA Hybrid (dispatching rules_GA)

Multi (costs; U) Cma´x

GA

GA

Multi(Cma´x; T)

WIP

GA


Criterion F

Multi (cost, T) Cma´x

Criterion E

Using Genetic Algorithms 417

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Rossi and Dini (2000) also used a pure approach but focused on solving the problem of dynamic scheduling in FMS. The proposed technique is based on optimizing the genetic complexity and reducing the time required to generate a new schedule. This Real-Time Genetic Algorithm (REGAL) is applied to an FMS with 16 machines and 1 material handling device to obtain the sequencing of parts resulting in the lowest makespan. The results are compared with other techniques, such as the rule-oriented algorithm (ROA) and the Generic Genetic Algorithm (GGA), and the proposed method produced the best result. Hsu et al. (2002) propose a pure GA approach to solve the problem of cyclical scheduling in FMS environments. The authors validate the algorithm by applying it to a flexible manufacturing system with 6 machines to achieve the optimal production speed while minimizing the work in process (WIP). The algorithm proposed by Hsu et al. (2002) was validated on 5 FMS cyclic scheduling problem tests. Chan et al. (2005), Chan et al. (2006a) and Chan et al. (2006b) presented a work sequence using a GA that incorporates the Dominant Genes technique. In Chan et al. (2005), a Genetic Algorithm with Dominant Genes (GADG) is proposed to deal with FMS problems with alternative production routing in two FMS environments: one with 3 machines and one with 33 machines. The objective was to minimize the makespan. The results were compared with other techniques such as Ant Colony Optimization (ACO) and Petri Nets (PNs). The proposed algorithm (GADG) exhibited better performance in the analyzed scenarios. Chan et al. (2006a) use the same approach (GADG) to deal with distributed FMS scheduling problems subject to machine maintenance constraints. In the two scenarios studied (one with one factory and another with two factories), the results of the GADG approach were compared with results from other approaches such as PNs, ACO and a simple Genetic Algorithm. The proposed approach presented the lowest makespan in the two considered environments. In Chan et al. (2006a), the same approach is applied to an environment with four plants containing three machines each and again aims to minimize the makespan. The authors highlight that the idea of dominant genes is to identify and record the critical genes in the chromosome to enhance the performance of the genetic search. The GADG results again exhibit better performance than other approaches such as SGA, Petri Nets and ACO. Kim et al. (2007b) use the ASMEA (symbiotic evolutionary asymmetric multileveled algorithm) to solve the scheduling problem in an FMS. The algorithm was applied to minimize the makespan in an FMS with 10 machines, and four types of flexibility were considered: machines, tools, process and sequencing flexibilities. The results were compared with other approaches: HEA (hierarchical evolutionary algorithm), TEA (traditional evolutionary algorithm) and SEA (Symbiotic Evolutionary Algorithm). The solution quality and the speed of convergence demonstrate the superiority of the proposed algorithm (ASMEA). The most recent work in this category is the work of Hsu et al. (2008), who, like Hsu et al. (2002) address the problem of sequencing cyclic tasks (the cyclic scheduling problem) and aim to reduce the Work In Process (WIP). After modeling the problem using Petri Nets, the authors use a GA to obtaining the sequence of tasks for a flexible manufacturing cell. The authors conclude that in 75 % of cases,

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the performance achieved by the proposed algorithm was equivalent to the best heuristics in the literature. Among the reviewed papers that only address the sequencing problem with only one measure of performance are some that used a hybrid approach. Unlike the work presented above, the following works use Genetic Algorithms combined with another approach. Holsapple et al. (1993), for example, propose a hybrid approach to solve the problem of static scheduling of an FMS with 3 machines. In addition to a GA, the authors use the problem-knowledge processing (PPK) heuristic. The benefits of this hybrid approach are seen in several tests aimed at reducing the makespan. The proposed method exhibited good performance and also demonstrated the importance of addressing the more complex problem of simultaneously satisfying multiple scheduling criteria. Rabelo et al. (1994) use a hybrid architecture that utilizes Neural Networks, Simulation, Genetic Algorithms and induction mechanisms to solve the problem of sequencing operations in an FMS. The results (in terms of WIP) of the proposed approach are compared against those from using a single dispatching rule at all times (a technique currently used in industry). Three other studies (Chiu and Fu (1997), Reyes et al. (2001), and Gang and Wu (2004)) use a hybrid approach combining Genetic Algorithms with Petri Nets. Chiu and Fu (1997) first develop a Petri-net model of an FMS composed of two submodels: a transportation model and a process-flow model. An embedded GA search method is applied on the basis of the full PNs model. The studied environment consists of 3 machines and 3 material handling devices. The evaluated measure of performance is the makespan. The authors conclude that the makespan obtained with this hybrid approach demonstrate that it is a good alternative to other techniques within this class of problems. Reyes et al. (2001) propose a hybrid FMS scheduling methodology that combines Petri Nets and GA techniques. Experiments on a three-machine FMS were presented to illustrate the degree of effectiveness of the proposed scheme. The operation sequencing seeks to provide the lowest makespan. The performance of the proposed method compared favorably with other concurrent work integrating PNs and heuristic search techniques. The authors suggest that further research into incorporating GA operators (crossover and mutation) into the method is required. Gang and Wu (2004) use such a hybrid approach (GA and PN) to solve sequencing problems in an FMS with three machines. To demonstrate the effectiveness of the proposed method, the authors present several examples in which they consider different buffer allocations and the corresponding makespans obtained with such allocations. Erkmen et al. (1997) also use a hybrid approach, but they combine Fuzzy Logic with Genetic Algorithms to solve FMS sequencing problems. Aiming to optimize due dates, the method is applied in an environment containing multiple cells with 5 numerical control machines and a material handling device. They consider a number of factors including machine availability and process time. The FMS sequencing problem is also addressed by Jawahar et al. (1998a), who approach a general shop scheduling and rescheduling problem with alternative route choices in an FMS environment. Their GA-based heuristic uses priority dispatching

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rules and is applied in a 5-machine scenario and in a three-machine scenario, both with a material handling system. The comparison in terms of makespan and computational time indicates that the GA-based heuristic search process is suitable for FMS scheduling problems. Also using makespan as the only performance measure, Yang (2001) proposes the use of a DDP-GA hybrid approach that uses Genetic Algorithms and discrete dynamic programming to solve sequencing problems in flexible manufacturing systems. The proposed approach is applied in an FMS with 5 machines to generate a sequence that results in the smallest makespan. The results from their research support the strategy of combining traditional algorithmic procedures with heuristics or adaptive search techniques to develop hybrid FMS scheduling approaches. Chiang and Fu (2004), in turn, address the sequencing problem in FMS and propose two hybrid approaches based on the critical ratio rule. The problem is divided into two sub-problems: job sequencing, for which the authors propose the ECR (enhanced critical ratio) rule, and dispatching, for which the MCR (minimum critical ratio) rule is proposed. The objective concerned is maximizing the meetdue-date rate. The results show that the rules perform well, and the simplicity of the rule ensures good user acceptance according to the authors. Finally, to improve the performance of the ECR solution, the authors apply a Genetic Algorithm called the TCGA (time-constrained Genetic Algorithm), which was able to reduce the computational time required by the proposed approach. The hybrid method proposed by Nearchou (2004) is used to solve sequencing problems in flow shop environments. This approach involves using Genetic Algorithms and Simulated Annealing and is applied to minimize the makespan in environments with 5, 10 and 20 machines. The solutions are of comparable quality to those produced by the best algorithms available in the heuristics literature. The authors conclude that hybridizing Simulated Annealing Algorithms with features from both global and local search techniques results in a robust optimization tool capable of producing high-quality solutions to flow shop scheduling problems. The final reviewed study that uses a hybrid approach to solving the sequencing problem considering only one measure of performance is the work of MohammadPour et al. (2010). The authors propose a hybrid method that uses Petri Nets, Genetic Algorithms and Tabu Search to solve the addressed problem. The algorithm is applied to minimize the makespan of a flexible manufacturing system with 4 machines. The performance of the proposed algorithm is compared with two other approaches (TPN and PN-GA-GA) and exhibits a higher measure of performance than the others. However, MohammadPour et al. (2010) observed that the proposed algorithm requires a longer computational time than the other two approaches because of the use of Tabu Search as the local search technique. 4.1.2 Papers that used more than one measure of performance (multi-criteria) Among the studies that use more than one performance measure, the following works use only Genetic Algorithms: Keung et al. (2001), Sankar et al. (2003), Sankar et al. (2004b), Sankar et al. (2005), Honghong and Zhiming (2003), Kim et al. (2007a) and Chan et al. (2008).

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Keung et al. (2001) use a genetic algorithm to solve sequencing problems from the perspective of ETPSP (earliness/tardiness production scheduling and planning). This method is applied to a flexible manufacturing cell with two numerical control machines and one material handling device. The results using the chosen objective function (minimizing the penalty cost) were compared with those from other two methods in the literature. The authors conclude that using the GA provides a lower cost penalty than the other two mentioned approaches. Sankar et al. (2003) propose a mechanism to perform the scheduling for an FMS based on Genetic Algorithms with two different GA coding schemes, namely, Pheno style codification and Binary codification. The scheme is applied on one FMS with 16 machines, 9 robots and 2 AGVs, and the makespan and idle time are used as the performance measures. The results from this combined objective function are compared with results obtained by some dispatching rules (EDD, HP, SPT, among others), and the proposed approach (GA) is shown to be superior. Honghong and Zhiming (2003) propose an FMS rescheduling system using an Adaptive Genetic Algorithm (AGA) and consider an environment with realistic interruptions and the constraint of a time-restricted response to rescheduling. The proposed rescheduling system is based on records from a dynamic database (DDB) and is tested on two scenarios: one with 33 machines and another with 6 machines. In these two tests, the performance measures are the weighted quadratic tardiness and makespan, respectively. The results obtained by applying the proposed AGA are compared with those obtained using a Simple Genetic Algorithm (SGA). The proposed Adaptive Genetic Algorithm exhibits better scheduling performance in less computational time than the SGA approach. Sankar et al. (2004a) propose using the Niched Pareto Genetic Algorithm (NPGA) to generate schedules for an FMS with multiple cells, a total of 16 CNC machines and 2 material handling devices, with the goal of obtaining an operation sequence that enables both lower cost and fewer idle machines. The results are compared with other approaches such as Tabu Search (TS), Simulated Annealing (SA) and dispatching rules. The results show that the proposed approach has a better performance than the other analyzed techniques. Sankar et al. (2005) use an algorithm called the multi-evolutionary algorithm (MOEA) that generates a near-optimal schedule by simultaneously achieving two contradictory objectives of a flexible manufacturing system. The approach is applied to a flexible manufacturing system with 16 machines, two material handling devices and two robots, with the objectives of maximizing machine utilization and minimizing tardiness. The authors conclude that the heterogeneous population concept introduced in the work allows MOEA to achieve genetic diversity more effectively than the traditional methods. Kim et al. (2007a) propose a multi-objective Genetic Algorithm (moGA) to solve a multistage job processing schedule problem in an FMS environment. The feasibility of the method is demonstrated through experimental results and a comparison with other approaches (shortest average processing time- SAP; discrete dynamic programming-DDP; GA-based discrete dynamic programming GADDP; and GA without local search). In the analyzed environment, which contains 5 machines, a multi-objective function compares the makespan and total flow time of

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solutions for all of the approaches. The conclusion is that the proposed moGA is more efficient and more flexible in locating the Pareto solution than the competing algorithms. Finally Chan et al. (2008) propose using a Genetic Algorithm with Dominant Genes (GADG) to solve sequencing problems in flexible manufacturing systems with alternative production routing. The authors test the performance of the proposed approach in three situations. In Example 1, the GADG is applied to an FMS with three machines with the goal of finding the sequence with the smallest makespan. The results are compared with those of Petri Nets and ant colony optimization. In the second example, the environment has 33 machines, and the objective is a sequence that achieves the lowest tardiness. In this case, the examples are compared with Lagrangian Relaxation, a Simple Genetic Algorithm (SGA) and an Adaptive Genetic Algorithm (AGA). Finally, for an FMS with 10 machines, the GADG performance is compared with that of an SGA to obtain a schedule with the lowest makespan. The authors conclude that the results obtained with the algorithm in each of the three examples are superior to those of the other approaches. Two works propose more than one approach to solving the problem of multicriteria sequencing. Although they are still pure GA approaches, Jerald et al. (2005) and Choudhury et al. (2009) propose different approaches and compare them in efforts to evaluate the performance of the proposed techniques. Jerald et al. (2005) develop optimization procedures on the basis of four different approaches: Genetic Algorithms, Simulated Annealing, memetic algorithms and particle swarm optimization. These approaches are implemented to solve the schedule optimization problem of three FMS (with 8, 15 and 16 machines), and the utilized measure of performance combines the total penalty cost and the machine idleness. In a comparison of the obtained results, particle swarm optimization proved to be superior to the other examined approaches and achieved the minimum combined objective function. Choudhury et al. (2009) address the sequencing problem in Flexible manufacturing systems through the use of Genetic Algorithms and Simulated Annealing to optimize a multi-criteria objective function. The authors apply the proposed approaches to an FMS with 4 machines to simultaneously minimize the penalty costs and maximize the machine utilization. The results show that GA scores better than SA in dealing with FMS scheduling under constrained conditions. The GA performs better because the GA is more capable than the SA at treating the complexity of the problem. Four papers were found that use hybrid approaches to solve sequencing problems using multiple performance measures. Fujimoto et al. (1995) propose a hybrid intelligent approach to a production scheduling problem in Flexible Manufacturing Systems. The authors evaluate the performance of the approach through two examples in which performance measures including the makespan and mean flow time are evaluated. The authors conclude that the proposed approach efficiently seeks the best combination of dispatching rules to obtain an appropriate production schedule given specific performance measures. Rabelo et al. (1993) propose a scheme for scheduling FMSs that integrates Neural Networks, parallel Monte-Carlo simulation, Genetic Algorithms and machine learning. To evaluate the method, the authors apply it to sequencing a

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flexible manufacturing cell with 5 machines and 1 material handling device. The mean flow time and maximum tardiness are used as performance measures. Chung et al. (1998), in turn, propose a systematic Petri Net model of an FMS that supports the use of an adaptive scheduling method incorporating Genetic Algorithm search to solve the sequencing problems. The authors apply this technique to an FMS with 5 machines and analyze 3 performance measures: makespan, due date and machine utilization. According to the authors, the proposed method not only generates an efficient schedule but also allows the user to set different priorities among the jobs. Saitou et al. (2002) also use Petri Nets with Genetic Algorithms, but they use them with dispatching rules. The authors present a Genetic Algorithm coupled to a specific dispatching rule (the shortest imminent operation time—SIO), which is used to simultaneously find the near-optimal resource allocation and the eventdriven schedule of a Colored Petri Net. This mechanism is formulated as a multiobjective optimization problem that aims to minimize the production costs and the reconfiguration costs due to changes in the production plan. To evaluate the method’s performance, the authors apply it to three different scenarios containing from 4 to 10 machines. The results demonstrate the satisfactory performance of the method as well as its ability to obtain a large number of feasible solutions to sequencing problems. 4.2 Articles that discuss sequencing problems along with other scheduling problems Eight papers were found that use Genetic Algorithms to solve more than one scheduling problem in flexible manufacturing systems. In addition to sequencing problems, these works also addressed AGV routing, allocation and loading. In the next section, this class of work is summarized and subdivided into single-criterion and multi-criteria techniques. 4.2.1 Papers that used only one measure of performance (single-criterion) Three papers address problems beyond the scheduling problem using only one performance measure. All of these works use makespan as the performance measure. Ulusoy et al. (1997) apply Genetic Algorithms to the problem of simultaneous scheduling of machines and a number of identical automated guided vehicles (AGVs) in a flexible manufacturing system (FMS). The authors analyzed the performance of the algorithm by applying it to three different layouts, all with six workstations and two AGVs. The resulting performance measures (makespan) were satisfactory, allowing the authors to conclude that the proposed algorithm is well suited to the proposed type of problem. Sankar et al. (2004b) deal with the simultaneous scheduling of incoming jobs, machines and AGVs. The authors make use of a hybrid method that includes optimization (using Genetic Algorithms) and computer simulation. The method was applied to an FMS with four machines and one AGV. The results are evaluated by

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comparing the obtained makespan with the results obtained by another algorithm in the literature (Kangaroo Algorithm). The results demonstrate that the proposed procedure performs better. Taghavifard et al. (2009) also use a hybrid approach consisting of dispatching rules and Genetic Algorithms to simultaneously schedule machines and AGVs. The authors apply the algorithm to a flexible manufacturing cell consisting of two machines and one material handling device with the objective of minimizing the makespan. The authors compare the results with the optimal values found in the literature and highlight the strong performance of the proposed method in terms of efficiency and solution quality. 4.2.2 Papers that use more than one measure of performance (multi-criteria) Keung et al. (2003) propose an intelligent hierarchical control technique for a flexible manufacturing system. The control model comprises four levels: selection of the production plan, master planning, sequencing and task control. At the sequencing level, the goal is to maximize machine utilization and balance the tool magazine capacity. The authors use Genetic Algorithms at all levels and evaluate the model using two criteria: earliness and tardiness penalty costs. The authors conclude that the intelligent hierarchical planning, scheduling and control model provides a systematic way to effectively allocate resources over different time horizons. Jerald et al. (2006) also make use of a pure approach (Adaptive Genetic Algorithm) to address the problem of simultaneously scheduling parts and AGVs in an FMS with 16 machines and 11 material handling devices. The authors use a combination of penalty costs and machine idle time as the performance measure. The schedule obtained from the Adaptive Genetic Algorithm is compared with that produced by a Genetic Algorithm, and experimental results have indicated that the proposed adaptive Genetic Approach is very effective. Three papers make use of hybrid approaches. Haq et al. (2003) deal with multilevel scheduling decisions for a flexible manufacturing system. The authors initially use the Giffler and Thompson (GT) algorithm with six different dispatching rules for operation sequencing to optimize the makespan. The result of this optimization is used to optimize a second objective function related to the routing of AGVs. This second objective function includes both the distance traveled by the AGVs and the number of backtrackings. The performance of Genetic Algorithms and Simulated Annealing are compared, and the results show that the hybrid approach using GA gives superior results. Reddy and Rao (2006) address simultaneous scheduling of machines and AGVs in FMSs using a multi-objective hybrid GA to minimize the makespan, mean flow time and mean tardiness objectives. The hybrid approach is a combination of Genetic Algorithms and heuristics and is applied to an FMS with six machines and two AGVs. The results are analyzed, and the authors conclude that the proposed algorithm presents many diverse solutions. Tu¨rkcan et al. (2007) propose using a genetic algorithm called the PSGA (Problem Space Genetic Algorithm) to simultaneously solve the problems of

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loading, sequencing and tool management in a flexible manufacturing system. The authors apply the method to an FMS with two CNC machines, two robots, and one conveyor and aim to minimize both the manufacturing costs and the total weighted tardiness. The performance of the proposed algorithm was compared with that of a sequential algorithm (PI) that sequentially solves the loading problem and the sequencing problem. Finally, the authors point out the superiority of the proposed algorithm as well as the significant interaction between the tool management and sequencing decisions that are considered in the proposed method.

5 Analysis In this section, a general analysis based on the proposed classification system is performed on the literature review. In Table 4, we present the frequencies of occurrence of the possible criteria values. It is important to note that Table 4 considers the possible criteria values presented in the Sect. 3. However, for better visualization some criteria present the combination or grouping of some criteria values.

Table 4 Number of articles by each classification criterion Criteria values

Number of papers

Frequency (%)

Criterion A

Criteria values

Number of papers

Frequency (%)

Criterion B

SFM

0

0.0

JC1; RF1

1

2.5

FMC

11

27.5

JC1; RF?

2

5.0

MMFMS

3

7.5

JC?; RF1

12

30.0

MCFMS

7

17.5

JC?; RF?

22

55.0

Not available

3

Total

40

Not available

19

47.5

Total

40

100.0

Machines (M)

18

45.0

Machines(M) e buffer (B)

1

2.5

Machines (M) e material handling Devices (HD)

18

45.0

M. B e HD

2

Not available

1

Total

40

100.0

Mono-criterion

22

55.0

Pure

20

50.0

Multi-criteria

18

45.0

Hybrid

20

50.0

Total

40

100.0

Criterion B

7.5 100.0

Criterion D Sequencing

32

80.0

Sequencing and AGV Routing

4

10.0

Sequencing and loading

3

7.5

5.0

Sequencing, loading and Routing

1

2.5

2.5

Total

40

Criterion E

100.0

Criterion F

Total

100.0

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Regarding Criterion B (resources and their constraints), 18 papers contain the number of machines and material handling devices that exist in the FMS environment in their constraints. One paper does not indicate the type of resources or the capacity constraints. It is also noted that only 2 reviewed papers consider the capacity constraints (machines, buffers and material handling device) in a simultaneously way. This analysis shows that there is an opportunity for future research to consider more complex scenarios that contain more constraints (such as those found in machines, storage buffers and material handling systems). When these constraints are considered, the studied problem becomes closer to reality, allowing the generation of practical scenarios for testing algorithms such as Genetic Algorithms. Analyzing Criterion C (job complexity and routing flexibility), it is notable that most of the reviewed papers treated the most complex scenario type (JC? ; JF?). The environment JC? ; RF1 was studied in 12 reviewed papers. It also becomes evident that there exists a relation between the complexity of the environment and the approach used to solve the problem. Meta-heuristics such as GAs are, according to the observed results, a viable solution for higher complexity environments. Figure 1 compares Criteria D and E. Most of the papers (32) focus only on the scheduling of operations or jobs. Of this total, 19 papers use only one objective function. Of these 19 papers, 14 use the makespan as the performance measure. Analyzing all of the papers studied in the review reveals that the makespan is used in 24 papers in total, either as the sole component of the objective function or in combination with other performance measures. The FMS environment is an important component of the complexity level of the studied scheduling problem, and Fig. 2 presents the frequency of each type of FMS (Criterion A) in this literature review. Figure 2 reveals that the FMC environment is studied most often. A simpler environment, the SFM, was not treated by any reviewed papers. However, this analysis is somehow impaired, as 19 researched papers did not specify the target environment. Table 4 indicates that the two approaches (pure GA or hybrid) are treated in an equal number of papers. However, in several papers in which the pure GA approach

Fig. 1 Relation between Criteria D and E

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Fig. 2 Types of productive environment studied

Fig. 3 Approaches used in the reviewed papers

was used, the authors considered the importance of analyzing combinations of GAs with other approaches presented in the literature. Figure 3 presents the distribution of the approaches found in the papers that use hybrid methods to solve the proposed problem. Of the 20 papers that use the hybrid approach, 10 use simulations or Petri Nets combined with GAs, 5 use other heuristics, and 3 use dispatching rules. Neural Networks and Simulated Annealing were each used in 2 papers, and DDP and Fuzzy Logic were each used in one paper.

6 Final remarks This paper presents a literature review on the application of Genetic Algorithms to solving FMS scheduling problems. The survey utilizes a classification system with six criteria: type of FMS, resources and constraints, job characteristics, scheduling problem approached, measure of performance and solution approach. All papers found in the literature review were classified according to these criteria and presented according to their characteristics. Some aspects of the review, classification and analysis can be highlighted: •

The solution approaches employed exhibit high diversity. There are several combinations of GAs and other techniques among the hybrid techniques. A

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•

•

•

•


combination of GAs and Petri Nets is a representative approach. Several authors, such as Chiu and Fu (1997), Gang and Wu (2004), Chung et al. (1998), Reyes et al. (2001), Rabelo et al. (1994), Saitou et al. (2002) and MohammadPour et al.(2010) use Petri Networks to construct the problem and increase the efficiency of the GA. However, a few authors, like MohammadPour et al. (2010), use mechanisms for local search. There are opportunities for future research in this area. Although all of the researched papers studied FMS environments, only a few authors explicitly state all of the characteristics of the environment they approached in their research: Jawahar et al. (1998a), Chiu and Fu (1997), Gang and Wu (2004), Rabelo et al. (1993), Chung et al. (1998), Rossi and Dini (2000), Jawahar et al. (1998a), Keung et al. (2001), Erkmen et al. (1997), Taghavifard et al. (2009), Tu¨rkcan et al. (2007), Jerald et al. (2005,2006), Haq et al. (2003), Ulusoy et al. (1997), Sankar et al. (2003), Sankar et al. (2004a, 2004b, 2005), Reddy and Rao (2006), Hsu et al. (2008), Keung et al. (2003). Because of this lack of information, classification by Criterion A is a difficult task. We understand that the studied scenarios allow the reader a greater comprehension of the complexity of the problem and the application of the developed techniques. The quantitative analysis demonstrated that most of the studies use the same measure of performance (the makespan). It appears that there exist opportunities to use further measures, either alone or in combinations, as is done by Sankar et al. (2003), Sankar et al. (2004b, 2005), Rabelo et al. (1993), Jerald et al. (2005, 2006), Keung et al. (2001), Choudhury et al. (2009), Tu¨rkcan et al. (2007), Haq et al. (2003) and Keung et al. (2003). We also considered that, in practical applications, the simultaneous use of manufacturing costs and makespan as performance measures could provide more information to the decision process. Although 100 % of the reviewed papers approached scheduling problems, only a few of them present a Gantt Chart with the final solution, which could be helpful when comparing different studies and aiming at providing a more practical solution for managers in the shop floor. Most of the papers use the following: (1) problems already approached by another, already published paper or (2) analysis that compares, for the problem analyzed, the results obtained with the proposed approach and approaches that have been studied in literature.

Finally, it can be stated that FMS scheduling continues to represent a great research opportunity for application of GAs and other Artificial Intelligence approaches, specially nowadays where FMS became widespread in a lot of manufacturing environments.

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Author Biographies Moacir Godinho Filho had done his postdoctoral research at North Carolina State University at Raleigh (USA), postdoctoral research at University of Wisconsin-Madison (USA), PhD in Industrial Engineering at Federal University of Saõ Carlos, and M.S. in Industrial Engineering at Federal University of Saõ Carlos. He is a Professor at Federal University of Saõ Carlos. Clarissa Fullin Barco is a M.Sc. student in Industrial Engineering at Federal University of Saõ Carlos and received Bachelors Degree in Industrial Engineering at Federal University of Saõ Carlos. Roberto Fernandes Tavares Neto had done his PhD in Industrial Engineering at Federal University of Saõ Carlos, M.S. in Industrial Engineering at Catholic University of Parana´, and Bachelors Degree in Electrical Engineering at Federal University of Parana´. He is a Professor at Federal University of Saõ Carlos.

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