Particle Swarm Optimization for Unplanned AGV ...

Particle Swarm Optimization for Unplanned AGV Routing in Kanban Systems Alper Özpınar 1 Emel Şeyma Lök 2 Abstract Optimization is one of the most important key factors in nowadays manufacturing processes. Since the new economic conditions forcing the competition in a multidimensional global paths, economically survival companies should improve their processes, adapt manufacturing tag times, lower their operation costs and increase the overall quality also focusing on CRM programs This paper introduces an alternative and dynamic algorithm for improving and optimizing the control of AGV’s that used to transfer equipment from stock zones to manufacturing zones as a part of ordinary and unplanned Kanban operations for a vehicle manufacturing factory by using particle swarm optimization. Key success factors for this operation are decreasing tag time per car and also eliminating the waiting time for unplanned equipment transfer within the factory area. Keywords: Particle swarm optimization, AGV routing, Kanban, just in time, vehicle routing, metaheuristics, manufacturing system

1 Introduction After the rapid development of industrialization in the early years of twentieth century the main aim of the production is to produce under any circumstances since the demand is higher than the supply. To overcome the gap between the demand and the supply mass production becomes as must which already started in the nineteenth century within the war economy in which the workshop was equated with craft restriction, low quality of output and moral laxity on the part of the workforce. [1] In the beginning of eighteenth century there were neither planning, slotting, nor shaping machines and with the exception of very imperfect lathes and few drills the preparatory operations of construction were effected entirely by the hand of workers. [2] Mass production, replacing a functional form of production with one based on flow, and the systematic reduction of individual tasks, had all been pioneered by other American manufacturers. Even the conception of a utilitarian vehicle priced for mass consumption had been widely discussed and implemented with the “curved dash” Oldsmobile by 1 2

American car-makers before the launch of the Ford’s famous Model T.[3] Assembly lines have been a significant development for managing operations – a mode that allows high-volume, low-cost, standardized production after the success of Ford’s Model T production in the assembly line. These benefits are often offset by drawbacks: perceptions of Fordist assembly lines consider them to be rigid and inflexible. [4] Ford’s achievement results in high production rates comparatively for those years in the assembly line production. After the second world war, still the demand is higher than the supply but the consumers looking for more choices and quality, another car manufacturing company Toyota makes a huge improvement and reset the rules of the manufacturing game that organizes manufacturing and logistics. The new system named “The Toyota Production System (TPS)” which is still commonly used in most of the biggest manufacturing companies.

2 Manufacturing Systems, Just in Time and Kanban TPS or in other words the “Toyota Way” can be considered as early development of the nowadays “Lean production”. Lean production simply means manufacturing without waste and aiming for the preserving the value with less work. The origin of Waste (“muda” in Japanese) has seven types: waste from over production, waste of waiting time, transportation waste, inventory waste, processing waste, waste of motion, and waste from product defects. [5] Companies that applies TPS for the planning and running their production systems based on the two basic concepts. First of all, the thing that corresponds to the first recognition of putting forth all efforts to attain low cost production is "reduction of cost through elimination of waste". This involves making up a system that will thoroughly. Eliminate waste by assuming that anything other than the minimum amount of equipment, materials, parts, and workers (working time) which are absolutely essential to production are merely surplus that only raises the cost. In order to obtain eliminating the wastes result in an another popular way of production named as “Just in time” production. In

Department of Mechatronics, İstanbul Commerce University, [email protected] Department of Industrial Engineering, Istanbul Commerce University, [email protected]

JIT in order to avoid such problems as inventory unbalance and surplus equipment and workers, companies recognizes the necessity of schemes adjustable to conform with changes due to troubles and demand fluctuations. For this purpose, companies put their efforts in development of a production system which is able to shorten the lead time from the entry of materials to the completion of vehicle. The just-in-time production is a method where by the production lead time is greatly shortened by maintaining the conformity to changes by having "all processes produce the necessary parts at the necessary time and have on hand only the minimum stock necessary to hold the processes together". In addition, by checking the degree of inventory quantity and production lead time as policy variables, this production method discloses existence of surplus equipment and workers. This is the starting point to the second characteristic of Toyota Production System, that is, to make full use of the workers' capability. In order to obtain such a perfect system, most of the operations should be automated and controlled. Over the years many production control systems have been proposed within the factories. Some have been push like buffered production lines, some pull like Kanban, and some hybrid like Conwip. All of these systems have one thing in common: the performance measures most of the time the output quantities used to evaluate the systems are a function of a quantity(s) which is naturally considered an integer most of the time the input quantity(s)). For buffered production lines the input quantities are the size of the buffers between each of the machines. For Kanban systems, the input quantities are the number of production and transfer Kanbans. For Conwip systems there is only one input quantity, the number of Conwip cards. [6] Like other systems, Kanban was created to fulfill specific needs of a company (Toyota), i.e. to work effectively under specific production and market conditions. [7] In the Kanban System, the production line is divided into several stages and at every stage there is a fixed number of tags (or tickets) so called Kanban. An arriving job receives a Kanban at the entrance of the stage and maintains possession of it until it exits the stage. If an arriving job does not find an available Kanban at the entrance, it is not allowed to enter that stage until a Kanban is freed; in this case, the job is forced to wait in the previous stage and becomes blocked. [8] These Kanban’s come in two kinds, one of which is called ‘conveyance Kanban’ that is carried when going from one process to the preceding process. The other is called, ‘production Kanban’ and is used to order production of the portion with drawn by the subsequent process. [9]

The Kanban system, as a JIT ordering system, releases an order to a stage only when a Kanban arrives from the succeeding stage (meaning a demand arrival from the succeeding stage), the parts are supplied from the preceding stage, and the orders previously released to the stage have been processed. [10] Kanban discipline constitutes a flexible system that promotes close coordination among workstations in repetitive manufacturing. The goal of the Kanban system is to achieve a total invisible conveyor system connecting all the external and internal processes. [11] The Kanban concept has evolved into a means of smoothing flow by balancing work with resource capability. It focuses more on limiting work in progress according to capacity. Work cannot be started until there is an available appropriate resource. [12] Another important subject in control systems is for the partially completed products that are currently in the shop are referred to as work-in progress (WIP). The WIP may be in a queue awaiting the availability of their next workstation, being loaded or processed on a machine, or being moved between workstations. In addition, WIP may exit because of parts being held in temporary storage pending approval from customer or instructions from engineering due to a design change, or a decision on disposition resulting from a quality problem, or arrival of other parts/materials to be mated with these parts in a next production operation. [13] An FMS (Flexible Manufacturing System) in a JIT (Just-In-Time) production system to be considered here consists various number of workstations labelled, dispatching stations and AGV (Automated Guided Vehicle). AGV’s are used for transportation mediums as single or multiple loads. [14] When processing of a component starts at a workstation, a withdrawal Kanban attached to the component is sent to the dispatching station without delay. The AGV chooses one from workstations whose withdrawal Kanban are accumulated at the dispatching station, and conveys a component together with a withdrawal Kanban from the dispatching station to the workstation. The AGV can convey only one component at a time. A dispatching policy of the AGV is a rule that specifies the workstation to which it is dispatched whenever it returns to D to find withdrawal Kanban.[15] Use of artificial intelligence and expert systems for controlling and routing the AGV’s have been used in the literature in different studies, some of them are directly related with AGV’s and some of are dealing the problem as a part of Travelling Salesman Problem (TSP), Vehicle Routing Problem (VRP) or Capacitated Vehicle Routing Problem (CVRP) .[1619]

3 PSO for AGV Routing in Kanban Systems In normal operating conditions AGV’s have deterministic routes and planned operations supported by the MRP and ERP systems. Since most of the logistics and transportation still operated by blue collar workers there is a possibility of stochastic and unplanned needs to fulfill Kanban operations such as misinformation, wrong parts delivery, barcode problems, jundate-ticket selection problems, wrong material flow, human error, database error, communication errors and expert system setting and definition errors. Most of these errors due to the rapid development and changes in the standard operating procedures within the factories since the needs for starting the manufacturing operation is most of the time called last minute changes in the system. Especially in car manufacturing factories where Kanban systems are successfully operated for lots of years a change in the model or change in the raw material type supplier leads to the risk of resulting for the following orders. For those type of Kanban and AGV operating systems for those times should be separated from normal operating condition to unexpected operating conditions. These problems can be so vital and big so that the whole manufacturing and assembly line has to be stopped in order to fix the problem or sometimes if the problem is related with just one car or one product than a hybrid solution applied. Normal assembly line continues to operate and the problem have been fixed manually by the related personnel. In that case the problem can be modelled by two approaches. First and a more simple one is considering the problem as a dynamic vehicle routing problem (DVRP) which is strongly related to the static VRP, as it can be described as a routing problem in which information about the problem can change during the optimization process. [20] Since the occurring of the problems most of the time is probabilistic so the problem can be considered as Stochastic Vehicle Routing Problem (SVRP). In Stochastic Vehicle Routing Problems (SVRPs) one parameter of the problem, like customers, customers’ demands or customers’ travel and service times, is a stochastic variable that follows a known (or unknown) probability distribution. Stochastic VRPs differ from the Capacitated Vehicle Routing Problems in several fundamental aspects. The concept of a solution is different, several fundamental properties of deterministic VRPs no longer hold in the stochastic case, and solution methodologies are considerably more intricate. [21] Since the origin and the parameters makes the problem as one of the NP-hard problems with some specific difficulties, confusions and dynamic constraints so that ordinary optimization techniques

even makes the problem yielded to more complex solutions. As an alternative to ordinary techniques, alternative optimization methods have been using to solve these problems. Use of artificial intelligence, artificial neural networks, fuzzy logic and metaheuristic methods commonly used for the solution, modelling and optimization of those NP problems.[22] For the last decades nature inspired approaches in optimization became more and more popular within complex domains of data or information, are those methods representing successful animal and microorganism team behavior, such as swarm or flocking intelligence (birds flocks or fish schools inspired Particle Swarm Optimization, artificial immune systems, optimized performance of bees, or ant colony optimization etc..) and the genetic algorithms.[23] There are five major swarm behaviors in the nature [24]; 1. Proximity: Ability to perform space and time computations. 2. Quality: Ability to respond to environmental quality factors. 3. Diverse response: Ability to produce a plurality of different responses. 4. Stability: Ability to retain robust behaviors under mild environmental changes. 5. Adaptability: Ability to change behavior when it is dictated by external factors. Moreover, the social sharing of information among individuals in a population can provide an evolutionary advantage. This general belief, which was suggested in several studies and supported by numerous examples from nature, constituted the core idea behind the development of PSO Particle Swarm Optimization. [25] PSO has been based on the above behaviors of the nature swarms and modelling them to use as an optimization techniques. PSO was originally proposed by Kennedy and Eberhart in 1995 and still developing by them in various studies.[23;26-28] In general PSO algorithm, candidate solutions of a population, called particles, coexist and evolve simultaneously based on knowledge sharing with neighboring particles. While flying through the problem search space, each particle generates a solution using directed velocity vector. Each particle modifies its velocity to find a better solution (position) by applying its own flying experience (i.e. memory having best position found in the earlier flights) and experience of neighboring particles (i.e.

best-found solution of the population). Particles update their positions and velocities as shown below: 𝑔

𝑖 𝑣𝑡+1 = 𝑤𝑡 𝑣𝑡𝑖 + 𝑐1 𝑟1 (𝑝𝑡𝑖 − 𝑥𝑡𝑖 ) + 𝑐2 𝑟2 (𝑝𝑡 − 𝑥𝑡𝑖 )

𝑖 𝑖 𝑥𝑡+1 = 𝑥𝑡𝑖 + 𝑣𝑡+1

(1)

(2)

𝑖 where 𝑥𝑡+1 represents the current position of particle i in solution space and subscript t indicates an iteration, 𝑝𝑡𝑖 is the best-found position of particle i up to iteration count t and represents the cognitive contribution to the search velocity v . Each component of 𝑣𝑡𝑖 can be clamped to the range [−𝑣𝑚𝑎𝑥 , 𝑣𝑚𝑎𝑥 ] to control excessive roaming of 𝑔 particles outside the search space; 𝑝𝑡 is the global best-found position among all particles in the swarm up to iteration count t and forms the social contribution to the velocity vector; 𝑟1 and 𝑟2 are random numbers uniformly distributed in the interval (0,1), while 𝑐1 and 𝑐2 are the cognitive and social scaling parameters, respectively; 𝑤𝑡 is the particle inertia, which is reduced dynamically to decrease the search area in a gradual fashion. The variable 𝑤𝑡 is updated as

𝑤𝑡 = (𝑤𝑚𝑎𝑥 − 𝑤𝑚𝑖𝑛 ) ∗

𝑡𝑚𝑎𝑥 − 𝑡 + 𝑤𝑚𝑖𝑛 𝑡𝑚𝑎𝑥

(3)

where, 𝑤𝑚𝑎𝑥 and 𝑤𝑚𝑖𝑛 denote the maximum and minimum of 𝑤𝑡 respectively; 𝑡𝑚𝑎𝑥 is a given number of maximum iterations. Particle I flies toward a new position according to above Equations 1-3. In this way, all particles P of the swarm find their new positions and apply these new positions to update 𝑔 their individual best 𝑝𝑡𝑖 points and global best 𝑝𝑡 of the swarm. This process is repeated until iteration count 𝑡 = 𝑡𝑚𝑎𝑥 (a user-defined stopping criterion is reached). [29;30]

3. Delivery of products by AGV’s to the assembly line as JIT principle. Assumptions  Parts are consuming in one assembly location and stored in one main warehouse and Kanban warehouse,  Main warehouse capacity assumed to be infinite,  Kanban warehouse capacity assumed to be finite and limited,  Manufacturing progress is mixed model so that consequent cars in the assembly line may be different in model, color and specs,  If a part is missing in the Kanban warehouse when needed an emergency event named “andon” generated in the information system so that the computer system informed where there is a problem,  All AGV’s acting as mobile agents that can communicate with each other and the system and sharing the location and dolly status,  AGV’s paths are clearly defined and no collusion or jamming occurs,  A specific number of emergency AGV’s waiting to operate according to modified PSO algorithm in proper distributed locations in the factory,  Emergency AGV’s dolly capacity is limited to one part,  Free emergency AGV’s returns to their initial locations.

4 Notations and Problem In this paper a modified PSO algorithm has been developed for the following imaginary car manufacturing factory assembly line using TPS such as Kanban and JIT. There are three main types of product delivery operations within the factory and to the factory. 1. Main supply for the products to the main warehouse in the long time table such as monthly or weekly 2. Daily delivery of the products from the main warehouse to the Kanban warehouse locations where workers fill the products according to the MRP in the proper positions of the dollies connected to AGV’s, hourly or according to the production plan and the usage frequency of the parts

Figure 1: Factory Layout Where MWp : main warehouse location for assembly part p, KWp : kanban warehouse location for assembly part p, ASk : assembly location k, AGVj : AGV number j, pAGVj (x,y): coordinates of the jth AGV in the factory vj : average velocity of the jth AGV Amissingp : assembly number where the missing part p belongs to,

Aproductionk : current assembly no within the assembly location k

So the pseudo-code for the algorithms is as follows, qk : tag time for manufacturing one vehicle in the ASk

(1) Do while andons are open and there are parts to deliver

m : number of AGV’s for emergency nt : number of andons at time t j

Tt : target of the

jth

1.1 initialize : randomly distribute the empty AGV’s to the targets

AGV at time t

(2) Do while target constraint is safe

5 Modified PSO for AGV Algorithm The modified PSO for AGV algorithm targeting the solution of stochastic and dynamic stock problems of Type 2 delivery problems affecting the Kanban warehouse locations pickups. The major aim of the optimization is to deliver the missing parts from the main warehouse to the assembly location before the part is needed according to JIT. Since the modified PSO Algorithm is a continuous solution for the problems the dynamic routing of the emergency AGV’s can be changed during the operation according to the priority of the parts needed. The major modification to the original PSO is to use the AGV’s target location function instead of a velocity component since the AGV’s operating on predefined paths. At each step new andons checked and the total timing for the delivery solution calculated for the need of stopping the assembly line required or not. For the 𝑗

𝑗

𝑗

𝑗

𝑔

𝑗

𝑓(𝑇𝑡+1 ) = 𝑤𝑡 𝑓(𝑇𝑡 ) + 𝑐1 𝑟1 (𝑝𝑡 − 𝑥𝑡 ) + 𝑐2 𝑟2 (𝑝𝑡 − 𝑥𝑡 )

(4) 𝑔

𝑗

where 𝑓(𝑇𝑡 ) : Target location function as index, 𝑝𝑡 is

the global shortest timing for visiting a warehouse location best-found travel timing with the selected target among the farest AGV’s. Instead of calculating the global AGV’s positions; modified PSO chooses among the farther AGV’s to the j th AGV for fast converging solution. 𝑝𝑡𝑖 is the shortest timing to reach a target of the jth AGV. 𝑥𝑡𝑗 is the current timing of the AGV to the target. Target locations should be placed into an array and selected from that array according to their locations within the main warehouse. 𝑗

𝑡𝑖𝑚𝑒𝑡𝑜𝐺𝑂 =

𝑋𝑡𝑜𝑊𝑎𝑟𝑒ℎ𝑜𝑢𝑠𝑒 + 𝑋𝑡𝑜𝐴𝑠𝑠𝑒𝑚𝑏𝑙𝑦𝑠ℎ𝑜𝑝 𝑆𝑝𝑒𝑒𝑑 𝑜𝑓 𝐴𝐺𝑉 𝑗

(5)

𝑝

𝑡𝑖𝑚𝑒𝑡𝑜𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = 𝐴𝑏𝑠(𝐴𝑃𝑚𝑖𝑠𝑠𝑖𝑛𝑔 − 𝐴𝑘𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 ) ∗ 𝑞𝑘 )

(6)

In order to optimize the system main objective function is to maximize the total available timing. # 𝑜𝑓 𝐴𝑛𝑑𝑜𝑛𝑠

𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒

∑

𝑝

𝑗

(𝑡𝑖𝑚𝑒𝑡𝑜𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 − 𝑡𝑖𝑚𝑒𝑡𝑜𝐺𝑂 )

𝑖=1

and crucial constraint is ∀ 𝑝 ∈ {𝐴𝑛𝑑𝑜𝑛𝑠}

𝑗 𝑡𝑖𝑚𝑒𝑡𝑜𝐺𝑂

≤

𝑝 𝑡𝑖𝑚𝑒𝑡𝑜𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛

(7)

2.1 Calculate the TimeToGo for the target locations and compare with the TimetoProduction values according to MWp , ASk , vj and pAGVj (x,y) 2.2 Apply modified PSO for finding the new target locations for the AGV’s , calculate timings 2.3 Check the total timing and maximum number of iterations if exceeds Stop the assembly line, add more emergency AGV to operate and run else continue loop by assigning the new indexes to the AGV’s.

2.4 Enddo (3) Enddo (4) Return the best AGV distribution and send commands to AGV’s

Conclusion and Future Work In this paper a modified PSO algorithm has been developed and tested with simulation parameters for the stochastic AGV routing for Kanban and JIT operating conditions of a car manufacturing company. For future work major modifications for the algorithms has planned for the following situations as the emergency AGV capacities will be adapted dynamically so they can take multiple parts and deliver multiple parts and AGV’s can transfer parts between each other during the operation.

References [1] C. Behagg, "Mass Production Without the Factory: Craft Producers, Guns and Small Firm Innovation, 1790-1815 1," Business History, vol. 40, no. 3, pp. 1-15, July1998. [2] A. E. Musson, "Joseph Whitworth and the Growth of Mass-Production Engineering," Business History, vol. 17, no. 2, pp. 109-149, July1975. [3] J. M. Wilson and A. McKinlay, "Rethinking the assembly line: Organisation, performance and productivity in Ford Motor Company, c. 1908-27," Business History, vol. 52, no. 5, pp. 760-778, Aug.2010. [4] J. M. Wilson, "Henry Ford vs. assembly line balancing," International Journal of Production Research, vol. 52, no. 3, pp. 757-765, Sept.2013. [5] N. A. A. Rahman, S. M. Sharif, and M. M. Esa, "Lean Manufacturing Case Study with Kanban

System Implementation," Procedia. Economics. and Finance., vol. 7, no. 0, pp. 174-180, 2013.

International Journal of Production Research, vol. 45, no. 13, pp. 2859-2873, May2007.

[6] Y. T. Herer and L. Shalom, "The Kanban assignment problem - A non-integral approach," European. Journal of Operational. Research., vol. 120, no. 2, pp. 260-276, Jan.2000.

[19] R. VUJOSEVIC, "Visual interactive simulation and artificial intelligence in design of flexible manufacturing systems," International Journal of Production Research, vol. 32, no. 8, pp. 1955-1971, Aug.1994.

[7] M. Lage Junior and M. Godinho Filho, "Variations of the Kanban system: Literature review and classification," International. Journal of Production. Economics., vol. 125, no. 1, pp. 13-21, May2010. [8] C. G. Panayiotou and C. G. Cassandras, "Optimization of Kanban-based manufacturing systems," Automatica., vol. 35, no. 9, pp. 1521-1533, Sept.1999. [9] Y. SUGIMORI, K. KUSUNOKI, F. CHO, and S. UCHIKAWA, "Toyota production system and Kanban system Materialization of just-in-time and respect-for-human system," International Journal of Production Research, vol. 15, no. 6, pp. 553-564, Jan.1977. [10] K. Takahashi and N. Nakamura, "Decentralized reactive Kanban system," European. Journal of Operational. Research., vol. 139, no. 2, pp. 262-276, June2002. [11] A. A. Andijani, "A multi-criterion approach for Kanban allocations," Omega., vol. 26, no. 4, pp. 483493, Aug.1998. [12] R. Turner, D. Ingold, J. A. Lane, R. Madachy, and D. Anderson, "Effectiveness of Kanban approaches in systems engineering within rapid response environments," Procedia. Computer. Science, vol. 8, no. 0, pp. 309-314, 2012. [13] M. D. Al-Tahat and A. M. Mukattash, "Design and analysis of production control scheme for Kanban-based JIT environment," Journal of the. Franklin. Institute., vol. 343, no. 4-5, pp. 521-531, July2006. [14] F. G. Maughan and H. J. Lewis, "AGV controlled FMS," International Journal of Production Research, vol. 38, no. 17, pp. 4445-4453, Nov.2000. [15] S. Hirao, M. Tamaki, and K. Ohno, "Optimal dispatching control of an AGV in a JIT production system," Production Planning & Control, vol. 13, no. 8, pp. 746-753, Nov.2002. [16] C. M. KLEI and J. KIM, "AGV dispatching," International Journal of Production Research, vol. 34, no. 1, pp. 95-110, Jan.1996. [17] A. Wallace, "Application of AI to AGV control agent control of AGVs," International Journal of Production Research, vol. 39, no. 4, pp. 709-726, Jan.2001. [18] I. Lee, "Evaluating artificial intelligence heuristics for a flexible Kanban system: simultaneous Kanban controlling and scheduling,"

[20] M. R. Khouadjia, B. Sarasola, E. Alba, L. Jourdan, and E. G. Talbi, "A comparative study between dynamic adapted PSO and VNS for the vehicle routing problem with dynamic requests," Applied. Soft. Computing., vol. 12, no. 4, pp. 14261439, Apr.2012. [21] Y. Marinakis, G. R. Iordanidou, and M. Marinaki, "Particle Swarm Optimization for the Vehicle Routing Problem with Stochastic Demands," Applied. Soft. Computing., vol. 13, no. 4, pp. 1693-1704, Apr.2013. [22] Q. Duan, T. W. Liao, and H. Z. Yi, "A comparative study of different local search application strategies in hybrid metaheuristics," Applied. Soft. Computing., vol. 13, no. 3, pp. 14641477, Mar.2013. [23] Y. Marinakis and M. Marinaki, "A hybrid genetic Particle Swarm Optimization Algorithm for the vehicle routing problem," Expert. Systems. with. Applications., vol. 37, no. 2, pp. 1446-1455, Mar.2010. [24] M. M. Millonas, "Swarms, phase transitions, and collective intelligence.," Addison-Welsey, 1994, pp. 417-445. [25] Konstantinos E.Parsopoulos and Michael N.Vrahatis, Particle Swarm Optimization and Intelligence: Advances and Applications (Premier Reference Source) IGI Global; 2010. [26] J. Kennedy and R. Eberhart, "Particle swarm optimization,", 4 ed 1995, pp. 1942-1948. [27] J. Kennedy, R. C. Eberhart, and Y. Shi, "chapter seven - The Particle Swarm," in Swarm Intelligence The Morgan Kaufmann Series in Artificial Intelligence. J. Kennedy, R. C. Eberhart, and Y. Shi, Eds. San Francisco: Morgan Kaufmann, 2001, pp. 287-325. [28] J. Kennedy, R. C. Eberhart, and Y. Shi, "Swarm intelligence. 2001," Kaufmann. , San. Francisco., 2001. [29] P. S. Shelokar, P. Siarry, V. K. Jayaraman, and B. D. Kulkarni, "Particle swarm and ant colony algorithms hybridized for improved continuous optimization," Applied. Mathematics. and Computation., vol. 188, no. 1, pp. 129-142, May2007. [30] X. H. Shi, Y. C. Liang, H. P. Lee, C. Lu, and Q. X. Wang, "Particle swarm optimization-based algorithms for TSP and generalized TSP," Information. Processing. Letters., vol. 103, no. 5, pp. 169-176, Aug.2007.