Tham khảo tài liệu 'swarm robotics, from biology to robotics part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | A New Hybrid Particle Swarm Optimization Algorithm to the Cyclic Multiple-Part Type Three-Machine Robotic Cell Problem 33 minimized. The same thing also can be achieved for M2 and M3 . Based on the choosing gate definition we simply have three choosing gates as o 3 and Y. Thus we can write the following formulation using 0-1 integer variables x1 j. x2 j and x3 j as n 1 S4 1 - S8 n Ct T x1in a s n Oj S4 1 - S8 j T x1j a s j 2 . n. n 3j S12 j - S6 T x2j bi s j . n. n Yj S10 - S2 j T x3j c z j V- n. Definition. A marked graph is a Petri-net such that every place has only one input and only one output. Theorem 1. For a marked graph which every place has i m tokens see figure 4 the following relation SB SA miCt where SA SB are starting times of transitions A and B respectively and Ct is cycle time is true. Fig. 4. The marked graph in theorem 1 Proof see ref. Maggot 1984 . In addition the following feasibility constraints assign unique positioning for every job T x1 j 1 j 1 - n i 1 T x1 j 1 i 1 . n. j 1 To keep the sequence of the parts between the machines in a right order we have to add the following constraints x1i j x2i j 1 i v. n j V n x2 i j x J 1 i 1 . n j v-s n. Where we assume that x1i 1 x1i 1 because of the cyclic repetition of parts. Thus the complete model for the three machine robotic cell with multiple-part would be as follows 34 Swarm Robotics From Biology to Robotics min Cf Subject to P1 1 S2 1 - S12 n Ct E 3 j 2 n 1 P1 j s2j - S12j E 3 j 1 - n 2 P3 j S4 J - s2 J - W1 J E 23 j 1 - n 3 P5 j s6 j - s4 j e 3 j 1 n 4 p7 j s8 j - s6 j 2e 33 j 1 n 5 P9 j s10 j - s8 j - w3 j e 23 j 1 n 6 p11 j s12 j - s10 j - w2 j 2e 33 j 1 n 7 n 1 s 4 1 - s7 1 Ct -2 x1in ai Paị E i 1 8 j s4 j - s7 j - 2 x1ij ai Vat E i 1 j 2 n 9 Pj s12 j - s6 j - 2 x2ij bi Vbi E i 1 j 1 n 10 n Tj s10 j - s2 j - 2 x3ij ci pCị E i 1 j 1 n 11 x1 i-1 x2 i j 1 n 12 x i j-1 x3i j i j 1 n 13 n 2 x1j 1 i 1 j 1 n 14 n 2 x1j 1 j 1 si J 0 wkj. 0 x1 x2 x3 e 0 1 i 1 n 15 4. The proposed hybrid particle .
