The Bees Algorithm was inspired by the honey bee swarm searching for flower groups in nature by Pham et al. [24]. Scout bees search randomly in nature and when they find efficient resources, they come to the hive and transfer the information to other bees with a special dance (waggle dance). Guidance with dance is at the basis of the Bees Algorithm. The local search section is divided into two parts which are elite sites and selected sites. In these sections, many searches are made in the neighborhood of optimum solutions, similar to doing guidance with real bees dance. In addition, random searches continue in the global search section, thus avoiding local optimum values [25]. The problem in this study is in combinatorial structure. In optimisation algorithms prepared for combinatorial problems, search sections and neighborhood definitions are different from continuous problems. In general, the positions of the members in the problem are changed according to certain rules, and new sequences are tried to be found with less cost. For the Bees Algorithm, Ismail et al. [26] suggested three different operators in the local search section, namely, Swap, Insertion, and Inversion.
The pseudo code of the Bees Algorithm and the pseudo code of the process optimisation section is given below together as shown in Fig. 2. As can be seen, there are 3 different operator selections within the general Bees Algorithm structure. In each iteration, one of these operators is applied randomly. Within the Bees Algorithm structure, more searches are made in elite sites. (Sections 21-36 are the same as sections 5-20, nsp come instead of nep.)
In the swap process, the order of two different vehicle groups chosen at random is changed with each other [26]. As an example in Fig. 3, changing the order of vehicle groups numbered 2 and 4 is shown. In the insertion process, the order of a randomly selected vehicle group is inserted to a different rank, also randomly selected [16]. It is shown in Fig. 3. As can be seen, the location of the number 2 vehicle group on the first plan is inserted into the section after the number 4 group. In the reversion process, the order between two randomly determined vehicle groups is reversed [16]. It is shown in Fig. 3. The order between vehicle groups number 2 and 5 on the first route has been reversed.
The algorithm parameters used in this study are given in Table 1.
Table 1 Parameter of the algorithms
Parameter
|
Value
|
Number of iterations
|
100
|
Number of scout bees (n)
|
40
|
Number of elite sites (e)
|
3
|
Number of selected sites (m)
|
9
|
Number of elite bees (nep)
|
60
|
Number of selected bees (nsp)
|
20
|
The general model consists of two parts. In the first part, the process plan is determined by optimising the starting vehicle and station values and the process begins. In the second part, online optimisation is done. When changes in station times are detected, a re-planning is made for vehicles that are not available on the line, and this process is repeated every time it is updated. A general view of the model is given in Fig. 4. The model consists of 4 main parts.
- Getting the starting data of the process.
- First optimisation.
- The section that follows the time updates at the stations.
- Online optimisation
The last column of the “Disassembly Times of Vehicles” matrix shows the vehicle numbers. After the data in the matrix is taken, the algorithm given in Fig. 2 is run and the first optimisation is made. The processes start according to the process sequence determined by this optimisation. The order of the first optimisation is shown with green blocks in Fig. 4. The first one shows the order of the vehicles, and the second shows the total duration times in the stations. After each operation in the stations, the times for the relevant station are updated in the “Detect of Changing Parameters” block. When updated, this block triggers the “Online Optimisation” block. In the online optimisation section, cars that are not on-line are determined first. The planning of these cars is re-optimised. Since the number of non-line cars is variable, the number of local search zones will also change dynamically. A section has been added to the first part of the algorithm to identify offline vehicles. By controlling the processing time, the place of the last online tool on the line is determined in the table. The flow chart of the online algorithm is given below.
The algorithm is developed in Matlab/Simulink. Information on the Simulink model is given below.
Model Configuration
Solver type : Fixed step
Solver : ode 3 (Bogacki-Shampine)
Fixed-step size : 1 [s]
Initial information on the process is given in Table 2.
Table 2 Initial information on the process
|
Rough inspected disassembly cost of vehicle parts at 14 workstations (min)
|
WS1
|
WS2
|
WS3
|
WS4
|
WS5
|
WS6
|
WS7
|
WS8
|
WS9
|
WS10
|
WS11
|
WS12
|
WS13
|
WS14
|
Car1
|
8
|
8
|
8
|
8
|
2
|
8
|
4
|
2
|
8
|
8
|
8
|
6
|
8
|
8
|
Car2
|
4
|
4
|
8
|
8
|
4
|
8
|
4
|
6
|
8
|
6
|
4
|
8
|
6
|
6
|
Car3
|
4
|
8
|
8
|
8
|
8
|
8
|
4
|
8
|
4
|
8
|
4
|
6
|
8
|
8
|
Car4
|
8
|
8
|
4
|
8
|
4
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
Car5
|
4
|
8
|
8
|
8
|
8
|
8
|
4
|
8
|
4
|
8
|
4
|
6
|
8
|
8
|
Car6
|
8
|
8
|
4
|
8
|
4
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
Car7
|
4
|
2
|
8
|
8
|
8
|
8
|
4
|
2
|
2
|
8
|
4
|
6
|
2
|
8
|
Car8
|
8
|
8
|
4
|
8
|
4
|
8
|
6
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
Car9
|
8
|
2
|
4
|
4
|
4
|
4
|
8
|
4
|
8
|
8
|
6
|
8
|
8
|
8
|
Car10
|
6
|
4
|
8
|
8
|
8
|
4
|
4
|
8
|
4
|
6
|
8
|
8
|
8
|
8
|
Car11
|
8
|
8
|
2
|
8
|
8
|
8
|
8
|
4
|
2
|
2
|
4
|
2
|
2
|
8
|
Car12
|
4
|
8
|
6
|
6
|
8
|
8
|
4
|
8
|
4
|
8
|
4
|
6
|
8
|
8
|
Car13
|
6
|
4
|
8
|
8
|
6
|
4
|
4
|
8
|
4
|
6
|
8
|
8
|
8
|
8
|
Car14
|
6
|
4
|
8
|
8
|
8
|
4
|
4
|
8
|
6
|
8
|
8
|
8
|
8
|
8
|
Car15
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
4
|
8
|
2
|
4
|
8
|
8
|
8
|
Car16
|
8
|
8
|
4
|
4
|
4
|
4
|
8
|
4
|
4
|
4
|
8
|
8
|
8
|
8
|
Car17
|
8
|
2
|
4
|
4
|
4
|
4
|
8
|
4
|
8
|
8
|
8
|
8
|
8
|
8
|
Car18
|
6
|
4
|
8
|
8
|
8
|
4
|
4
|
8
|
4
|
8
|
8
|
8
|
8
|
8
|
Car19
|
8
|
8
|
8
|
8
|
8
|
8
|
8
|
4
|
8
|
2
|
4
|
8
|
8
|
8
|
Car20
|
8
|
8
|
4
|
4
|
8
|
4
|
8
|
4
|
2
|
8
|
8
|
8
|
6
|
8
|