2.2.1. Disassembly Sequence Evaluation
Once a free node is identified, pruning the CRG indicates that the related disassembly operations are carried out. Many different sequences can be feasible to get the target component but disassembly operations performed in different sequences will be at different costs. Among all these feasible sequences, the one at minimum cost needs to be found. In general, the cost can be evaluated by the following factors [
16,
17,
18,
19,
32,
33]:
- (1)
Basic operation-preparing time;
- (2)
Time of disassembly tools change;
- (3)
Time of disassembly operation direction change, with tools or not;
- (4)
Time, economic or energy costs caused by disassembly operations.
From an energy perspective, all the factors can increase the total energy consumption of the disassembly process.
The basic operation-preparing time affects the basic energy consumption caused by clamping equipment, including equipment starting and stopping, equipment idling and auxiliary (such as coolant and lighting). So the total basic equipment energy consumption can be expressed as:
where
is the average power,
is the toal preparing time of the
i-th equipment and
M is the number of equipment.
To accomplish the disassembly process, the disassembly tool may change according to the types of connection between every two adjacent components. Since each time the tool changes will cause energy consumption, the total energy consumption of tool changes of the disassembly process can be expressed as:
where
is the energy consumption of the
i-th tool change and
is the time of tool changes.
Similarly, disassembly operations often need to be performed from different directions, which may require the components to be repositioned. The total energy consumption caused by disassembly operation direction changes can be expressed as:
where
is the energy consumption of the
i-th disassembly operation direction change and
is the time of disassembly operation direction changes.
,
and
are all about the energy consumed by support work
. The largest part of energy consumption during the disassembly process is caused by disassembly operations which include releasing the inter-connection constraints and removing the free component. The research in [
34] shows that the physical energy which is required for release of an inter-connection is determined by the type of connection. In [
35], Zhang quantifies the relative impact of the type of connection on the energy consumption in the disassembly process considering manufacturing process, material, recovery level and assembly/disassembly performance. The total energy consumption caused by releasing the inter-connections is expressed as:
where
is the energy consumption of releasing the
i-th inter-connection and
is the number of releasing operations.
The total energy consumption caused by component-removing operations is expressed as:
where
is the energy consumption of the
i-th component-removing operation and
is the number of component-removing operations. In the CRG, the weight
loaded in the edge connecting nodes
i and
j represents the energy consumption when releasing the inner-connection between the components and removing the disassembled component.
is determined by connection type and the disassembly operations, that is,
is related to the corresponding
and
.
Based on the foregoing analysis about the energy consumption, the total energy consumption required to complete the disassembly process can be calculated as:
To minimize Energy, the corresponding parameters , , , and are expected to be as small as possible. But it should be noted that , , and are not constants, they are all variable according to the disassembly sequence. For example, two successive disassembly operations using the same tool in the same disassembly direction consume less energy than that using different tools in different disassembly directions.
When the number of components to be disassembled gets large, the solution space of feasible disassembly sequences becomes incredibly wide and calculating the energy consumption of each feasible sequence to find the optimal one becomes very complicated. Heuristic algorithms have a lot of advantages in this issue, so in this paper the IACO is used to solve this problem.
2.2.2. Disassembly Sequence Planning
The sequence planning for a target-oriented disassembly process is an optimization problem with a variable number of components. ACO is an efficient artificial intelligence procedure that imitates the behavior of an ant colony finding the shortest path between the nest and the source of food. Each ant leaves volatile secretion (pheromone) on the path it passed; then the following ants will either repeat the path or find a new one. The more the pheromone is left on the path, the more attractive the path becomes to the following ants. The amount of pheromone on the paths with less or no ants repeating will decrease because the pheromone volatiles at a certain rate. Therefore, the shortest path will be visited most with the continuous action of the colony.
In the ACO algorithm, the total pheromone Q released by each ant in the entire route is a constant. In this paper, a new pheromone factor is proposed to improve the performance of the algorithm because it can adapt to the variable number of the components to be disassembled. That is, the smaller the number of components to be disassembled is, the larger the pheromone factor becomes. The experiment results show that this method can speed up the convergence of the algorithm.
To combine IACO and CRG to determine the minimum energy consumption, some issues have to be addressed:
- (1)
For the disassembly problem, each ant’s path represents a disassembly sequence and the nodes on the path represent disassembled components. Due to the constraints between the components, the ants are supposed to follow certain rules when passing through these nodes. The matrices of undirected edge (UM) and directed edge (DM) are adopted in this paper to reflect the constraint relationship between the components.
- (2)
When an ant moves from node i to node j, the constraints between the components represented by these two nodes are released. The distance traveled by the ant represents the energy consumption caused by the disassembly operation.
- (3)
For a complete disassembly problem, the end of the algorithm is that all the components are disassembled. But for a selective disassembly problem, the algorithm comes to an end when the target component is disassembled.
Then the optimal sequence can be obtained using IACO. The detailed description for each step of the proposed algorithm are as follows:
- (1)
Initialization. The number of ants in colony is m and the number of components to be disassembled is n (m is constant and n is variable). In the disassembly process, the total energy consumption removing component j from its adjacent component i is . At time t, the pheromone concentration on the path between the nodes is . At the initial moment, is the same everywhere and is set .
- (2)
Sequence planning. To apply the IACO to plan the disassembly sequence, the subassembly identified by pruning the CRG must be converted into numerical data form using constraint matrices. There are two kinds of constraint matrices, which are obtained according to the information of directed and undirected edges in the CRG, respectively. The constraint matrices represent the constraint relationship between parts in Boolean form. In the matrix of undirected edge (UM), each element is defined as follows:
UM is a symmetric matrix and every diagonal element is zero. In the matrix of directed edge (DM), each element is defined as follows:
The same as UM, each diagonal element is zero. The component i whose constraint matrices satisfy the following conditions can be identified as a free node:
- (1)
In the UM, there is no more than one “1” in the row ;
- (2)
In the DM, there is no “1” in the row .
When the component represented by a free node i is disassembled, every element of the i-th row and the i-th column in both UM and DM becomes “0” and new free nodes appear. Repeat the process until the target point becomes a free node, which means the target component can be disassembled from the product.
Every free node found by pruning the initial CRG can be settled as the starting point of the IACO. The starting point is also the beginning of the disassembly sequence. When an ant visited point
i, the related constraints are released and the energy consumption is recorded. Then some new free nodes appear and are put into the point set
, in which all the points are allowed to visit. The ordered point set
records the points that the ant has visited as the disassembly sequence. Ants will decide the node to visit next according to the pheromone concentration. The probability that the ant
k will transfer from point
i to point
j at time
t is:
where
is the heuristic function representing the expectation degree to which the ants are moving from point
i to point
j;
is the importance degree factor of pheromone; the bigger it is, the greater the pheromone will impact the transfer process;
is the importance degree factor of heuristic function; the bigger it is, the greater the heuristic function will impact the transfer process. Once the target point is visited by the ant
k, the disassembly process finishes and the total energy consumption
will be output according to point set
. Then the (
k + 1)-th ant will repeat the process and that total energy consumption
is obtained. Finally, the minimum value in the energy consumption vector
consisting of
is found and the corresponding disassembly sequence is the result of this generation. The result will be used to adjust the pheromones concentration of the next generation and guide the ants to plan their paths.
(3) Pheromone updating. While the ants are releasing pheromone, the pheromones between the nodes are gradually volatilizing. After the whole generation has finished the searching process, the pheromones need to be updated as follows:
where
is the volatilization factor; the bigger it is, the faster the pheromones volatilize;
is the amount of pheromone that the
k-th ant left between node
i and node
j, and
is the sum amount of pheromones that all the ants left between the two nodes. In this paper,
is calculated as:
where
is the pheromone factor.
indicates the number of the components included in the subassembly and is a constant,
indicates the number of components in the disassembly sequence represented by the
k-th ant’s path and can be variable. Obviously we have:
When , the remains a constant which indicates that this is a complete disassembly problem. When , it becomes a selective disassembly problem and the k-th ant leaves more pheromone on the path than others, that is, the k-th ant’s path is more attractive to the following ants.
Repeat the above process and the best disassembly sequence containing the target component aiming at lowest energy consumption will be found. The architecture of the proposed method combining CRG and IACO is summarized in
Figure 3. The content inside the red dotted line is the process about establishment and pruning of the CRG and the content inside the blue dotted line is the process about using the IACO to get the best disassembly sequence.