Multi-Objective Ant Lion Optimizer for Stochastic Robotic Disassembly Line Balancing Problem Subject to Resource Constraints

With the development of manufacturing and society, a large amount of end-of-life products are generated but with reuse value. Therefore, it is of great significance to dismantle and reuse them. A robotic linear disassembly line plays an important role and promotes the disassembly efficiency in a disassembly process. In this work, we establish a mathematical model of a linear robotic disassembly line balancing problem, which requires the maximization of profit and minimization of energy consumption. Then, an improved ant lion optimizer is proposed to optimize the objectives of the multi-objective robotic disassembly line balancing problem. The experimental results show that the multi-objective ant lion optimizer has good performance, and the diversity and convergence are better than its peers.


Introduction
The recycling of wasted products has always been a concern of the society [1][2].Our goals are to achieve the optimal reuse value [3]. A Disassembly Line Balancing Problem (DLBP) is an NP-hard problem. Some heuristic algorithms are applied to solve multi-objective DLBPs [4] including gray wolf algorithm [5], artificial bee colony algorithm [6], and cook search [7]. But these algorithms also have some shortcomings.To improve the speed of some algorithms, the diversity of the solutions is sacrificed in the iterative process [8].
Ant lion algorithm is a kind of swarm intelligence technology that comes from ant lion hunting ants [8,9], which brings us the inspiration like many heuristic algorithms such as Genetic Algorithm [10], Cuckoo Search and Ant Colony Optimizer (ACO).
In this work, we use ant lion algorithm to solve the multi-objective robotic disassembly-line-balancing-problem (MRD) under the premise of resource constraints, failure risk, and minimum energy consumption. This paper has three contributions: 1) The mathematical model of MRD is established to meet an actual disassembly process. It achieves the objectives of minimizing the energy consumption and maximizing the disassembly profit by taking the failure cost, resource constraints, and the priority relationship of the components into consideration.
2) A multi-objective ant lion algorithm (MALA) is designed to solve MRD, and an archive mechanism is used to ensure the diversity and convergence of the proposed algorithm.
3) Multi-objective Evolutionary Algorithm Based on Decomposition (MOEAD) and Non-dominated sorting genetic algorithm Ⅱ (NSGA-II) are compared with the proposed algorithm. The index analysis of the solution shows that Mala algorithm is better.

Problem Description
In this paper, we make some assumptions: 1) For each type of robots, the average disassembly time of each disassembly task and the time of conversion task are known. 2) Disassembly cost and energy consumption per time unit of each type of robots are known.
3) The conversion cost per time unit and the conversion energy consumption per time unit when the workstation completes the disassembly tasks are given. 4) The supply of EOL products is unlimited. 5) Only robots are responsible for performing disassembly tasks. A robot can only perform one disassembly task at a time, and each operation must be handled by one robot. 6) AND/OR graphs of multiple EOL products are known. 7) When the disassembly task needs to be operated by a specific robot, the type of robots should be informed to the workstation.
We use an AND/OR graph to describe the priority relationship of disassembly products .We select the mouse to simulate the disassembly line. The disassembly sequence of the linear line disassembly line is shown in Fig. 2. A disassembly sequence 1→4→8→11→13 is executed, task 1 needs robot 1, and robot 3 needs resource 1 and resource 3 to execute the disassembly, and component 2 and component 11 are obtained. As shown in Figure 1.

Mathematical model
Objective function (1) is for maximizing expect profit of disassembly product. (2) is to minimize expect disassembly energy consumption. (3) guarantees that each task is executed once. (4) ensures that a disassembly task cannot be performed more than once. (5) ensures that disassembly tasks are assigned when the workstation is turned on. (6) ensures that the disassembly sequence satisfies the conflicted relation constraints. (7) ensures that the disassembly sequence satisfies the priority relation matrix (8) represents that a disassembly sequence satisfies the resource constraints in a disassembly process. (9) means that the disassembly time of each workstation cannot exceed the cycle time of workstations. In (10), when disassembly failure occurs, the probability that the failure cost of

Population initialization
We can describe the solution of disassembly line as π = (π ' , π '' ), π ' ={h 1 , h 2 , …, h J } represents the disassembly sequence with a set of strings, and h j represents the disassembly index at position J. π '' ={q 1 , q 2 , …, q J } is a binary string representing whether the task at this position is executed. If q j = 0, the task in the j-th position in π ' cannot be performed; otherwise, q j = 1. And initialize the first generation population coding information according to the case information.

Position-based mutation operation
Before the completion of the iteration, the population needs mutation operation to maintain the diversity of the population. In the mutation operation, a random number is generated to perform a mutation operation, exchange the values of two genes on π v ' , reverse the values at a certain position of π v '' , or both, as shown in Algorithm 1.

Population iteration
Ants are randomly assigned to ant lions, and those with high fitness become ant lions. The elite ant lion is selected by a fitness value, which represents the optimal solution. If the archive is full, we delete some individuals by roulette to store the elite ant lions with better fitness until the maximum number of iterations is met. The elite ant lion represents the optimal solution.

Case study
We verify the effectiveness and feasibility of the algorithm by a copying machine and washing machine. We use the other two algorithms, NSGA-II and MOEAD, to verify the superiority of MALA.
The following table shows the performance of the algorithm solution.

Analysis of experimental results
We use GD(N) index to evaluate the convergence of the algorithm , IGD(N) index evaluates the diversity of algorithms. And Epsilon (N) to evaluate the degree of approximation. Hypervolume to reflect the comprehensive performance of the algorithm. As shown in Table 1 and Table2.

5.CONCLUSION
Aiming at the linear DLBP with multi-objective constraints, the single objective version of ant lion algorithm is improved. The MALA algorithm is designed to maximize the disassembly profit and minimize the disassembly energy consumption. The feasible solution is calculated from the actual disassembly case. The superiority of Mala is verified by comparison with NSGA-II and MOEAD. In the future, we will use more advanced operators to optimize MALA, so as to better solve the problems in the field of disassembly.