### The Disassembly Line: Balancing and Modeling

NP-complete or NP-hard definition are ways of showing that certain classes of problems are not solvable in realistic time Tovey, Exhaustive search works well enough in obtaining optimal solutions for small-sized instances; however its exponential time complexity limits its application on large-sized instances Kalayci and Gupta, c. Thus, an efficient search method needs to be employed to attain a near optimal condition with respect to objective functions.

## (PDF) A variable neighbourhood search algorithm for disassembly lines | Olcay Polat - bursretino.tk

This quickly becomes unsolvable for a practical-sized problem due to its combinatorial nature. The rest of the paper is organized as follows: Problem definition and formulation is given in Section 2. Section 3 describes the proposed VNS algorithm for disassembly lines. The computational experience to evaluate its performance on numerical examples and the comparisons are provided in Section 4. Finally some conclusions are presented in Section 5. The first objective given in Equation 3 is to minimize the number of workstations A variable for a given cycle time the maximum time available at each workstation.

The second neighbourhood objective given in Equation 4 is to minimize the total idle time by evenly distributing it among workstations, though at the expense of the generation of a non-linear objective search function. The third objective see Equation 5 , rewards the removal of hazardous parts algorithm early in the part removal sequence while the fourth objective Equation 6 rewards the removal of high demand parts early in the part removal sequence. The constraint given in Equation 9 ensures that the workstation content should never exceed the cycle time during any cycle and for any model considered.

Equation 10 imposes the restriction that all the disassembly precedence relationships between tasks should be satisfied. Proposed variable neighborhood search approach As mentioned in Section 1, exact solution approaches for solving DLBPs are not practical for large-scale instances. Here we propose a heuristic approach based on a VNS algorithm. The structure of the heuristic is given in Figure 1 as a pseudo-code. The algorithm starts with a randomization function in order to obtain a feasible initial solution see Section 4.

A VNS algorithm is applied to improve the initial solution over several generations see Section 4. The respective neighborhood structures are explained in Section 4. We use a station-oriented procedure for a creating a solution in which solutions are generated by filling workstations successively one after the other Kalayci and Gupta, c. First, a vector for schedulable operations are created according to the precedence constraints.

A task is only schedulable if it or its predecessors has already been assigned to a workstation. Second, after creating the schedulable operations vector, a sub-vector for candidate operations are constructed. A task is considered as a candidate operation if and only if it satisfies cycle time constraint, or in other words, if there is enough time to be assigned to current workstation for the task under consideration.

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Finally, a task is randomly selected from candidate operations vector and assigned to the current workstation. If the time slot left at the current workstation is not enough, a new workstation is opened for the awaiting task. The procedure finalizes when there are no more tasks to be assigned. Thus, an initial feasible solution is created. VNS uses the idea of systematically changing the neighborhoods in order to improve the current solution and aims to further explore the solution space, which may not be explored by a simple local search technique Hansen et al.

The shaking operator decides the search direction of the VNS from a set of neighborhoods. After a set of preliminary experiments, we may observe that the probability of escaping from local optima increases when the shaking operator is integrated with local search rather than using a single shaking operator.

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Therefore, each solution obtained by the shaking operator is further evaluated with the local search operator in order to explore new promising neighborhoods of the current solution. After each shaking operation, the VND algorithm allows up to n-max trials of A variable possible improvements.

At the end of the VND algorithm, if there is an improvement, then neighbourhood the shaking operations start from the first operation. Otherwise, shaking continues with the next operation. After reaching the maximum number of shaking operations search k-max , the search procedure continues with the first operation in the new iteration. In order to avoid redundant moves, in the neighborhood structures, only feasible moves are allowed, i. Figure 3 illustrates the different neighborhood structures. It reconstructs a new sub-sequence for the tasks which corresponds to ones while keeping the positions of tasks which correspond to zeros in the binary vector Figure 3 g.

Please note that, the main idea behind these operators is to construct a new sequence which satisfies the precedence constraints. These three benchmark data instances are solved using our VNS approach and compared to those that can be found in the literature. Because highly probabilistic, VNS was run 30 times to obtain the average results. Average CPU mark value, that represents the power of a processor, was calculated using the performance test software of PassMark that gives an idea by comparing processor speed of different hardware. Since the part product instance is a relatively small example and its optimal solution is known , all of the techniques were able to reach optimality see Table II.

Therefore its robustness is also confirmed Tables V and VI. In brief, the above comparisons demonstrate that the near optimal solutions generated by the proposed VNS approach surpasses the current best known solutions obtained via the single or multi objective approaches available in the literature. MOACO 9 11 — RL 9 9 97 — — — — Kalayci et al.

ABC 9 9 Gupta 1. Kalayci and TS 10 These comparison results confirm the competence of our proposed algorithm for solving the multi-objective DLBPs.

Conclusions The main objective of this paper was to present a VNS algorithm for disassembly lines. Four primary problem instances available in the literature were used to compare the performance of VNS and the results available in the literature in terms of time complexity and solution quality. VNS sought to provide a feasible disassembly sequence, minimize the number of workstations, minimize the total idle time and minimize the variation of idle times between workstations while attempting to remove hazardous and high-demand components as early as possible in a disassembly line.

It is ideally suited for non-linear and integer problems which are not easily solved by traditional optimum solution generating mathematical programming techniques. Other types of combinatorial optimization methodologies or hybrid approaches might show interesting results when applied to DLBPs. After that, the multi-objective robotic disassembly line balancing problem is proposed.

With the help of efficient non-dominated Pareto sorting method, the improved multi-objective discrete bees algorithm is proposed to find Pareto optimal solutions.

Based on a gear pump and a camera, the performance of the improved multi-objective discrete bees algorithm is analyzed under different parameters and compared with the other optimization algorithms. In addition, Pareto fronts of robotic disassembly line balancing problem are also compared with those of the other two cases. The result shows the proposed method can find better solutions using comparable running time compared with the other optimization algorithms.

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