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The end-of-life (EOL) disassembly sequencing problem (DSP) has become increasingly important in the process of handling EOL products. This paper proposes a solution procedure for the “EOL DSP”; the procedure is based on a novel soft-computing algorithm that utilizes modified “simplified swarm optimization,” and the procedure combines the precedence preservative operator, feasible solution generator, self-adaptive parameter control, and repetitive pairwise exchange procedures. By taking into consideration the non-deterministic polynomial time (NP)-complete nature of the problem, the proposed algorithm efficiently seeks the optimal disassembly sequence with a novel approach; this approach involves reducing the initial solution space and using a combination of soft-computing algorithms for achieving higher computational efficiency and solution quality. The results presented in this paper show that the proposed algorithm outperforms the existing algorithms in terms of solution quality achieved in a limited computation time.