Product disassembly is an effective means of waste recycling and reutilization that has received much attention recently. In terms of disassembly efficiency, the number of disassembly skills possessed by workers plays a crucial role in improving disassembly efficiency. Therefore, in order to effectively and reasonably disassemble discarded products, this paper proposes a partial parallel disassembly line balancing problem (PP-DLBP) that takes into account the number of worker skills. In this paper, the disassembly tasks and the disassembly relationships between components are described using AND–OR graphs. In this paper, a multi-objective optimization model is established aiming to maximize the net profit of disassembly and minimize the number of skills for the workers. Based on the bat algorithm (BA), we propose an improved discrete bat algorithm (IDBA), which involves designing adaptive composite optimization operators to replace the original continuous formula expressions and applying them to solve the PP-DLBP. To demonstrate the advantages of IDBA, we compares it with NSGA-II, NSGA-III, SPEA-II, ESPEA, and MOEA/D. Experimental results show that IDBA outperforms the other five algorithms in real disassembly cases and exhibits high efficiency.