The disassembly of end-of-life (EOL) products is increasingly inseparable from the disassembly line. Effective disassembly planning and reasonable disassembly line layout can bring significant benefits to the related industry. Considering the requirements of disassembly enterprises for lean production, this work proposes a multiple-product partial U-shaped disassembly-line-balancing (MPUD) problem. In this MPUD problem, multiple different types of EOL products can be disassembled simultaneously on a U-shaped layout disassembly line. A multi-objective MPUD problem is stated to maximize the disassembly profit and minimize disassembly resource consumption. A multi-objective discrete migrating birds optimizer (MDMBO) is designed to solve it. The proposed MDMBO and two others commonly used multi-objective optimization algorithms are compared for practical cases. The calculation results show that MDMBO's practicability and superiority over its two peers.