This research concerns the complex housing optimization problem encountered in engineering design, where the volume in space occupied by components need to be minimized along with other objectives and constraints. Since in real applications the constraints are usually complex, the formulation of computationally tractable optimization becomes challenging. In this research, we first develop the mathematical model of such optimization problem, then propose two versions of an improved multi-objective simulated annealing (MOSA) approach towards the design optimization, i.e., optimizing the placement of cylinders under prescribed constraints to minimize the volume occupied, and the estimated plumbing line length. Our case study indicates that the new MOSA algorithm has improved performance towards complex housing with hard constraints and the design can indeed be automated. The outcome of this research may benefit both existing manufacturing practice and future additive manufacturing.

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