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The aim of this paper is to solve the problems of multi-target tracking in clutter. Firstly, the data association of measurement-to-target is formulated as an integer programming problem. Through using the linear programming (LP) based branch-and-bound method and adjusting the constraint conditions, an optimal set integer programming (OSIP) algorithm is then proposed for tracking multiple non-maneuvering targets in clutter. For the case of maneuvering targets, this paper introduces the OSIP algorithm into the filtering step of the interacting multiple model (IMM) algorithm resulting in the IMM based on OSIP algorithm. Extensive Monte Carlo simulations show that the presented algorithms can obtain superior estimations even in the case of high density noises. [ABSTRACT FROM AUTHOR]