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In this paper, three heuristic solution algorithms, (the Dive-and-Fix method, the Ratio-cluster method, and the Cumulative-departure method) are specially designed to solve the traffic signal control problem formulated as a 0-1 mixed-integer linear programming problem with cell transmission model. These three solution algorithms are based on two fundamental approaches. First, the 0-1 mixed-integer linear program is solved via linear relaxation (LR). Second, the non-integer solutions obtained from the LR are converted into the integer solutions by taking advantage of the underlying physical mechanism embedded in the LR solutions that lead to the optimal signal control. In particular, proportional capacities for different approaches and the cumulative exit flow at each intersection obtained from the LR solutions are utilized to determine green time allocation for each approach. It is demonstrated that the near-optimal solutions obtained with these algorithms are very close to the optimal solutions under both uncongested and congested traffic conditions.