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One particular challenging environment for multicast is a mobile ad-hoc network (MANET). Existing studies show that tree-based and mesh based on-demand protocols are not necessarily the best choice, since associated overhead will be more. Several algorithms based on the ant colony optimization (ACO) approach minimizes the cost of the tree under multiple constraints. These algorithms treat the traffic engineering multicast problem as a single-purpose problem with several constraints. The main disadvantage of this approach is the necessity of a predefined upper bound that can exclude good trees from the final solution. This paper presents a design on ant-colony based multicast routing (AMR) algorithm for MANETs, to solve the traffic Engineering multicast problem that optimizes several objectives simultaneously. The algorithm calculates one more additional constraint in the cost metric, which is the product of average-delay and the maximum depth of the multicast tree and try to minimize this combined cost metric. Simulation results show that the proposed algorithm outperforms all previous algorithms by forming the multicast tree with varying sizes.