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The bin packing problem is widely found in applications such as loading of tractor trailer trucks, cargo airplanes and ships, where a balanced load provides better fuel efficiency and safer ride. In these applications, there are often conflicting criteria to be satisfied, i.e., to minimize the bins used and to balance the load of each bin, subject to a number of practical constraints. Unlike existing studies that consider only the minimization of bins, a two-objective mathematical model for the bin packing problem with multiple constraints is formulated in this paper. Without the need of combining both objectives into a composite scalar, a hybrid multiobjective particle swarm optimization algorithm (HMOPSO) incorporating the concept of Pareto's optimality to evolve a family of solutions along the trade-off is proposed. The algorithm is also featured with bin packing heuristic, variable length representation, and specialized mutation operator to solve the multiobjective and multi-model combinatorial bin packing problem. Extensive simulations are performed on various test instances, and their performances are compared both quantitatively and statistically with other optimization methods. Each of the proposed features is also explicitly examined to illustrate their usefulness in solving the multiobjective bin packing problem.