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This paper presents ABLA, a novel multiobjective ant colony-based optimization algorithm to address the bin packing problem with load balancing. ABLA incorporates (1) a new probabilistic decision rule that builds solutions by making use of individual pheromone matrices for each objective function; (2) a new pheromone updating approach in which ants deposit variable amounts of pheromone; (3) two new local search methods to improve load balancing: LBH and LBH-AB; and (4) the Pareto dominance approach to select optimal solutions. ABLA is compared to a Multiobjective Max-Min Ant System (MO-MMAS) and an adapted multiobjective version of the First-Fit Decreasing (FFD) algorithm, which is the best known ρ-approximation algorithm for the bin packing problem. Results show that ABLA finds better solutions than both FFD and MO-MMAS, and that LBH and LBH-AB noticeably improve the load balancing across bins.