In this work, we propose an optimization scheme based on a multi-objective Genetic Algorithm (GA) for the design of orthogonal filter banks for speech compression. A parameterization is adopted to assure that the resulting filter banks satisfy perfect reconstruction and have at least two vanishing moments. We search for a parameter set that optimizes the coding gain and the frequency selectivity. As the objectives are conflicting, we investigate the solution that realizes the best compromise between the objectives criteria using the Non-dominated Sorting Genetic Algorithm (NSGAIII). Experimental results have shown that the optimized filter banks provide a significant gain in coding performances when comparing with the Daubechies orthogonal filter banks for test speech signals.