This study presents a seasonal multi-product multi-period inventory control model with inventory costs obtained under inflation and all-unit discount policy. The products are delivered in boxes of known quantities and both backorder and lost-sale quantities are considered in case of shortage. The goal is to find a representative set of Pareto optimal solutions (including the ordering quantities) in different periods and to minimize both the total inventory cost (i.e. ordering, holding, shortage, and purchasing costs) and the total storage space, simultaneously. Three multi-objective optimization algorithms of non dominated sorting genetic algorithm (NSGA-II), non-dominated ranked genetic algorithm (NRGA), and multi-objective particle swarm optimization (MOPSO) are proposed to solve the problem. The Taguchi approach with a novel metric (based on the coefficient of variation) is utilized to model the response variable and compare the performances of the algorithms. Three numerical examples are used to demonstrate the applicability and exhibit the efficacy of the procedures and algorithms. The results of statistical analyses show significant differences in the performance metrics for all three algorithms and in all three numerical examples.