Efforts to apply economic complexity to identify diversification opportunities often rely on diagrams comparing the relatedness and complexity of products, technologies, or industries. Yet, the use of these diagrams, is not based on empirical or theoretical evidence supporting some notion of optimality. Here, we introduce a method to identify diversification opportunities based on the minimization of a cost function that captures the constraints imposed by an economy's pattern of specialization and show that this ECI optimization algorithm produces recommendations that are substantially different from those obtained using relatedness-complexity diagrams. This method advances the use of economic complexity methods to explore questions of strategic diversification.