In this paper, we perform theoretical analysis and experiments on the Simplex Crossover (SPX), which we have proposed. Real-coded GAs are expected to be a powerful function optimization technique for real-world applications where it is often hard to formulate the objective function. However, we believe there are two problems which will make such applications difficult; 1) performance of real-coded GAs depends on the coordinate system used to express the objective function, and 2) it costs much labor to adjust parameters so (...) that the GAs always find an optimum point efficiently. The result of our theoretical analysis and experiments shows that a performance of SPX is independent of linear coordinate transformation and that SPX always optimizes various test function efficiently when theoretical value for expansion rate, which is a parameter of SPX, is applied. We also show that BLX-α is equivalent to degenerate form of SPX. Experiments show that we have something misunderstood effect of epistasis on performance degradation of real-coded GAs. (shrink)

This article studies the treatment effect models in which individuals are classified into unobserved groups based on heterogeneous treatment rules. By using a finite mixture approach, we propose a marginal treatment effect framework in which the treatment choice and outcome equations can be heterogeneous across groups. Under the availability of instrumental variables specific to each group, we show that the MTE for each group can be separately identified. On the basis of our identification result, we propose a two-step semiparametric procedure (...) for estimating the group-wise MTE. We illustrate the usefulness of the proposed method with an application to economic returns to college education. (shrink)