Stock market index tracking is a typical multi-objective optimization problem among conflicting objectives. The authors of this paper introduce a “heuristic searching approach on [the] construction of a tracking portfolio, which is able to get the average market return and can even outperform some hedge funds that are managed actively.” According to the authors, “the mathematical model … proposed is based on a hybrid genetic algorithm with a self-adaptive evolving mechanism.”

In section 2, they show how different methods (goal programming and genetic algorithms) can be combined for the general solution. This section also provides a very interesting discussion on how the general framework is applied to the specific problem domain. By careful introduction and placement of important notions of the domain, the complex method can be made efficient for the application area. Section 3 covers concrete parameterization of the algorithm, experimental results, and comparisons to other systems.

Once the parameters have been carefully determined, the combined method is automatic. Its flexibility is assured by the genetic algorithm and the adaptive complex constraints that guide it. Results and comparisons show the convergence and the efficiency of the solution for the selected three concrete markets. However, in general, the convergence and efficiency of the algorithm have yet to be proved. This will require a more precise specification of the application domain and the generalization of some constraints.

The authors do not give a hint about implementation details, such as platform, packages, language of application, and so on. Some readers may be bothered by the grammatical errors, but the meaning of the awkward sentences remains clear.

I recommend the paper not only to readers working on stock index tracking, but also to those interested in combining different methods and determining domain-specific adaptive constraints for solving multi-objective optimization problems.