Improving multi-objective evolutionary algorithms using Grammatical Evolution

Multi-objective evolutionary algorithms (MOEAs) have become an effective choice to solve multi-objective optimization problems (MOPs). However, it is well known that Pareto dominance-based MOEAs struggle in MOPs with four or more objective functions due to a lack of selection pressure in high dimensional spaces. The main choices for dealing with such problems are decomposition-based and indicator-based MOEAs. In this work, we propose the use of Grammatical Evolution (an evolutionary computation search technique) to generate functions that can improve decomposition-based and indicator-based MOEAs. Namely, we propose a methodology to generate new scalarizing functions, which are known to have a great impact in the performance of decomposition-based MOEAs and in some indicator-based MOEAs. Additionally, we propose another methodology to generate hypervolume approximations, since the hypervolume is a popular performance indicator used not only in indicator-based MOEAs but also to assess performance of MOEAs. Using our first methodology, we generate two new scalarizing functions and provide their corresponding experimental validation to show that they exhibit a competitive behavior when compared against some well-known scalarizing functions such as ASF, PBI and the Tchebycheff scalarizing function. Using our second methodology, we produce 4 different hypervolume approximations and compare their performance against the Monte Carlo method and against two other state-of-the-art hypervolume approximations. The experimental results show that our functions exhibit a good compromise in terms of quality and execution time.