Utilizing dependence among variables in evolutionary algorithms for mixed-integer programming: A case study on multi-objective constrained portfolio optimization.

• The paper shows the challenge of a direct coding scheme in portfolio optimization. • The paper proposes a compressed coding scheme to deal with mixed variables. • The paper introduces some search operators for portfolio optimization. • The scheme and operators are integrated into three main kinds of algorithms. • Statistical results on 20 instances have shown the superiority. Mixed-Integer Non-Linear Programming (MINLP) is not rare in real-world applications such as portfolio investment. It has brought great challenges to optimization methods due to the complicated search space that has both continuous and discrete variables. This paper considers the multi-objective constrained portfolio optimization problems that can be formulated as MINLP problems. Since each continuous variable is dependent to a discrete variable, we propose a Compressed Coding Scheme (CCS), which encodes the dependent variables into a continuous one. In this manner, we can reuse some existing search operators and the dependence among variables will be utilized while the algorithm is optimizing the compressed variables. CCS actually bridges the gap between the portfolio optimization problems and the existing optimizers, such as Multi-Objective Evolutionary Algorithms (MOEAs). The new approach is applied to two benchmark suites, involving the number of assets from 31 to 2235. The experimental results indicate that CCS is not only efficient but also robust for dealing with the multi-objective constrained portfolio optimization problems. [ABSTRACT FROM AUTHOR]