  Several real-world applications could be modeled as Mixed-Integer Non-Linear
Programming (MINLP) problems, and some prominent examples include portfolio
optimization, remote sensing technology, and so on. Most of the models for
these applications are non-convex and always involve some conflicting
objectives. The mathematical and heuristic methods have their advantages in
solving this category of problems. In this work, we turn to Multi-Objective
Evolutionary Algorithms (MOEAs) for finding elegant solutions for such
problems. In this framework, we investigate a multi-objective constrained
portfolio optimization problem, which can be cast as a classical financial
problem and can also be naturally modeled as an MINLP problem. Consequently, we
point out one challenge, faced by a direct coding scheme for MOEAs, to this
problem. It is that the dependence among variables, like the selection and
weights for one same asset, will likely make the search difficult. We thus,
propose a Compressed Coding Scheme (CCS), compressing the two dependent
variables into one variable to utilize the dependence and thereby meeting this
challenge. Subsequently, we carry out a detailed empirical study on two sets of
instances. The first part consists of 5 instances from OR-Library, which is
solvable for the general mathematical optimizer, like CPLEX, while the
remaining 15 instances from NGINX are addressed only by MOEAs. The two
benchmarks, involving the number of assets from 31 to 2235, consistently
indicate that CCS is not only efficient but also robust for dealing with the
constrained multi-objective portfolio optimization.
