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.
翻译:几个真实世界应用可以模拟为混合- 内向非内向编程( MINLP) 问题, 一些突出的例子包括组合优化、 遥感技术等等。 这些应用的模型大多是非混凝土, 并且总是涉及一些相互矛盾的目标。 数学和重力方法在解决这类问题方面有其优势。 在这项工作中, 我们转向多目标进化算法( MOEAs), 以找到解决这些问题的优雅的解决方案。 在这个框架内, 我们调查一个多目标的有限组合优化问题, 这个问题可以作为一个典型的财务问题, 也可以自然地模拟成一个MILP问题。 因此, 我们指出一个挑战, 由MOEAs直接编码方案面对的难题。 数学和重心法方法的变量之间的依赖性可能会使搜索变得困难。 因此, 我们建议一个压缩的编码计划( CCSCS), 将两种依赖性的变量压缩成一个变量, 而不是一个典型的组合35, 我们从数学模型中进行一个详细的经验研究。