Large-Scale Portfolio Optimization Problem Under Cardinality Constraint With Enhanced Multi-Objective Evolutionary Algorithms
2026-07-10 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and ScienceArtificial Intelligence
AI summaryⓘ
The authors address the challenge investors face when deciding how to allocate money across many financial assets. They focus on improving portfolio optimization, which becomes very hard to solve exactly when real-world rules limit how many assets can be chosen. To tackle this, they create new methods to speed up and improve evolutionary algorithms, including unique ways to represent solutions and combine them. Testing their approach shows it finds good investment mixes faster than traditional methods without losing quality, even as markets include more assets.
portfolio optimizationmulti-objective evolutionary algorithmscardinality constraintNP-hard problemsconvergence ratesolution representationmating strategiesrepair mechanismsfinancial marketsbenchmark testing
Authors
Danial Ramezani, Mostafa Abouei Ardakan
Abstract
Decision-making is posing an increasingly formidable challenge to investors because of the growing number of alternatives available in financial markets. A hot area of research over the past few decades has been portfolio optimization that seeks to determine how much an investor should invest in which asset. Introducing real-world conditions to the optimization model turns the problem into an NP-hard one for whose solution exact methods become inefficient; hence, researchers have turned to evolutionary algorithms to approximate solutions. In this paper, strengthening strategies are presented for multi-objective evolutionary algorithms that can provide a faster convergence rate and extensive search ability in the portfolio optimization problem under the cardinality constraint. To implement those features, a unique solution representation, a novel operator, and new repair mechanisms are introduced for solving the aforementioned problem in which lower and upper limits are set on the number of assets in the portfolio. For this purpose, new mating strategies along with the aforesaid package are implemented in well-known multi-objective evolutionary algorithms to solve the problem. The customized algorithms are subsequently tested against traditional ones using well-known market indices as benchmarks. Results indicate that the proposed strategy not only provides better approximations but also converges faster as well at no loss of performance with an increasing number of assets in the market.