Werry Febrianti, Novriana Sumarti, Achmad Suryadi Nasution, Andi Fitriawati, Desi Era P. Siregar, Yolanda Sari S.
This research investigates ESG-constrained mean-variance portfolio optimization by incorporating buy-in threshold constraints using data from the Indonesian stock market. The optimization problem is formulated as a mixed-integer nonlinear programming (MINLP) model, which captures both the discrete investment decisions and the nonlinear nature of risk-return trade-offs. To solve this complex model, the spiral optimization algorithm (SOA) is employed due to its flexibility and efficiency in handling constrained optimization problems. The performance of SOA is benchmarked against other well -known metaheuristic algorithms, namely Particle Swarm Optimization (PSO) and Grey Wolf Optimizer (GWO), using portfolios consisting of 5 and 10 ESG-compliant stocks. Based on the empirical results for 5 stocks, we show that SOA gives the same results with PSO and GWO results. Meanwhile for 10 stocks, SOA gives consistent results than the results of PSO and GWO. Therefore, we conclude that SOA can be used in small number of stocks or extended stocks in solving this ESG-portfolio problems. Copyright: © 2026 by the author(s). Licensee Pandawa Institute, Metro, Indonesia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/4.0/
Mathematics Department, Institut Teknologi Sumatera, South Lampung, 35365, Indonesia; Industrial and Financial Mathematics Research Group, Institut Teknologi Bandung, Bandung, 40132, Indonesia; Actuarial Science Department, Institut Teknologi Sumatera, South Lampung, 35365, Indonesia