Epoch-based Application of Problem-Aware Operators in a Multiobjective Memetic Algorithm for Portfolio Optimization

TL;DR

This work tackles the intensification/diversification trade-off in multiobjective portfolio optimization with cardinality constraints by deploying problem-aware operators guided by the Sharpe index within a memetic algorithm built on IBEA. The authors introduce an epoch-based framework that alternates between unbiased search and Sharpe-driven refinement, using local search and elite memory as problem-aware operators. Through sensitivity analyses and comparisons with non-memetic MOEAs, the approach demonstrates robustness to parameter settings and often yields superior Sharpe index performance while remaining competitive on hypervolume and generational distance. The study suggests that simple epoch-based scheduling can effectively steer searches toward Sharpe-optimal regions, with potential extensions to adaptive strategies and other datasets.

Abstract

We consider the issue of intensification/diversification balance in the context of a memetic algorithm for the multiobjective optimization of investment portfolios with cardinality constraints. We approach this issue in this work by considering the selective application of knowledge-augmented operators (local search and a memory of elite solutions) based on the search epoch in which the algorithm finds itself, hence alternating between unbiased search (guided uniquely by the built-in search mechanics of the algorithm) and focused search (intensified by the use of the problem-aware operators). These operators exploit Sharpe index (a measure of the relationship between return and risk) as a source of problem knowledge. We have conducted a sensibility analysis to determine in which phases of the search the application of these operators leads to better results. Our findings indicate that the resulting algorithm is quite robust in terms of parameterization from the point of view of this problem-specific indicator. Furthermore, it is shown that not only can other non-memetic counterparts be outperformed, but that there is a range of parameters in which the MA is also competitive when not better in terms of standard multiobjective performance indicators.

Figures (2)

• Figure 1: Flowchart of the memetic approach considered
• Figure 2: Depiction of the combined Pareto fronts of MA$_{0,40}^{1,1}$ and HypE. The left plot shows the fronts achieved in the biobjective space. The middle and right plots show the Sharpe index for each solution in the front as a function of risk (middle) and performance (left).