A level-based learning swarm optimizer with a hybrid constraint-handling technique for large-scale portfolio selection problems

This paper proposes a variant of the dynamic level-based learning swarm optimizer algorithm for solving large-scale constrained portfolio optimization problems. More specifically, we aim to maximize the inner rate of risk aversion, a recently proposed performance measure that incorporates higher moments of the portfolio return distribution and disaster risk. Our portfolio design includes cardinality, box, and budget constraints; an upper bound for the portfolio turnover maintains a control on the transaction costs during rebalancing phases. The algorithm uses a compressed coding scheme to encode the dependent variables into continuous ones to handle portfolio cardinalities. A repair operator deals with box and budget constraints, and an adaptive penalty function approach is used for the turnover constraint. The profitability of the developed investment strategy is tested using data from the MSCI World Index. The out-of-sample results show that our approach can consistently outperform the benchmark index and the cardinality constrained mean-variance model.