Set-based particle swarm optimization for portfolio optimization

Thesis (MSc)--Stellenbosch University, 2021.ENGLISH ABSTRACT: Portfolio optimization is a complex problem, not only in the depth of the topics it covers but also in breadth. It is the process of determining which assets to include in a portfolio while simultaneously maximizing profit and minimizing risk. Portfolio optimization is rich with interesting research not only by researchers in finance, but also in computer science. The overlap of these fields has lead to an increase in the use of meta-heuristics to make intelligent investment decisions. This thesis conducts a thorough investigation into the current state of evolutionary and swarm intelligence algorithms for portfolio optimization. The investigation showed that these algorithms suffer from stability issues for larger portfolio optimization problems. A new approach using set-based particle swarm optimization (SBPSO) is proposed to reduce the dimensionality, and therefore complexity, of portfolio optimization problems. The results show that SBPSO is capable of obtaining good-quality solutions while being relatively fast. New set-based diversity measures are developed in order to better understand the exploration and exploitation behaviour of SBPSO, and set-based algorithms in general. It is shown that SBPSO fails to converge to a single solution and uses an inadequate process to determine the contribution of each asset to the portfolio. Based on these findings, improvements are made to the proposed SBPSO approach that yield significant gains in performance. The first multi-objective adaptation of SBPSO is also developed and is shown to scale to larger portfolio problems better than the multi-guided particle swarm optimization (MGPSO) algorithm, with lower levels of risk.AFRIKAANSE OPSOMMING: Portefeulje-optimering is 'n ingewikkelde probleem, nie net in die diepte van die onderwerp wat oorgesien word nie maar ook in geheel. Dit is die proses om vas te stel watter bates om in 'n portefeulje op te neem, terwyl gelyktydig die wins te maksimeer en risiko te minimeer. Portefeulje-optimalisering is ryk aan interessante navorsing nie net deur finansiële navorsers nie, maar ook in rekenaarwetenskap. Die oorvleueling van hierdie velde het gelei tot 'n toename in die gebruik van meta-heuristieke om intelligente beleggingsbesluite te neem. Hierdie tesis sluit 'n deeglike ondersoek in na die huidige stand van evolusie en swerm intelligensie algoritmes vir portefeulje-optimalisering. Die ondersoek het getoon dat hierdie algoritmes aan stabiliteitskwessies ly vir groter portefeuljeoptimalisering probleme. 'n Nuwe benadering met behulp van versameling gebaseerde deeltjieswerm optimering (SBPSO) word voorgestel om die dimensionaliteit, en dus die kompleksiteit, van portefeulje-optimaliseringsprobleme te verminder. Die resultate toon aan dat SBPSO in staat is om oplossings van goeie gehalte te verkry, terwyl dit relatief vinnig is. Nuwe versameling gebaseerde diversiteitsmaatreëls word ontwikkel vir die verkenning en ontginning van SBPSO, en versameling gebaseerde algoritmes in die algemeen. Daar word aangetoon dat SBPSO nie daarin slaag om op 'n enkele oplossing te konvergeer nie, en gebruik 'n onvoldoende proses om die bydrae van elke bate tot die portefeulje te bepaal. Op grond van hierdie bevindings word verbeteringe aan die voorgestelde SBPSO-benadering aangebring wat beduidende winste in prestasies lewer. Die eerste meervoudige doelwit aanpassing van SBPSO word ook ontwikkel, en daar word gewys dat dit beter skaal na groter portefeuljeprobleme as die meervoudige-gids deeltjieswerm optimering (MGPSO) algoritme, met laer risiko vlakke.Master