Set-based Particle Swarm Optimisation for Dynamic Optimisation Problems

Many real-world optimisation problems are inherently dynamic, defined by changes in their underlying properties over time. Real-world problems also frequently require optimisation over discrete-valued decision variables. However, the solution of problems that are simultaneously dynamic and combinatorial remains a significant challenge, as limited prior research has addressed this intersection of characteristics. Most studies on dynamic optimisation focus on problems formulated with real-valued variables, where continuous population-based metaheuristics have emerged as the predominant class of solution methods. This thesis investigates the application of set-based particle swarm optimisation (SBPSO) to dynamic combinatorial optimisation problems and dynamic multivariate regression problems, which involve bilevel optimisation over both continuous and discrete domains. After a review of relevant optimisation theory and related literature, the thesis first investigates strategies that improve the computational efficiency of SBPSO for stationary multivariate polynomial regression. This initial study establishes a foundation for the practical extension of SBPSO to dynamic regression problems and for the integration of the algorithm into more sophisticated modelling frameworks. Theoretical and empirical analyses of the swarm behaviour of SBPSO are conducted and demonstrate that the swarm fails to converge in most practical scenarios. Although convergence generally proves detrimental in dynamic environments, the findings from these analyses are used to inform the design of adaptive mechanisms that continuously adapt the behaviour of the swarm based on the immediate state of the search process. The devised adaptive strategies are first evaluated on stationary multivariate polynomial regression problems. The best-performing adaptive SBPSO variant identified in this preliminary study is subsequently extended to detect and respond to changes in dynamic environments. This modified SBPSO variant is then evaluated against alternative population-based algorithms on two types of dynamic combinatorial optimisation problems, namely dynamic multidimensional knapsack and dynamic bit-matching problems. Additionally, three distinct SBPSO variants are evaluated across several dynamic multivariate regression problems. The results indicate that SBPSO generally outperforms the alternative population-based algorithms on the evaluated combinatorial problems, while the findings for the regression problems validate the contribution of the incorporated adaptive strategies to the performance of the algorithm.

Grantor dc:publisher

Stellenbosch : Stellenbosch University

Year dc:date.issued

2026

Author dc:creator

• Steyn, Gary Jared

Advisor dc:contributor.advisor

• Engelbrecht, A. P.

Language dc:language.iso

en

Repository record dc:identifier.uri

https://scholar.sun.ac.za/handle/10019.1/135798

OAI identifier oai:identifier

oai:scholar.sun.ac.za:10019.1/135798