A pragmatic approach to multi-objective optimisation for portfolio asset management

Abstract

Among the reliability engineering and asset management problems addressed in the literature, those pertaining to multi-unit systems have particularly intrigued researchers because of their profound effects on the organisational performance. Despite impressive strides made in improving maintenance planning for assets of a single type, only a paucity of research has delved into a pragmatic approach to managing an asset portfolio — a system of heterogeneous assets. Specifically, existing portfolio management studies readily assume inter-asset performance independence due to the formulation complexity. Budget allocation across different asset types is one of the most prevalent problem classes in the portfolio management literature. Although assets in a portfolio are associated with different maintenance options and performance metrics, they are all under the control of a single entity and compete for central budget. This problem is inherently multi-objective as it entails multiple performance metrics are not directly comparable. Approaches adopted in existing portfolio management studies either consolidate multiple goals to form a single objective (a priori) or populate the entire Pareto optimal set (a posteriori). Nonetheless, neither of these methods adequately address the problem. While the a priori method relies heavily on subjective judgment of a decision maker (DM) to accommodate incommensurable objectives, the a posteriori method often delivers a Pareto optimal set with too many options, making it counter-productive. This thesis is dedicated to developing a pragmatic approach to a portfolio budget allocation problem with an objective to deliver the DM with a diverse yet compact solution set. To model intricate inter-asset performance dependence within an asset type, polynomial and Gaussian radial basis functions were employed to capture the relationship between intervention investment and collective performance of assets. The use of these approximation functions, coupled with newly proposed solution adjustment and validation operations, was proved to be applicable to any continuous multi-objective evolutionary algorithm (MOEA), thereby facilitating the efficient optimisation across different asset types. To overcome the limitations of the a posteriori method, the K-means and K-medoids methods were applied to pruning Pareto optimal solutions obtained from a selected MOEA. We also presented two novel indicators based on average Euclidean distance and cosine similarity metrics. The application of these indicators not only enabled the DM to objectively measure the relative diversity of the pruned solutions but also offered guidance on choosing the appropriate number of such solutions. The findings were corroborated by three numerical examples including a practical case in a rail network. Through these examples, the proposed approach was demonstrated to produce a pruned solution set that maintains high integrity of the Pareto front.