A Bi-Objective Markov Decision Process Design approach to redundancy allocation with dynamic maintenance for a parallel system
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918189615546368 |
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| author | Fairley, Luke Shone, Rob Jacko, Peter Huang, Jefferson |
| author_facet | Fairley, Luke Shone, Rob Jacko, Peter Huang, Jefferson |
| contents | The reliability of a system can be improved by the addition of redundant elements, giving rise to the well-known redundancy allocation problem (RAP). We propose a novel extension to the RAP called the Bi-Objective Integrated Design and Dynamic Maintenance Problem (BO-IDDMP) which allows for future dynamic maintenance decisions to be incorporated. This leads to a problem with first-stage redundancy design decisions and second-stage sequential maintenance decisions under uncertainty. To the best of our knowledge, this is the first use of a continuous-time Markov Decision Process Design framework to formulate a problem with non-trivial dynamics, as well as its first use alongside bi-objective optimization. A general heuristic optimization methodology for bi-objective MDP Design problems is developed, and then applied to the BO-IDDMP. The efficiency and accuracy of our methodology are demonstrated against an exact mixed-integer linear programming solver. The heuristic is shown to be orders of magnitude faster in the majority of cases, and in only 2 out of 84 cases produces a solution that is dominated by the exact method. The inclusion of dynamic maintenance policies is shown to yield stronger and better-populated Pareto fronts, allowing more flexibility for the decision-maker. The impacts of varying parameters unique to our problem are also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12944 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Bi-Objective Markov Decision Process Design approach to redundancy allocation with dynamic maintenance for a parallel system Fairley, Luke Shone, Rob Jacko, Peter Huang, Jefferson Optimization and Control The reliability of a system can be improved by the addition of redundant elements, giving rise to the well-known redundancy allocation problem (RAP). We propose a novel extension to the RAP called the Bi-Objective Integrated Design and Dynamic Maintenance Problem (BO-IDDMP) which allows for future dynamic maintenance decisions to be incorporated. This leads to a problem with first-stage redundancy design decisions and second-stage sequential maintenance decisions under uncertainty. To the best of our knowledge, this is the first use of a continuous-time Markov Decision Process Design framework to formulate a problem with non-trivial dynamics, as well as its first use alongside bi-objective optimization. A general heuristic optimization methodology for bi-objective MDP Design problems is developed, and then applied to the BO-IDDMP. The efficiency and accuracy of our methodology are demonstrated against an exact mixed-integer linear programming solver. The heuristic is shown to be orders of magnitude faster in the majority of cases, and in only 2 out of 84 cases produces a solution that is dominated by the exact method. The inclusion of dynamic maintenance policies is shown to yield stronger and better-populated Pareto fronts, allowing more flexibility for the decision-maker. The impacts of varying parameters unique to our problem are also investigated. |
| title | A Bi-Objective Markov Decision Process Design approach to redundancy allocation with dynamic maintenance for a parallel system |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.12944 |