142 Part III: Maintenance optimisation of multi-state components Multi-objective optimisation Multi-objective optimisation aims to optimise multiple, often conflicting, objectives simultaneously. João A. Zeferino and Cunha, 2010 addresses the minimisation of capital and operating maintenance costs, alongside the maximisation of dissolved oxygen, by employing a weighting method and a simulated annealing algorithm. Yang and Su, 2007 investigates sewer rehabilitation to achieve high e!ectiveness with minimal costs, utilising multi-objective genetic algorithms (GA). Similarly, Marzouk and Ibrahim, 2013 considers the condition of sewer networks and life-cycle maintenance costs as distinct objectives, integrating Monte Carlo simulations, discrete-time Markov chains for degradation modelling, and multi-objective genetic algorithms to identify optimal maintenance strategies. Furthermore, Elmasry, Zayed, and Hawari, 2019 focus on enhancing sewer inspection strategies by optimising inspection times, costs, and frequencies through Mixed Integer Linear Programming (MILP), demonstrating superior performance over GA. Based on Markov decision processes AMarkov decision process is a widely used mathematical framework for modelling decision-making, also with applications in MPO. Abraham, Wirahadikusumah, Short, et al., 1998 employs deterministic dynamic programming to determine optimal strategies for sewer rehabilitation. Wirahadikusumah, Abraham, and Castello, 1999 models the rehabilitation of sewer networks as an MDP, incorporating life-cycle cost analysis and sewer network deterioration through discrete-time Markov chains, and addresses the problem using dynamic programming alongside the policy improvement algorithm. Further, Wirahadikusumah and Abraham, 2003 utilises probabilistic dynamic programming for sewer maintenance and rehabilitation, focusing on constraints to enhance the understanding of sewer life-cycle costs. Considering sewer network structure Moving towards system-level analysis, studies that explicitly model network structure and augment the optimisation problem with features relevant to system-level analysis are distinguished. R. A. Fenner, Sweeting, and Marriott, 2000 proposes a method that combines Geographical Information Systems (GIS) tools, risk analysis and Bayesian statistics. Similarly, Inanloo, Tansel, Shams, et al., 2016 GIS-based risk assessment, integrating component failure probabilities, consequences, and potential interactions with other infrastructure networks for a comprehensive asset management analysis of transport, water, and sewer network systems. Hamid Zaman and Lorentz, 2017 tackles the schedule optimisation issue by framing it within the context of combinatorial optimisation and addressing it through genetic and heuristic algorithms. Qasem and Jamil, 2021 applies GIS-based financial analysis for integrated maintenance, rehabilitation, and replacement planning for water, sewer, and road networks. Kerkkamp, Bukhsh, Y. Zhang, et al., 2022 employs
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