A total of 9 decision variables have been defined in the optimisation problem. These variables include parameters representing maintenance frequencies and large-scale interventions for each subsystem, as well as a width parameter representing the road geometry. Thanks to this structure, maintenance decisions have been evaluated not only in terms of timing but also in terms of their impact on material usage, energy consumption, and emissions.<\/p>\n\n\n\n
Objective functions represent the following engineering goals:<\/p>\n\n\n\n
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- Minimizing total maintenance time,<\/li>\n<\/ul>\n\n\n\n
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- Maximising the minimum time interval between interventions,<\/li>\n<\/ul>\n\n\n\n
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- Minimizing energy consumption, emissions (CO\u2082, NOx, SO\u2082) and total life cycle cost.<\/li>\n<\/ul>\n\n\n\n
These goals are inherently contradictory. For example, more frequent maintenance strategies can reduce operational uptime but increase environmental and economic burdens. Therefore, the problem requires identifying equilibrium solutions rather than a single \u201cbest\u201d solution.<\/p>\n\n\n\n
Evaluation of Optimization Results<\/strong><\/h2>\n\n\n\n
The conflicting nature of the defined objective functions necessitates evaluating optimization results not based on a single solution, but on the entire solution space. The results obtained in this context were analyzed using two main graphs to reveal the interaction between maintenance time, cost, and design decisions. Figures 1 and 2, presented below, illustrate in detail the equilibrium solutions resulting from multi-objective optimization and the engineering decisions that define these solutions.<\/p>\n\n\n\n
![\"\"](\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2026\/02\/Cost-duration-last-image.png\")
<\/a><\/figure>\n\n\n\nFigure 1 illustrates the relationship between total maintenance duration and total lifecycle cost for all candidate maintenance and design combinations. Each point in the figure represents a solution defined by different maintenance frequencies and design parameters, while the red points indicate Pareto-optimal solutions and the blue line represents the Pareto front.<\/p>\n\n\n\n
The graph reveals a non-linear trade-off relationship between total maintenance duration and total lifecycle cost. Very short maintenance durations are associated with higher costs due to intensive intervention strategies, while moderate increases in maintenance duration lead to a rapid stabilization and reduction in total cost. Solutions with shorter total maintenance time are often associated with higher costs. This is because maintaining high system performance requires more frequent and intensive maintenance interventions, resulting in increased material usage, energy consumption, and emissions. Beyond a certain maintenance duration threshold, total costs remain relatively stable, indicating diminishing economic benefits from further extending maintenance time.<\/p>\n\n\n\n
The clustering of Pareto-optimal solutions within a moderate maintenance duration range, combined with relatively low and stable cost values, demonstrates that both overly aggressive maintenance strategies and excessively delayed intervention approaches are not engineering-wise sound. In contrast, it appears that moderate and balanced maintenance strategies offer more rational and feasible solutions in terms of both system performance and cost. Overall, this result indicates that, from an engineering perspective, there is a balanced and viable solution range between system performance and economic and environmental efficiency.<\/p>\n\n\n\n
The figure 2 represents a comparative analysis of Pareto-optimal and non-Pareto-optimal solutions obtained from multi-objective optimization, based on the relationships between decision variables and output parameters. In the graph, red lines represent Pareto-optimal solutions, while blue lines represent other candidate solutions. This representation allows for a holistic assessment of how different combinations of maintenance and design decisions affect system performance in a multidimensional way.<\/p>\n\n\n\n
![\"\"](\"http:\/\/141.23.68.248\/wp\/wp-content\/uploads\/2026\/02\/Final-NSGA-1024x515.jpeg\")
<\/a><\/figure>\n\n\n\nThe graph clearly shows that Pareto-optimal solutions cannot be defined through a single decision variable. Instead, optimal solutions emerge as a result of specific combinations of maintenance frequencies, intervention timings, and geometric design decisions. Pareto-optimal solutions exhibit moderate and balanced configurations that avoid extreme values \u200b\u200bin terms of maintenance intervals (M_h, M_u) for highway and urban road systems, large-scale interventions (O_h, U_u), and decision variables related to drainage systems (C_d, R_d). In particular, Pareto-optimal solutions tend to focus around intermediate values \u200b\u200bin terms of total maintenance time and maintenance-intervention timing. This situation demonstrates that neither excessively frequent maintenance practices nor strategies that unnecessarily delay interventions produce optimal results at the system level. Similarly, decision variables related to the drainage system do not lean towards extreme values; they are positioned within balanced ranges that support integrated maintenance strategies, in harmony with surface and superstructure systems. This finding reveals that the drainage system, rather than being the sole determining factor in the optimization process, plays a complementary role in interaction with other infrastructure components.<\/p>\n\n\n\n
Engineering Perspective<\/strong><\/h2>\n\n\n\n
When Figures 1 and 2 are considered together, it is clear that maintenance planning is not merely a mathematical optimisation problem but rather a multidimensional decision-making process requiring engineering judgement. Pareto-optimal solutions offer a technically consistent and feasible space of solutions, rather than imposing a single \u201cbest\u201d solution on the decision-maker.<\/p>\n\n\n\n
The results obtained at this stage show that integrated maintenance planning requires a balanced approach between the objectives of operational continuity, environmental sustainability, and economic efficiency. The developed optimisation approach provides a powerful decision support framework that enables engineers to make informed, transparent, and technically consistent decisions under different priority scenarios.<\/p>\n\n\n\n
R code:<\/strong><\/h2>\n\n\n\n
Click below for Downloading R-Code File:<\/strong><\/code><\/pre>\n\n\n\nFinal R Code<\/a>Download<\/a><\/div>\n\n\n\nReferences:<\/strong><\/h2>\n\n\n\n
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- Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6<\/em>(2), 182\u2013197.<\/li>\n\n\n\n
- Miettinen, K. (1999). Nonlinear Multiobjective Optimization<\/em>. Boston: Springer.<\/li>\n\n\n\n
- Hakanen, J., Sahlstedt, K., & Miettinen, K. (2021). Multiobjective optimization and decision making in engineering design. Optimization and Engineering<\/em>.<\/li>\n\n\n\n
- Santos, J., Bryce, J., Flintsch, G., Ferreira, A., & Diefenderfer, B. (2017). A multi-objective optimization-based pavement management decision-support system. Journal of Cleaner Production, 164<\/em>, 1380\u20131393.<\/li>\n\n\n\n
- Chong, D., Wang, Y., Kendall, A., & Harvey, J. (2024). Multi-objective optimization for sustainable pavement maintenance planning considering life-cycle cost and environmental impacts. Sustainability, 16<\/em>(3).<\/li>\n\n\n\n
- International Organization for Standardization (ISO). (2006). ISO 14040: Environmental management \u2014 Life cycle assessment \u2014 Principles and framework<\/em>. Geneva: ISO.<\/li>\n\n\n\n
- International Organization for Standardization (ISO). (2006). ISO 14044: Environmental management \u2014 Life cycle assessment \u2014 Requirements and guidelines<\/em>. Geneva: ISO.<\/li>\n<\/ul>\n\n\n\n
\n\n\n Home<\/a> |\n individual systems<\/a> |\n integration context<\/a> |\n Maintenance Planning<\/a> |\n Maintenance Timelines<\/a> |\n Scenarios Exploration<\/a> |\n Sustainability Assessment<\/a> |\n System (Multi-Objective)-Optimization<\/a>\n<\/div>\n","protected":false},"excerpt":{"rendered":"The integrated maintenance, life cycle assessment (LCA), and cost model developed in previous stages have revealed a strong and inevitable interaction between maintenance duration, intervention intervals, environmental impacts, and economic performance. This interaction points toContinue reading<\/a><\/p>\n","protected":false},"author":293,"featured_media":0,"parent":24384,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-26166","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/26166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/users\/293"}],"replies":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26166"}],"version-history":[{"count":14,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/26166\/revisions"}],"predecessor-version":[{"id":28168,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/26166\/revisions\/28168"}],"up":[{"embeddable":true,"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=\/wp\/v2\/pages\/24384"}],"wp:attachment":[{"href":"http:\/\/141.23.68.248\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Miettinen, K. (1999). Nonlinear Multiobjective Optimization<\/em>. Boston: Springer.<\/li>\n\n\n\n
- Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6<\/em>(2), 182\u2013197.<\/li>\n\n\n\n
- Minimizing energy consumption, emissions (CO\u2082, NOx, SO\u2082) and total life cycle cost.<\/li>\n<\/ul>\n\n\n\n
- Maximising the minimum time interval between interventions,<\/li>\n<\/ul>\n\n\n\n