This paper provides an overview of the state-of-the art and the current research trends concerning shortest paths problem on dynamic graphs. The discussion is divided in two main topics: reoptimization and time-dependent shortest paths. Reoptimization consists in the solution of a sequence of shortest path problems in which each instance slightly differs from the previous one. The reoptimization tackles this problem wisely using information stored in an optimal solution previously computed. On the other hand, shortest path problems on time-dependent graphs are characterized by a weight function which not only depends upon the arcs but changes in time according to a certain time horizon.

Several variants of the classical Constrained Shortest Path Problem have been presented in the literature so far. One of the most recent is thek-Color Shortest Path Problem( $$k$$k -CSPP), that arises in the field of transmission networks design. The problem is formulated on a weighted edge-colored graph and the use of the colors as edge labels allows to take into account the matter of path reliability while optimizing its cost. In this work, we propose a dynamic programming algorithm and compare its performances with two solution approaches: a Branch and Bound technique proposed by the authors in their previous paper and the solution of the mathematical model obtained with CPLEX solver. The results gathered in the numerical validation evidenced how the dynamic programming algorithm vastly outperformed previous approaches.

The growing importance of state assessments in civil engineering has led to intensive research into the development of damage identification methods based on vibrations. Natural frequencies and modal shapes have garnered great interest because modal parameters are invariant of structure. Moreover, thanks to the global nature of modal parameters, their variations are not limited to the location of the damage. This is an important advantage that offers the opportunity to identify damage with sensors whose position does not have to coincide with the damaged area. The integration of MEMS sensors into structural health monitoring (SHM) systems offers a promising approach to long-term structural maintenance, especially in large-scale infrastructure. This paper presents an anomaly detection technique that analyzes raw sequential data within a statistical framework to detect damage that causes prestress loss of the tendon by exploiting a distributed monitoring system composed of six high-performance MEMS sensors. The proposed system is preliminarily evaluated to identify the frequency of the first mode, and then the proposed methodology is validated on acceleration data collected on a 240 cm beam in three different damage configurations, achieving a high detection accuracy and showing that its output can also evaluate the damage localization.

Designing maintenance strategies for a vast portfolio of aging infrastructures requires decision-makers to ensure adequate safety levels while addressing the requirements on service interruptions, costs, and workforce availability. This study addresses the problem of scheduling maintenance interventions for a portfolio of bridges, aiming to minimize $C{O}_2$ emissions while meeting minimum reliability requirements and adhering to workforce and budget constraints. To achieve this, we present a Simheuristic algorithm that combines a metaheuristic core based on the Adaptive Large Neighborhood Search metaheuristic with a Monte Carlo simulation module. This integration allows for the evaluation of optimized scheduling solutions, accounting for the inherent randomness in the structural deterioration process. The proposed approach is tested in a comparative analysis against traditional time-based and condition-based scheduling methods. Results from diverse bridge portfolios demonstrate that the proposed algorithm offers improved performance in terms of both total costs and $C{O}_2$ emissions.