Averbakh, I., & Pereira, J. (2018). Lateness Minimization in Pairwise Connectivity Restoration Problems. INFORMS J. Comput., 30(3), 522–538.
Abstract: A network is given whose edges need to be constructed (or restored after a disaster). The lengths of edges represent the required construction/restoration times given available resources, and one unit of length of the network can be constructed per unit of time. All points of the network are accessible for construction at any time. For each pair of vertices, a due date is given. It is required to find a construction schedule that minimizes the maximum lateness of all pairs of vertices, where the lateness of a pair is the difference between the time when the pair becomes connected by an already constructed path and the pair's due date. We introduce the problem and analyze its structural properties, present a mixedinteger linear programming formulation, develop a number of lower bounds that are integrated in a branchandbound algorithm, and discuss results of computational experiments both for instances based on randomly generated networks and for instances based on 2010 Chilean earthquake data.

Averbakh, I., & Pereira, J. (2021). Tree optimization based heuristics and metaheuristics in network construction problems. Comput. Oper. Res., 128, 105190.
Abstract: We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than its travel speed, so relocation times are negligible with respect to construction times. It is required to find a construction schedule that minimizes a nondecreasing function of the times when various connections of interest become operational. Most problems of this class are strongly NPhard on general networks, but are often treeefficient, that is, polynomially solvable on trees. We develop a generic local search heuristic approach and two metaheuristics (Iterated Local Search and Tabu Search) for solving treeefficient network construction problems on general networks, and explore them computationally. Results of computational experiments indicate that the methods have excellent performance.
