Solving the length constrained <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"><mml:mi>K</mml:mi></mml:math>-drones rural postman problem

In this paper we address the Length Constrained K-Drones Rural Postman Problem (LC K-DRPP). This is a continuous optimization problem where fleet of homogeneous drones have to jointly service (traverse) set (curved or straight) lines network. Unlike vehicles in classical arc routing problems, drone can enter line through any its points, portion that line, exit another then travel directly point on and so on. Moreover, since range restricted, length each route limited by maximum distance. Some applications for problems include inspection pipelines, railway power transmission traffic monitoring. To deal with problem, LC K-DRPP instances are digitized approximating polygonal chain finite number points allowing only at these points. way obtain an instance K-vehicles K-RPP). If used discretize large, K-RPP be extremely large and, hence, very difficult solve optimally. Even heuristic algorithms fail providing feasible solutions reasonable computing times. An alternative generate smaller few but “significant” segments. We present formulation some valid inequalities K-RPP. Based this, designed implemented branch-and-cut algorithm solution. order capable good instances, propose matheuristic begins finding obtained single segment. Then, find better solutions, promising intermediate sequentially incorporated. Extensive computational experiments assess performance both performed several sets from literature.