Optim Lett (2016) 10:169–180 DOI 10.1007/s11590-015-0913-4 ORIGINAL PAPER A metaheuristic framework for Nonlinear Capacitated Covering Problems Enrico Malaguti 1 · Rosa Medina Durán 2 · Paolo Toth 1 Received: 20 May 2014 / Accepted: 12 June 2015 / Published online: 25 June 2015 © Springer-Verlag Berlin Heidelberg 2015 Abstract Several relevant optimization problems can be formulated as generaliza- tions of Capacitated Covering Problems, by considering a cost function that combines a linear term with a nonlinear one. In this paper we introduce the Staircase Capacitated Covering Problem, where the nonlinear term has a staircase shape, and we propose a framework based on a Metaheuristic algorithm for solving problems having this formulation. The performance of the Metaheuristic algorithm in solving the Stair- case Capacitated Covering Problem is evaluated on a set of instances derived from an industrial application, and it is compared with a linearized formulation of the problem solved by CPLEX. In particular, the experiments show that the former produces better solutions in the same computing time. Keywords Integer nonlinear programming · Capacitated Covering Problems · Metaheuristic algorithm 1 Introduction In the Set Covering Problem, we are given a set I of m elements and a collection S of n subsets, each subset s ∈ S with an associated positive cost c s ; the problem is to B Enrico Malaguti enrico.malaguti@unibo.it Rosa Medina Durán rosmedina@udec.cl Paolo Toth paolo.toth@unibo.it 1 DEI, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy 2 Departamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad de Concepción, Concepción, Chile 123