Submodular maximization of concave utility functions composed with a set-union operator with applications to maximal covering location problems

Abstract We study a family of discrete optimization problems asking for the maximization expected value concave, strictly increasing, and differentiable function composed with set-union operator. The is computed respect to set coefficients taking values from scenarios. models utility decision maker, while operator covering relationship between two ground sets, items metaitems. This problem generalizes introduced by Ahmed S, Atamtürk A (Mathematical programming 128(1-2):149–169, 2011), it can be modeled as mixed integer nonlinear program involving binary variables associated Its goal find subset metaitems that maximizes total corresponding covers. It has applications to, among others, maximal location, influence problems. In paper, we propose double-hypograph decomposition which allows projecting out separately exploiting structural properties Thanks it, linearized via an exact outer-approximation technique, whereas in ways: either ( i ) reformulation based on submodular cuts, or ii Benders decomposition. analyze theoretical perspective strength inequalities resulting reformulations, embed them into branch-and-cut algorithms. also show how extend our reformulations case where not necessarily increasing. then experimentally compare algorithms inter se , standard state-of-the-art global-optimization solver, greedy algorithm function. results reveal that, testbed, method combining outer approximation cuts significantly outperforms other ones.