@techreport{795b6c0cc7bc4ced9d6ba6d9409866be,

title = "A Renewed Take on Weighted Sum in Sandwich Algorithms: Modification of the Criterion Space",

abstract = "Sandwich algorithms are commonly used to approximate the Pareto front of a multiobjective (MO) convex problem by enclosing it between an inner and outer approximation. By iteratively improving the approximations, the distance between them is minimized which gives an estimate of how well the Pareto front is approximated. A wellexplainable type of sandwich algorithm is based on weighted sum scalarization (WSS), where the next set of weights is determined by the most promising inner normal of the inner approximation. As these normals can contain negative values, not every optimization will result in finding an efficient point. In order to reduce the number of searches towards the dominated part, we propose an elegant modification of the criterion space which is an advancement on the formulation of Solanki et al. In addition to being well-explainable and easy to integrate within an existing optimization procedure, this modification is theoretically able to obtain all nondominated points of an MO linear programming problem in a finite number of expansions of the inner approximation. Furthermore, we propose two heuristic approaches to determine the distance between the inner and outer approximation that can be used as an alternative for the distance calculation of Solanki et al. These heuristics incorporate the ideas of Solanki et al. And Craft et al. to obtain straightforward and faster methods. ",

keywords = "Convex multi-objective, sandwich algorithm, weighted sum scalarization, multi-objective linear programming",

author = "Melissa Koenen and Marleen Balvert and H.A. Fleuren",

note = "CentER Discussion Paper Nr. 2023-012",

year = "2023",

month = may,

day = "25",

language = "English",

volume = "2023-012",

series = "Center Discussion Paper",

publisher = "CentER, Center for Economic Research",

type = "WorkingPaper",

institution = "CentER, Center for Economic Research",

}