arXiv subjects

Christof Brandstetter

Publications and source records attributed to Christof Brandstetter.

2 recordsLinked to original sources

arXiv2026

An semidefinite programming-based $\varepsilon$-constraint method for the bi-objective single-row facility layout problem

In this work, we introduce a multi-objective version of the well-known single-row facility layout problem (SRFLP). In the SRFLP, a set of one-dimensional facilities should be placed along a single line such that the weighted sum of the center-to-center distances of each pair of facilities is minimized. In our multi-objective extension, there are multiple such weighted-sum objectives which we consider under the concept of Pareto optimality. We develop a solution algorithm based on the $\varepsilon$-constraint method to solve the bi-objective SRFLP. Many existing works on the $\varepsilon$-constraint method use integer linear programming (ILP) solvers in a black-box fashion for solving the problems at the individual iterations of the method. In contrast to that, we use our own branch-and-bound procedure based on semidefinite programming (SDP), as SDP relaxations are known to be more effective for solving the SRFLP than linear programming relaxations of ILPs. This allows us to propose several enhancements procedures for our $\varepsilon$-constraint approach, such as non-binary branching and reusing of nodes within the branch-and-bound trees, which are usually not possible when using black-box solvers. We present a computational study to demonstrate the effectiveness of our solution approach and its enhancements.

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arXiv2024

Mixed-integer linear programming approaches for nested $p$-center problems with absolute and relative regret objectives

We introduce the nested $p$-center problem, which is a multi-period variant of the well-known $p$-center problem. The use of the nesting concept allows to obtain solutions, which are consistent over the considered time horizon, i.e., facilities which are opened in a given time period stay open for subsequent time periods. This is important in real-life applications, as closing (and potential later re-opening) of facilities between time periods can be undesirable. We consider two different versions of our problem, with the difference being the objective function. The first version considers the sum of the absolute regrets (of nesting) over all time periods, and the second version considers minimizing the maximum relative regret over the time periods. We present three mixed-integer programming formulations for the version with absolute regret objective and two formulations for the version with relative regret objective. For all the formulations, we present valid inequalities. Based on the formulations and the valid inequalities, we develop branch-and-bound/branch-and-cut solution algorithms. These algorithms include a preprocessing procedure that exploits the nesting property and also begins heuristics and primal heuristics. We conducted a computational study on instances from the literature for the $p$-center problem, which we adapted to our problems. We also analyse the effect of nesting on the solution cost and the number of open facilities.

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