Taesu Cheong | Searcharxiv

arXiv2026

Exact Methods for the Generalized Multiple Strip Packing Problem with Heterogeneous Costs

We study the Generalized Multiple Strip Packing Problem (GMSPP) with heterogeneous per-unit-area costs, in which rectangular items of fixed dimensions must be packed without overlap into multiple open-ended strips of different widths, each incurring a cost proportional to the area used. This cost-weighted area objective is introduced here for the first time and unifies several objectives studied separately in the literature, including total area, total height for identical strips, and makespan. We propose two exact integer programming formulations for this problem: a big-M formulation adapted from recent work, and a normal-position formulation extending an earlier single-strip approach to multiple heterogeneous strips. For the normal-position formulation, we develop an exact Benders decomposition algorithm, called BendM (Benders' Method for Multiple strips). Comprehensive computational experiments on 180 instances derived from standard strip-packing benchmarks compare both formulations and demonstrate the effectiveness of BendM across three cost structures.

math.OC↗

arXiv2020

A Mathematical Programming Approach for Integrated Multiple Linear Regression Subset Selection and Validation

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are met. Most traditional approaches require human decisions at this step. For example, the user adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose a fully automated model building procedure for multiple linear regression subset selection that integrates model building and validation based on mathematical programming. The proposed model minimizes mean squared errors while ensuring that the majority of the important regression assumptions are met. We also propose an efficient constraint to approximate the constraint for the coefficient t-test. When no subset satisfies all of the considered regression assumptions, our model provides an alternative subset that satisfies most of these assumptions. Computational results show that our model yields better solutions (i.e., satisfying more regression assumptions) compared to the state-of-the-art benchmark models while maintaining similar explanatory power.

stat.ML↗