Efficient SAT and MaxSAT techniques for solving the Two-Dimensional Strip Packing Problem

Abstract

The NP-hard Two-Dimensional Strip Packing Problem (2SPP) demands efficient exact solutions. This paper presents SAT-based Order Encoding models incorporating item rotation and adapted symmetry-breaking (SB). It compares three height-minimization strategies: Non-Incremental SAT Bisection, Incremental SAT Bisection, and Direct Weighted Partial MaxSAT Optimization. Benchmarks on established 2SPP instances show our Non-Incremental SAT and Direct MaxSAT strategies significantly outperform earlier incremental techniques. Direct MaxSAT excelled for non-rotational 2SPP, while Non-Incremental SAT was superior for rotational cases among our methods. Google OR-Tools (CP) performed best overall, yet our SAT/MaxSAT methods were highly competitive, outperforming other CP and all tested MIP solvers. SB was generally beneficial. Item rotation increased encoding complexity; while yielding improved optimal heights for some instances, it did not increase the total number of instances solved optimally by our SAT/MaxSAT methods. This work offers insights into SAT/MaxSAT strategy trade-offs and their performance against general solvers.