Cargo Placement as MINLP: A Local Search Formulation for RORO Ships
Translated title
Fragt Placering som MINLP: A Local Search Formulation for RORO Ships
Author
Engberg, Jacob
Term
4. term
Education
Publication year
2026
Submitted on
2026-05-27
Pages
94
Abstract
This project examines how to place rolling cargo on Roll‑On/Roll‑Off (RoRo) ships so the vessel remains as level as possible. The hull shape is modeled mathematically: globally with NURBS curves (smooth curves that can represent complex shapes) and locally with quadratic polynomials. Based on this model, the ship’s tilt is described as a function of cargo placement and computed using integrals. The required integrals are evaluated both numerically with the Gauss–Legendre approximation (a standard method for numerical integration) and symbolically when possible. To keep the calculations tractable, the angles are linearized using a first‑order approximation. Using this setup, an algorithm is developed to suggest cargo placements that minimize the ship’s angles. The algorithm is tested on a range of cases. It produces unsatisfactory placements in up to 53% of the cases. The thesis discusses why the algorithm often fails and which modeling and computational choices may contribute.
Projektet undersøger, hvordan rullende fragt på Roll‑On/Roll‑Off (RoRo) skibe kan placeres, så skibet står mest muligt lige. Skrogets form modelleres matematisk: overordnet med NURBS‑kurver (glatte kurver, der kan beskrive komplekse former) og lokalt med 2.-gradspolynomier. På baggrund af denne model beskrives skibets hældning som en funktion af, hvor lasten placeres, og hældningen beregnes ved hjælp af integraler. De nødvendige integraler findes både numerisk med Gauss–Legendre‑approksimation (en standard metode til numerisk integration) og symbolsk, når det er muligt. For at gøre beregningerne mere håndterbare lineæriseres vinklerne (første‑ordens/1.-grad‑approksimation). Med denne tilgang udvikles en algoritme, der foreslår, hvor lasten bør placeres for at minimere skibets vinkling. Algoritmen testes på en række eksempler. Resultatet er, at den giver utilfredsstillende placeringer i op til 53 % af tilfældene. Afhandlingen diskuterer, hvorfor algoritmen ofte fejler, og hvilke forudsætninger i model og beregninger der kan spille ind.
[This apstract has been rewritten with the help of AI based on the project's original abstract]