Primerjava algoritmov linearnega programiranja s pomočjo sistema ALGator

PERČIČ, ANDREJA (author), Dobravec, Tomaž (mentor)

Problem linearnega programiranja se v praksi pojavlja na številnih področjih. Denar, čas, surovine, prostor in podobne dobrine so pogosto omejene, hkrati pa z njimi želimo optimalno ravnati, da bi povečali svoj dobiček in zmanjšali stroške. Če se zahteve lahko zapišejo v linearni obliki, nam do optimizacije stroškov pomagajo algoritmi linearnega programiranja. V sklopu diplomskega dela smo v sistemu ALGator implementirali dva algoritma za reševanje linearnih programov. Simpleksni algoritem, ki se v praksi najpogosteje uporablja ter afino skaliranje, ki optimalno rešitev išče v notranjosti dopustnega območja.

• Language: Slovenian
• Keywords: linearno programiranje, optimizacija, ALGator
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science ; FMF - Faculty of Mathematics and Physics
• Year: 2020
• PID: 20.500.12556/RUL-113860
• COBISS.SI-ID: 1538529219
• Publication date in RUL: 07.02.2020

Secondary language

• Language: English
• Title: Comparison of linear programming algorithms using the ALGator system

Abstract

The problem of linear programming is often seen in many industries. Money, time, space and other resources are often limited, while we want to optimaly handle them to maximize our profit and minimize our costs. If we can write the constraints in a linear form, linear programming algorithms can help us get the optimal profit. In this diploma we implemented two linear programming algorithms in the ALGator system. The simplex algorithm, which is most often used in practice, and affine scaling which moves in the interior of the feasible region, to get to the optimal solution.

• Keywords: linear programming, optimization, ALGator