# 3-D Packing in Container using Teaching Learning Based Optimization Algorithm

## Authors

• Linda Fitriyani Department of Mathematics Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia.
• Larissa Alva Zerinda Department of Mathematics Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia.
• Asri Bekti Pratiwi Department of Mathematics Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia. https://orcid.org/0000-0002-8881-3377
• Edi Winarko Department of Mathematics Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia. https://orcid.org/0000-0001-7617-6115

## Keywords:

Container, Gravitational Search Algorithm, Mathematics, Teaching Learning Based Optimization Algorithm, 3-D Packing

## Abstract

The paper aims to propose Teaching Learning based Optimization (TLBO) algorithm to solve 3-D packing problem in containers. The objective which can be presented in a mathematical model is optimizing the space usage in a container. Besides the interaction effect between students and teacher, this algorithm also observes the learning process between students in the classroom which does not need any control parameters. Thus, TLBO provides the teachers phase and students phase as its main updating process to find the best solution. More precisely, to validate the algorithm effectiveness, it was implemented in three sample cases. There was small data which had 5 size-types of items with 12 units, medium data which had 10 size-types of items with 106 units, and large data which had 20 size-types of items with 110 units. Moreover, it was also compared with another algorithm called Gravitational Search Algorithm (GSA). According to the computational results in those example cases, it can be concluded that higher number of population and iterations can bring higher chances to obtain a better solution. Finally, TLBO shows better performance in solving the 3-D packing problem compared with GSA.

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