A memetic algorithm for two-dimensional multi-objective bin-packing with constraints

Abstract

Over recent years, a number of independent researchers have shown that meta-heuristics are effective strategies for solving hard combinatorial optimization problems. In particular, Memetic Algorithms (MA) are population-based meta-heuristic search methods that are inspired by Darwinian principles of natural selection and Dawkins' notion of meme that have successfully been applied to single- and multi-objective optimization problems. The two-dimensional bin-packing problem (2D-BPP) [1] with rotations is an important optimization problem which has a large number of practical applications. It consists of the non-overlapping placement of a set of rectangular pieces in the lowest number of bins of a homogenous size, with the edges of these pieces always parallel to the sides of bins, and with free 90 degrees rotation. Bin-packing problems are complex combinatorial optimization problems included in the category of NP-hard problems of fundamental importance in industry, transportation, computer systems, machine scheduling, etc. The multi-objective two-dimensional bin-packing problem considers other objectives to optimize, such as the imbalance of the objects according to a centre of gravity of the bin. The balance in the bin loads has important applications in container loading, tractor trailer trucks, pallet loading and cargo airplanes. This paper analyzes the performance of a Pareto-based memetic algorithm, which operators have been specially designed to solve this problem while considering some contraints. Results obtained in some test problems show the good performance of this approach in comparison with multi-objective Particle Swarm Optimization.