Genetic Algorithm for the Knapsack Problem with Irregular Shaped Items

The two-dimensional knapsack problem with irregularly shaped items is solved in this work. It is utilized the concept of inner-fit raster and no-fit raster to verify packing feasibility, which stands for non-overlapping between items that are entirely contained inside the bin. The problem solution is obtained with a biased random-key genetic algorithm in which each chromosome contains information related to the order and rotation where each item should be packed into the bin. The chromosome also contains information about which heuristic has to be used to pack items and the probability of an offspring inheriting information from an elite parent. It is adopted three heuristics for positioning items, which are: bottom-left, left-bottom, and horizontal zig-zag. The experiments over literature instances showed that the developed genetic algorithm is very effective since it could obtain an optimal solution for 53.4% of the instances and improved the bin's occupancy ratio in about 2.1% when observing all the instances.