# Using Secondary Fitness to Break Ties in a Genetic Algorithm for the One-Dimensional Bin-Packing Problem

7-2011

Thesis

## Degree Name

Computer Science: M.S.

## Department

Computer Science and Information Technology

## College

School of Science and Engineering

Bryant Julstrom

Jayantha Herath

Genetic Algorithms, Bin Packing, Secondary Fitness, Evolutionary Computation, Genetic Programming

## Abstract

The one-dimensional bin-packing problem (BPP) is a well known problem in the realm of operations research. In the BPP, objects with pre-defined "weights" are packed into bins, each having a maximum weight capacity. The goal is to minimize the number of bins needed to hold objects.

In a Genetic Algorithm for this problem, an individual candidate solution consists of a permutation of object~ representing their order of placement. A heuristic is then used to place objects in bins according to their specified order. The heuristic chosen is generally First Fit, Best Fit, or Worst Fit. The number of bins needed to store the objects is a solution's fitness. In Genetic Algorithms, the fitness value of a solution represents its likelihood to pass on its genetic material to new generations. In the case of the BPP, the less the number of bins needed, the greater a solution's fitness. To create new generations, solutions are "crossed-over" to combine features of their particular solutions and create a new organism. New generations are then created in a cycle until a predetermined limit has been reached and the best organism found becomes the solution to the problem.

Many situations arise where two solutions may have the exact same fitness value according to the number of bins. However, these two solutions may not be equivalent in terms of solving the BPP. Solutions which pack objects more tightly in bins are more desirable because they have more potential to be improved in future generations. To distinguish these solutions, we propose a second fitness criterion: the free space in the final bin of a solution.

By adding this secondary fitness criterion, the performance of the standard GA algorithm for the BPP can be improved by a significant margin. This has implications for any implementation of bin-packing GAs, as the modification is relatively minor and produces better results; therefore being a cost-effective improvement.

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