A Heuristic for Improved Genetic Bin Packing

The bin packing optimization problem packs a set of objects into a set of bins so that the amount of wasted space is minimized The bin packing problem has many important applications These include multiprocessor scheduling resource allocation and real world planning packing routing and scheduling optimization problems The bin packing problem is NP complete Since there is therefore little hope in nding an e cient deterministic solution to the bin packing problem approximation methods have been developed The advantage of these methods is that they have guaranteed packing performance bounds A survey of approximation algorithms for bin packing and their respective performance bounds are reported by Garey and Johnson in the one dimensional case Co man et al in the two dimensional case and Li and Cheng in the three dimensional case In many practical applications of bin packing a small improvement in packing e ciency can result in great cost savings For example when a bin represents a truck ship or airplane a large sum of money can be saved by using one less bin Genetic algorithms have been used on the bin packing problem with great success A genetic algorithm is an iterative procedure which borrows the ideas of natural selection and survival of the ttest from natural evolution By simulating natural evolution in this way a genetic algo rithm can easily solve complex problems Furthermore by emulating biological selection and reproduction techniques a genetic algorithm can e ectively search the problem domain in a general representation in dependent manner The genetic algorithm maintains a population of chromosomes which represent points in the problem domain Each chromosome is evaluated by a user de ned objective function The genetic algorithm relys on operators such as reproduction crossover and mutation to evolve from one generation to the next Reproduction ensures the ttest chromosome will survive Crossover and mutation alter the chromosomes so that new points in the solution space are explored