The Scalability of Evolved On Line Bin Packing Heuristics

The on line bin packing problem concerns the packing of pieces into the least number of bins possible, as the pieces arrive in a sequential fashion. In previous work, we used genetic programming to evolve heuristics for this problem, which beat the human designed ‘best fit ’ algorithm. Here we examine the performance of the evolved heuristics on larger instances of the problem, which contain many more pieces than the problem instances used in training. In previous work, we concluded that we could confidently apply our heuristics to new instances of the same class of problem. Now we can make the additional claim that we can confidently apply our heuristics to problems of much larger size, not only without deterioration of solution quality, but also within a constant factor of the performance obtained by ‘best fit’. Interestingly, our evolved heuristics respond to the number of pieces in a problem instance although they have no explicit access to that information. We also comment on the important point that, when solutions are explicitly constructed for single problem instances, the size of the search space explodes. However, when working in the space of algorithmic heuristics, the distribution of functions represented in the search space reaches some limiting distribution and therefore the combinatorial explosion can be controlled