CHAMP: Creating heuristics via many parameters for online bin packing

Abstract

The online bin packing problem is a well-known bin packing variant which requires immediate decisions to be made for the placement of a lengthy sequence of arriving items of various sizes one at a time into fixed capacity bins without any overflow. The overall goal is maximising the average bin fullness. We investigate a 'policy matrix' representation which assigns a score for each decision option independently and the option with the highest value is chosen for one dimensional online bin packing. A policy matrix might also be considered as a heuristic with many parameters, where each parameter value is a score.We hence investigate a framework which can be used for creating heuristics via many parameters. The proposed framework combines a Genetic Algorithm optimiser, which searches the space of heuristics in policy matrix form, and an online bin packing simulator, which acts as the evaluation function. The empirical results indicate the success of the proposed approach, providing the best solutions for almost all item sequence generators used during the experiments.We also present a novel fitness landscape analysis on the search space of policies. This study hence gives evidence of the potential for automated discovery by intelligent systems of powerful heuristics for online problems; reducing the need for expensive use of human expertise.

Sparse, Continuous Policy Representations for Uniform Online Bin Packing via Regression of Interpolants

“…Existing methods used for comparison are the classic Best Fit (BF), First Fit (FF), Worst Fit (WF) and Harmonic [4] heuristics as given by Asta et al [13], in addition to more recent methods: policy matrix based approaches of Yarimcam et al [14], Asta et al [13] and Asta andÖzcan [27]. From this table, we can see that the performance of different interpolation methods varies depending on the size of the instance considered.…”

“…An additional parameter, the total number of items, was kept constant at 10 5 in every test. The first 10 UBP problems that we have used were taken directly from the work of Asta et al [13]. An 11th and 12th have also been introduced in this paper in order to demonstrate the scalability of our technique.…”

“…Our experimental design follows the same methodology used by Asta et al [13] to enable us to fairly compare against both their technique and the state of the art. Each algorithm compared was tested on a set of progressively larger configurations of the Uniform Bin Packing problem, referred to as UBP's.…”

“…In developing these approaches Ozcan and Parkes found that the ideal solution was often one which could not easily be expressed through via an arithmetic function. This demonstrates an advantage over GP which is designed to find solutions, expressed through arithmetic functions [11,13]. Moreover, it was observed that GP mutations often correspond to large moves within the space of policy matrices [19].…”

“…A recent study byÖzcan and Parkes found that good (optimal) policies could actually be 'spiky' and complex [11,13]. Recent research in bin packing has tended to focus on metaheuristic strategies capable of automatically devising policies which are more complex than FF or BF and better suited to solving the problem [11,14,13].…”