{'fraction_non_alphanumeric': 0.02530459231490159, 'fraction_numerical': 0.030927835051546393, 'mean_word_length': 4.900552486187845, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Solving the single-container loading problem by a fast heuristic method

This paper presents a new heuristic algorithm for solving the single-container loading problem. The algorithm is to formalize human experience formed in the last 1000 years by modern mathematical tools, and to refine it by a new observation. Its key issue is the cavity degree of an action that packs an item into a layer of the container, such that the item is packed as compactly as possible to other items already packed in the same layer. For the 1500 well-known benchmark problems from Bischoff, Ratcliff, and Davies, the new algorithm achieves an average container volume utilization of 89.59% with a reasonable average computing time of 27.78 min. This improves the current best utilization record reported in the literature considerably by 0.62%. Of those 1500, for the 800 strongly heterogeneous problems especially, where other algorithms usually achieved lower utilizations, it achieves an average volume utilization of 89.77%, which breaks the current best record markedly by 2.08%.