Metaheuristic Approaches for One-Dimensional Bin Packing Problem: A Comparative Performance Study

Abstract

Nature-inspired metaheuristic algorithms have steadily gained popularity over the last two decades. They have been applied to a plethora of optimization problems both in continuous and combinatorial domains. In this paper, the one-dimensional bin packing problem is solved through the implementation of two underlying heuristics, namely, best fit and better fit, and four representative state-of-the-art global metaheuristic algorithms, namely, firefly algorithm, genetic algorithm, adaptive cuckoo search algorithm, and artificial bee colony algorithm. The underlying best fit and better fit heuristics are employed by the four aforementioned global metaheuristic algorithms as reordering heuristics and local search improvement mechanisms are used for generating good packing schema. Furthermore, these two local heuristics possess special characteristics which, when incorporated into the global metaheuristics, allow them to escape local optimums and avoid getting stuck, and more so, enables the algorithms to generate good quality solutions. The main focus of this paper is the presentation of a systematic performance evaluation study for the representative algorithms, with some initial computational results that show the effectiveness of the respective algorithms and their ability to achieve promising solutions. The experiments conducted here were carried out using three standard bin packing problem datasets categories with over 1,210 instances in total, each with differing capacities, number of items and distributions between item weights. The numerical results of the representative algorithms were compared with the solutions achieved with the underlying heuristic techniques, in this case, the best fit and better fit heuristics, respectively. Similarly, the analysis of the initial computational results obtained revealed the superior performance of the individual algorithm implementation. Moreover, performance was established by taking into account both the algorithms computational time and the solution quality. Overall, several observations regarding the solution and the underlying heuristics were made. It is worth noting that by utilizing best fit heuristic, the algorithms attained optimal solutions for instances of the easy dataset requiring smaller capacity bins. However, as the complexity of the instances increased, the ability to produce high-quality results decreased. Nevertheless, this heuristic can produce near-optimal solutions and a good packing schema for most instances. On the other hand, utilizing better fit as the underlying heuristic results in optimal solutions almost all the time, regardless of capacity and number of items.