A Hybrid Meta-heuristic for the Container Loading Problem

ABSTRACT It is very common in an enterprise daily operation to solve Container Loading Problem (CLP). Especially, it is an important issue in the logistic management. The problem aims to determine the arrangement of objects with the best utilization ratio in a container. It belongs to the combinatorial optimization problem. In this paper, a two-phased method focusing on the improvement of the efficiency and on the reducing of the problem size is proposed. In the first phase, a constructive method incorporated with a decision rule borrowing from ant colony optimization is used to construct tower set. The pheromone updating mechanism is useful in choosing proper object while constructing tower using decision rule. In the second phase, an improvement method based on genetic algorithm is used. First, the method sorts the towers by the utilization ratio and then assigns a number to each tower accordingly. The chromosome is a sequence of tower numbers which represents the arrangement of towers in the container's bottom plane. The fitness function is defined as the utilization ratio. A new structure to store the pheromone is proposed which can help the ant in choosing the appropriate object while constructing tower. In this way, the efficiency of the method and the utilization of the container are improved. INTRODUCTION Logistics and storage management have already become key factors for modern enterprises to succeed in the market. For enterprises, common problems include transportation routing, human appointment, resource distribution, and etc. Container Loading Problem is one of the problems too. Its application is more extensive, and it can solve the container utilizing of logistics industry or warehousing problem. The main purpose of the problems of this kind is to increase space utilization ratio and reduce the cost. So, the effective space utilization becomes the main core of the problem. The kind of problem belongs to the combinatorial optimization problem. The problem focuses on how to achieve optimal space utilization in a limited space. The given objects are arranged, according to respective constraints and characteristics to achieve effective space utilization and maximize space utilization ratio. Container Loading Problem is a kind of scholarly research topic. Its application is quite widespread and it has practical values. It belongs to the combinatorial optimization problem. In operation management, it is an important topic. According to the existing literatures, if considered from the loading space and the object, there are mainly four kinds of fitting situations, namely the single and the multi container fittings, the same and the different volume object fittings. And the research methods include Linear Programming, Dynamic Programming, Heuristics, and Meta-heuristics. Meta-heuristics is the most common method. RELATED WORKS Container Loading Problem has already been solved by many scholars by different solutions. Bortfeldt and Gehring (2001) first solved the problem by a two-phased method. In the first phase, they used the greedy method to choose the objects whose volume is comparatively bigger to build the tower T gradually. In the second phase, they could only consider the arrangement of the tower T on the container's bottom plane directly and used the GA (Genetic Algorithm) to solve. Bortfeldt and Gehring also proposed the new method based on the phased concept. He built the objects into several layers then the GA is used. Moura and Oliveira (2005) also used the phased method by constructing wall-build. It is known from the literature, when the most of scholars are solving CLP optimization problem, in order to avoid involving too many considerations to complicate problems, they all simplify the problem by the gradual method. In this paper, we propose a two-phased method focusing on the improvement of the efficiency and the reduction of the problem size. …