The multiple container packing problem: A genetic algorithm approach with weighted codings

This paper presents a genetic algorithm (GA) approach to the problem of choosing C disjoint subsets of n items to be packed into distinct containers, such that the total value of the selected items is maximized, without exceeding the capacity of each of the containers. This so-called multiple container packing problem (MCPP) has applications in naval as well as financial management. It is a hard combinatorial optimization problem comprising similarities to the knapsack problem and the bin packing problem. A novel technique for encoding MCPP solutions is used within the GA: The genotype is a vector of numerical weights associated with the items of the problem. The corresponding phenotype is obtained by temporarily modifying the original problem according to these weights and applying a greedy decoding heuristic for the MCPP to the new problem. This solution is then evaluated using the original problem data again. Two different techniques for biasing the original problem and four decoding heuristics are discussed. They were tested in a weight-coded steady-state GA on a variety of MCPP instances. One biasing technique and one decoding heuristic turned out to be clearly more effective than the others, and the GA using them found solutions of significantly higher quality than direct-encoded and order-based GAs from a previous work