The heuristic demonstrates ways to maximize space utilization by fitting the appropriate rectangle from both sides of the wall of the current residual space layer by layer. This article presents an efficient heuristic placement algorithm, namely, a bidirectional heuristic placement, for solving the two-dimensional rectangular knapsack packing problem. Shiangjen, Kanokwatt Chaijaruwanich, Jeerayut Srisujjalertwaja, Wijak Unachak, Prakarn Somhom, Samerkae Īn iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the numÂ ber of knapsacks, as well as the modification of the problem structure concerning the available item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years.

However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes. On this occasion a former colleague exclaimed back in 1990: 'How can you write 250 pages on the knapsack problem?' Indeed, the definition of the knapsack problem is easily understood even by a non-expert who will not suspect the presence of challenging research topics in this area at the first glance. Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared.

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