Method for the Solution of the Multi-Dimensional 0/1 Knapsack Problem (Classic Reprint)

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Excerpt from Method for the Solution of the Multi-Dimensional 0/1 Knapsack Problem In the knapsack problem, given the desirability of each of a number of items, one seeks to find that subset which satisfies a constraint on total weight. The multi-dimensional variant imposes constraints on addi tional variables of the items, the specification means that an item is either taken or not, i.e., multiples of the same item are not con sidered, except possibly indirectly. Traditionally the l-dimensional knapsack problem is solved by means of dynamic programming. The multi dimensional problem is usually reduced to a one-dimensional one by use of Lagrangian Multipliers which, however, do not generally yield the exact solution to the problem posed. The present paper considers methods for obtaining the exact solution to the problem, and not an approximate one. Additional algorithms are developed which are applied within a dynamic programming framework. Given these, the object is to obtain solutions efficiently, and in attaining this goal heuristic methods are employed. Efficiency of the methods is based upon the use of an inter active computer system in which the heuristics of the problem solver are applied and changed as the character of the solution process evolves. The project was conducted with the Compatible Time Sharing System of Project mac. The problem arises in the context of capital budgeting, but has obvious applications in a variety of other areas. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.