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- 0-1 Knapsack Optimization with Branch-and-Bound Algorithm
- An Exact Algorithm for Bilevel 0-1 Knapsack Problems
- Title : Implementation of 0-1 knapsack problem using branch and bound approach
- 0-1 Knapsack Optimization with Branch-and-Bound Algorithm

Research efforts on parallel exact algorithms for the 0—1 knapsack problem have up to now concentrated on solving small problems at most 1, objects and in many cases results have only been obtained by simulation of the parallel algorithm.

After a brief review of a well known sequential branch-and-bound algorithm we discuss a new parallel algorithm for the 0—1 knapsack problem which exploits the potential parallelism that exists during the backtracking steps of the branch-and-bound algorithm.

We report results for our parallel algorithm on a transputer network for problems with up to 20, objects. The speedup obtained is nearly linear for 2, 4, and 8 processors except when there is a strong correlation between the profit and weight of the objects. This is a preview of subscription content, access via your institution.

Rent this article via DeepDyve. Martello and P. Toth, The 0—1 knapsak problem, N. Christofides, A. Mingozzi, P. Toth, and C. Sandi, eds. Toth, A new algorithm for the 0—1 knapsack problem, Management Science , 34 5 — Google Scholar. Lai and S. Sahni, Anomalies in parallel branch-and-bound algorithms, Comm. Horowitz and S. Sahni, Computing partitions with applications to the knapsack problem, Journal of the ACM , 21 , — Janakiram, E.

Gehringer, D. Agrawal, and R. Kindervater and H. Trienekens, Experiments with parallel algorithms for combinatorial problems, European Journal of Oper. Lee, E. Shragowitz, and S. Lin and J. Storer, Processor-efficient hypercube algorithms for the knapsack problem, Journal of Parallel and Distributed Computing , 13 — Dantzig, Discrete variable extremum problems, Operations Research , 5 — El-Dessouki and W. Loots and T. Smith, A parallel three phase sorting procedure for a k -dimensional hypercube and a transputer implementation, Parallel Computing , 18 : — Casella and R.

Berger, Statistical Inference , Wadsworth, California, Download references. Box , , Johannesburg, South Africa. Reprints and Permissions. Loots, W. A parallel algorithm for the 0—1 knapsack problem. Int J Parallel Prog 21, — Download citation. Received : 15 July Revised : 15 April Issue Date : October Search SpringerLink Search. Abstract Research efforts on parallel exact algorithms for the 0—1 knapsack problem have up to now concentrated on solving small problems at most 1, objects and in many cases results have only been obtained by simulation of the parallel algorithm.

Immediate online access to all issues from Subscription will auto renew annually. References 1. Box , , Johannesburg, South Africa W. Smith Authors W. Loots View author publications.

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We propose a new exact method for solving bilevel knapsack problems. A bilevel problem models a hierarchical decision process that involves two decision makers called the leader and the follower. In these processes, the leader takes his decision by considering explicitly the reaction of the follower. From an optimization standpoint, these are problems in which a subset of the variables must be the optimal solution of another parametric optimization problem. These problems have various applications in the field of transportation and revenue management, for example.

PDF | In this paper, we propose an out-of-core branch and bound (B&B) method for solving the 0–1 knapsack problem on a graphics.

The knapsack problem where we have to pack the knapsack with maximum value in such a manner that the total weight of the items should not be greater than the capacity of the knapsack. In this item cannot be broken which means thief should take the item as a whole or should leave it. Example: The maximum weight the knapsack can hold is W is There are five items to choose from. Their weights and values are presented in the following table:.

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The multidimensional knapsack problem MKP is a resource allocation model that is one of the most well-known integer programming problems. During the last few decades, an impressive amount of research on the knapsack problem has been published in the literature, and efficient special-purpose methods have become available for solving very large-scale instances. However, the multidimensional case has received less attention from the operational research community. Although recent advances have made solving medium size instances possible, solving the NP-hard problem remains a very interesting challenge, especially when the number of constraints increases.

*The question was changed to maximize the benefits to minimize the problem. Description: No option selected in order to press the article so as to arrive on the next item boundary. Problem Description: Given n kinds of items and a backpack.*

Skip to Main Content. A not-for-profit organization, IEEE is the world's largest technical professional organization dedicated to advancing technology for the benefit of humanity. Use of this web site signifies your agreement to the terms and conditions. The algorithm solves different instances uncorrelated, weakly and strongly correlated in time Kn. The proposed algorithm was experimentally compared with the Pisinger Model, based on the obtained results it is demonstrated the ability of the proposed algorithm to solve problems that the Pisinger algorithm cannot solve.

Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[ Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. Method 1 : Recursion. Approach: A simple solution is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W.

To browse Academia. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Title : Implementation of knapsack problem using branch and bound approach.

PDF | A branch and bound algorithm for solution of the "knapsack problem," max \sum vixi where \sum wixi \leqq W and xi - 0, 1, is presented.

The knapsack problem is a problem in combinatorial optimization : Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century, with early works dating as far back as

Research efforts on parallel exact algorithms for the 0—1 knapsack problem have up to now concentrated on solving small problems at most 1, objects and in many cases results have only been obtained by simulation of the parallel algorithm. After a brief review of a well known sequential branch-and-bound algorithm we discuss a new parallel algorithm for the 0—1 knapsack problem which exploits the potential parallelism that exists during the backtracking steps of the branch-and-bound algorithm. We report results for our parallel algorithm on a transputer network for problems with up to 20, objects. The speedup obtained is nearly linear for 2, 4, and 8 processors except when there is a strong correlation between the profit and weight of the objects.

Branch and bound is an algorithm design paradigm which is generally used for solving combinatorial optimization problems. These problems typically exponential in terms of time complexity and may require exploring all possible permutations in worst case. Branch and Bound solve these problems relatively quickly.

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## 3 Comments

## Kezoobylu

We develop a branch-and-bound algorithm to solve a nonlinear class of 0—1 knapsack problems.

## Reapoklipi1964

algorithms to exactly solve the. knapsack problem. In Dantzig gave an Example (continued) using an appropriate branch-and-bound.

## Emmanuelle D.

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