Exact algorithms for the guillotine strip cutting/packing problem

In this paper we propose two exact algorithms for solving both two-staged and three-staged unconstrained (un) weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [10]. The three-staged problem is solved by using a top-down approach combined with a dynamic programming procedure. The performance of the exact algorithms are evaluated on some problem instances of the literature and other hard randomly-generated problem instances (a total of 53 problem instances). A parallel implementation is an important feature of the algorithm used for solving the three-staged version.

Exact Algorithms for Large-Scale Unconstrained Two and Three Staged Cutting Problems

In this paper we propose two exact algorithms for solving both two-staged and three staged unconstrained (un)weighted cutting problems. The two-staged problem is solved by applying a dynamic programming procedure originally developed by Gilmore and Gomory [Gilmore and Gomory, Operations Research, vol. 13, pp. 94–119, 1965]. The three-staged problem is solved by using a top-down approach combined with a dynamic programming procedure. The performance of the exact algorithms are evaluated on some problem instances of the literature and other hard randomly-generated problem instances (a total of 53 problem instances). A parallel implementation is an important feature of the algorithm used for solving the three-staged version.

The DH/KD algorithm: a hybrid approach for unconstrained two-dimensional cutting problems

https://homepages.laas.fr/elbaz/sdarticle.pdf

Load balancing methods and parallel dynamic programming algorithm using dominance technique applied to the 0--1 knapsack problem

Dynamic programming is one of the most powerful approaches to many combinatorial optimization problems. In this paper, we present pipeline architectures for the dynamic programming algorithms for the knapsack problems. They enable us to achieve an optimal speedup using processor arrays, queues, and memory modules. The processor arrays can be regarded as pipelines where the dynamic programming algorithms are implemented through pipelining.

Pipeline architectures for dynamic programming algorithms

A parallel algorithm based on a technique called delayed dominance is proposed for solving the 0/1 knapsack problem. This parallel algorithm is a modification of Chen, Chern and Jang's algorithm. Experiments show that the new algorithm has a better performance than Chen et al.'s algorithm.

Jin Hwang Jang

Papers

Pipeline architectures for dynamic programming algorithms

An improved parallel algorithm for 0/1 knapsack problem