A hybrid dynamic programming/branch-and-bound algorithm for the multiple-choice knapsack problem

Dyer, Martin; Riha, W.; Walker, James S.

doi:10.1016/0377-0427(93)e0264-m

Cited by 33 publications

(22 citation statements)

References 18 publications

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“…Dyer, Riha and Walker [125], however, presented a specialized algorithm for deriving U2, which is specially designed for reducing states in a dynamic programming algorithm. Dyer, Riha and Walker [125], however, presented a specialized algorithm for deriving U2, which is specially designed for reducing states in a dynamic programming algorithm.…”

Section: Bounds From Lagrangian Relaxationmentioning

confidence: 99%

“…Several enumerative algorithms for (MCKP) have been presented during the last two decades: Nauss [355], Sinha and Zoltners [436], Dyer,Kayal and Walker [124], Dudzinski and Walukiewicz [117], Dyer, Riha and Walker [125]. In order to obtain an upper bound for the problem, most of these algorithms start by solving C(MCKP) in two steps:…”

Section: Branch-and-boundmentioning

confidence: 99%

“…Dyer, Riha and Walker [125] presented a hybrid algorithm based on the concept of dynamic programming with upper bound tests as described in Section 3.5.…”

Section: Hybrid Algorithms and Expanding Core Algorithmsmentioning

confidence: 99%

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Knapsack Problems

2004

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PrefaceThirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. 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.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. Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the number 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.Hence, two years ago the idea arose to produce a new monograph covering not only the most recent developments of the standard knapsack problem, but also giving a comprehensive treatment of the whole knapsack family including the siblings such as the subset sum problem and the bounded and unbounded knapsack problem, and also more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters.Furthermore, attention is paid to a number of less frequently considered variants of the knapsack problem and to the study of stochastic aspects of the problem. To illustrate the high practical relevance of the knapsack family for many industrial and economic problems, a number of applications are described in more detail. They are selected subjectively from the innumerable occurrences of knapsack problems reported in the literature.Our above-mentioned colleague will be surprised to notice that even on the more than 500 pages of this book not all relevant topics could be treated in equal depth but decisions had to be made on where to go into details of constructions and proofs and where to concentrate on stating results and refer to the appropriate publications. Moreover, an editorial deadline had to be drawn at some point. In our case, we stopped looking for new publications at the end of June 2003. VI PrefaceThe audience we envision for this book is threefold: The first two chapters offer a very basic introduction to the knapsack problem and the main algorithmic concepts to derive optimal and approximate solution. Chapter 3 presents a number of advanced algorithmic techniques which are used throughout the later chapters of the book. The style of presentation in these three chapters is kept rather simple and assumes only minimal prerequisites. They should be accessible to students and graduates of business administration, economics and engineering as well as practitioners with little knowledge of algorithms and optimization.This first part of the book is also well suited to introd...

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Section: Bounds From Lagrangian Relaxationmentioning

confidence: 99%

Section: Branch-and-boundmentioning

confidence: 99%

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Knapsack Problems

2004

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“…If one is not necessarily interested in obtaining a FPTAS for the rate allocation problem, one can use other approximation or exact algorithms described in the literature (see e.g. [5] for a fast branch and bound algorithm). Clearly, any algorithm for the multiple choice knapsack problem, should take into account the specific choice for the utility function.…”

Section: Remarkmentioning

confidence: 99%

A Combinatorial Approximation Algorithm for CDMA Downlink Rate Allocation

Boucherie

Bumb

Endrayanto

et al. 2006

Operations Research/Computer Science Interfaces Series

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This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for a given downlink rate allocation. Based on the Perron-Frobenius eigenvalue, we reduce the downlink rate allocation problem to a set of multiple-choice knapsack problems. The solution of these problems provides an approximation of the optimal downlink rate allocation and cell borders for which the system throughput, expressed in terms of utility functions of the users, is maximized.

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“…Dynamic programming algorithm are proposed in [8,9]. Two hybrid algorithms that combine dynamic programming and branch-and-bound are proposed in [10,9].…”

Section: Introductionmentioning

confidence: 99%

A Parallel Chemical Reaction Optimization for Multiple Choice Knapsack Problem

Truong

Salah

et al. 2014

Communications in Computer and Information Science

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Abstract. This research proposed a new parallel algorithm based on chemical reaction optimization for multiple-choice knapsack problem (MCKP). In the proposed algorithm, master-slave parallel architecture is used and four problem-specific chemical reaction operators are suggested. The experimental results have proven the superior performance of the proposed algorithm compared to the basic chemical reaction optimization.

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A hybrid dynamic programming/branch-and-bound algorithm for the multiple-choice knapsack problem

Cited by 33 publications

References 18 publications

Knapsack Problems

Knapsack Problems

A Combinatorial Approximation Algorithm for CDMA Downlink Rate Allocation

A Parallel Chemical Reaction Optimization for Multiple Choice Knapsack Problem

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