Solving 0-1 knapsack problem by greedy degree and expectation efficiency

Lv, Jianhui; Wang, Xingwei; Huang, Min; Cheng, Hui; Li, Fuliang

doi:10.1016/j.asoc.2015.11.045

Cited by 37 publications

(17 citation statements)

References 37 publications

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“…The complexity of the BB parallel algorithms that solve the KP 0-1 is a function of the problem instance variables. For example, when the computer architecture is a hypercube, the complexity is given by [12,15] O nc p w max w min (3) for a number of processors of p < c log w max . In Equation (3), one of the terms is w max w min .…”

Section: Related Workmentioning

confidence: 99%

“…Uncorrelated problems model any problem in which the weights of the elements are not correlated with their benefit. The weakly correlated problem model offers many practical applications, such as capital budgeting, project selection, resource allocation, cutting stock, and investment decision-making [3]. In this way, if an algorithm performs well in solving these instances, it is likely to solve a problem in everyday life.…”

Section: Introductionmentioning

confidence: 99%

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A Multi-Branch-and-Bound Binary Parallel Algorithm to Solve the Knapsack Problem 0–1 in a Multicore Cluster

Dı́az

Cruz-Chávez²,

López-Calderón

et al. 2019

Applied Sciences

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Featured Application: An uncorrelated instance is equivalent to solving any problem where the benefit is independent of the weight. A weakly correlated instance has a high correlation between the benefit and the weight of each element. Typically, the benefit differs from the weight by a small percentage. Such instances are the most practical in administration, such as with a return on an investment, which is generally proportional to the sum of the amount invested. Abstract: This paper presents a process that is based on sets of parts, where elements are fixed and removed to form different binary branch-and-bound (BB) trees, which in turn are used to build a parallel algorithm called "multi-BB". These sequential and parallel algorithms calculate the exact solution for the 0-1 knapsack problem. The sequential algorithm solves the instances published by other researchers (and the proposals by Pisinger) to solve the not-so-complex (uncorrelated) class and some problems of the medium-complex (weakly correlated) class. The parallel algorithm solves the problems that cannot be solved with the sequential algorithm of the weakly correlated class in a cluster of multicore processors. The multi-branch-and-bound algorithms obtained parallel efficiencies of approximately 75%, but in some cases, it was possible to obtain a superlinear speedup.The characteristic of this problem is that its items cannot be split among themselves and is classified as an NP-hard problem, where NP, indicates non-polynomial behavior problems. For certain sizes of the instances of these problems, it is possible to calculate their optimal solution by means of algorithms and parallel computers. Therefore, a parallel BB (Branch and Bound) algorithm is proposed to calculate the exact solution of KP 0-1 for instances of medium and low complexity (weak and uncorrelated [2], respectively).The novelty of this work is that using a different approach to a binary tree (from a formulation of a set of parts), we propose generating several different trees to find the optimal solution [4-10]. Each of these trees represents a decision tree that is generated by fixing or removing elements, so the roots of these trees are located in different search spaces with respect to the initial tree. Each binary tree forms new search spaces, and consequently there are a greater number of feasible solutions available. Because each decision tree is independent of the others, each of them is assigned in a processing unit for execution, and therefore it is possible to calculate the optimal solution more quickly and thus reduce the computation time, sometimes determining superlinear speedup as well as solving the instances that cannot be resolved with a sequential approach.The factors involved in efficient parallel implementation are diverse: those corresponding to the algorithm and those inherent in the use of parallel computers. It is important to consider algorithms that are efficiently parallelizable, i.e., algorithms whose execution times are polylogarithmic and use a number of...

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Multi-Branch-and-Bound Binary Parallel Algorithm to Solve the Knapsack Problem 0–1 in a Multicore Cluster

Dı́az

Cruz-Chávez²,

López-Calderón

et al. 2019

Applied Sciences

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“…A common reason for discrete variables occurring is when the resources of interest are quantified in terms of integers or Boolean values, for example, in production lines, scheduling processes, or resource assignments. There is a set of classic problems that can be treated in binary form, such as the well-known knapsack problem [53], the set covering problem [54], and the traveling salesman problem [55].…”

Section: Search Spacementioning

confidence: 99%

Putting Continuous Metaheuristics to Work in Binary Search Spaces

et al. 2017

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“…Under such context, the heuristic approach is usually employed to solve KP01. In fact, the existing heuristic approaches include the general heuristics with the self-established rules (e.g., expectation efficiency [10] and differential evolution [11]) and the intelligent heuristics with the ready-made natural laws (e.g., bee colony algorithm [12] and butterfly optimization algorithm [13]), in which the former shows good execution efficiency and the latter shows the relatively optimal solution. Given this, we plan to integrate their advantages and design a hybrid heuristic approach for solving KP01.…”

Section: Introductionmentioning

confidence: 99%

A Heuristic Transferring Strategy for Heterogeneous-Cached ICN

Zhao

2020

IEEE Access

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The in-network caching is a considerably significant feature of Information-Centric Networking (ICN), especially the heterogeneous-cached ICN has been widely investigated since it accords with the actual network deployment. For the heterogeneous-cached ICN, although there have been many proposals to improve network performance, it is very difficult for these approaches to reach the optimal network performance with multiple metrics consideration. Therefore, in this paper, we propose a heuristic transferring strategy which selects some Content Routers (CRs) and combines them to facilitate the optimal network performance under a constrained total cache budget. At first, we quantify energy consumption, CR load, cache hit ratio and throughput, because the optimal network performance depends on four objects, i.e., minimizing energy consumption and CRs load as well as maximizing cache hit ratio and throughput. Then, based on the given network constraints and objects, we convert the CR transferring problem into 0-1 Knapsack Problem (KP01). Finally, in order to effectively obtain the optimal solution, we propose a heuristic approach based on Ant Colony Optimization (ACO) and expectation efficiency to solve KP01. The simulation is driven by the real YouTube dataset from campus network measurement over GTS and Deltacom topologies, and the experimental results demonstrate that the proposed strategy is more efficient compared to three baselines.

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Solving 0-1 knapsack problem by greedy degree and expectation efficiency

Cited by 37 publications

References 37 publications

A Multi-Branch-and-Bound Binary Parallel Algorithm to Solve the Knapsack Problem 0–1 in a Multicore Cluster

A Multi-Branch-and-Bound Binary Parallel Algorithm to Solve the Knapsack Problem 0–1 in a Multicore Cluster

Putting Continuous Metaheuristics to Work in Binary Search Spaces

A Heuristic Transferring Strategy for Heterogeneous-Cached ICN

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