New binary bat algorithm for solving 0–1 knapsack problem

Rizk‐Allah, Rizk M.; Hassanien, Aboul Ella

doi:10.1007/s40747-017-0050-z

Cited by 80 publications

(43 citation statements)

References 36 publications

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“…Sequential execution was carried out on the Ioevolution server. To verify that the proposed method solved the knapsack problem 0-1, the instances published by References [26][27][28] were resolved. Tables 2-4 show the results obtained.…”

Section: Results Of the Sequential Algorithmmentioning

confidence: 99%

“…In the first test, it was verified that the algorithm elaborated using sets of parts calculated the optimal solution. For this purpose, the optimal solution (based on the published instances with solutions) was calculated [26][27][28]. The second part consisted of solving the instances classified as uncorrelated and weakly correlated: their coefficients were given by equations as each author calculated them [14].…”

Section: Computational Experimentationmentioning

confidence: 99%

“…Optimal Solution Reference f opt Kp_01 4 100 473 473 Kp_02 10 100 798 798 Kp_03 25 300 3307 3307 Kp_04 40 600 4994 4994 Table 4. Tests of the instances from Reference [28].…”

Section: Instance Dimension Knapsack Capacitymentioning

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: Results Of the Sequential Algorithmmentioning

confidence: 99%

Section: Computational Experimentationmentioning

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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show abstract

“…The convergence speed of BAT is high when the switching happens in between the stages of exploitation and exploration. In the article [16], the authors say that compared to PSO and GA, the BAT algorithm solves different nonlinear optimization problems with high efficiency. The main features of BAT algorithm are, they can sense the distance between food source and obstacle without visibility and their flying velocity, position and frequency are constant when they go for searching for food.…”

Section: Bat Algorithm Based Mppt Techniquementioning

confidence: 99%

Recent Nature Inspired Techniques for Solar Power Point Tracking Application

Kiran*,

Reddy

2019

IJITEE

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Photovoltaic (PV) array generates non-linear I-V and P-V characteristics. As a result, it is difficult to transfer the maximum power from source to load. The Maximum Power Point Tracking (MPPT) is used to track the Maximum Power Point (MPP) and extract the maximum power of solar PV. The disadvantages of conventional MPPT techniques are less MPP tracking speed, high MPP settling time and less accuracy. In order to overcome the disadvantages of conventional techniques, in this article different types of recent nature inspired optimization techniques are reviewed to track the MPP. In addition, the application of optimization technique based Maximum Power Point Tracking (MPPT) technique for standalone and grid connected application is explained in detail. The advantages of optimization techniques are highly reliable, better accuracy, less time to convergence and fast response.

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“…The experimental results show that EADE is very competitive algorithm for solving large-scale global optimization problems. Authors in [28] combined two binary bat algorithm (BBA) and with local search scheme (LSS)to improve the diversity of BBA and enhance the convergence rate. The results show that the proposed hybrid algorithm obtained promising results for solving large-scale 01 knapsack problems.…”

Section: B Gehad Ismail Sayedmentioning

confidence: 99%

A hybrid SA-MFO algorithm for function optimization and engineering design problems

Sayed

Hassanien

2018

Complex Intell. Syst.

Self Cite

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This paper presents a hybrid algorithm based on using moth-flame optimization (MFO) algorithm with simulated annealing (SA), namely (SA-MFO). The proposed SA-MFO algorithm takes the advantages of both algorithms. It takes the ability to escape from local optima mechanism of SA and fast searching and learning mechanism for guiding the generation of candidate solutions of MFO. The proposed SA-MFO algorithm is applied on 23 unconstrained benchmark functions and four well-known constrained engineering problems. The experimental results show the superiority of the proposed algorithm. Moreover, the performance of SA-MFO is compared with well-known and recent meta-heuristic algorithms. The results show competitive results of SA-MFO concerning MFO and other meta-heuristic algorithms.

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New binary bat algorithm for solving 0–1 knapsack problem

Cited by 80 publications

References 36 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

Recent Nature Inspired Techniques for Solar Power Point Tracking Application

A hybrid SA-MFO algorithm for function optimization and engineering design problems

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