A Master-Slave Model NGA and its Application in the Multidimensional 0-1 Knapsack Problem

2013 ◽  
Vol 433-435 ◽  
pp. 566-569
Author(s):  
Zi Bin Man ◽  
Ting Hong Zhao
Keyword(s):  
Genetic Algorithm ◽  
Knapsack Problem ◽  
Euclidean Distance ◽  
Hard Problem ◽  
Np Hard ◽  
Test Results ◽  
Np Hard Problem ◽  
The Individual ◽  
Slave Mode

The Multidimensional 0-1 knapsack problem is a NP hard problem, though there are many algorithm is used to solve the problem, but there is still not a good solution to solving the problem. This paper improved niche genetic algorithm, established a master-slave mode niche genetic algorithm, and carried on adaptive setting the individual Euclidean distance criterion, making it can changed with the evolving algebra incremental. At last, used master-slave niche genetic algorithm to solve the Multidimensional 0-1 knapsack problem, test results showed, the algorithm has good applicability and superiority in solving the Multidimensional 0-1 knapsack problem.

scholarly journals Perbandingan Fluid Genetic Algorithm dan Genetic Algorithm untuk Penjadwalan Perkuliahan

2020 ◽  
Vol 9 (3) ◽  
pp. 350
Author(s):  
Muhammad Ezar Al Rivan ◽  
Bhagaskara Bhagaskara
Keyword(s):  
Genetic Algorithm ◽  
Learning Rate ◽  
Hard Problem ◽  
Np Hard ◽  
Global Learning ◽  
Mutation Process ◽  
Hard Constraint ◽  
Multi Objective ◽  
Several Variables ◽  
Np Hard Problem

The lecture schedule is a problem that belongs to the NP-Hard problem and multi-objective problem because it has several variables that affect the preparation of the schedule and has limitations that must be met. One solution that has been found is using a Genetic Algorithm (GA). GA has been proven to be able to provide a schedule that can meet limitations in scheduling. Besides, it also found a new concept of thought from GA, namely the Fluid Genetic Algorithm (FGA). The most visible difference between FGA and GA is that there is no mutation process in each iteration. FGA has a new stage, namely individual born and new constants, namely global learning rate, individual learning rate, and diversity rate. This concept of thinking was tested in previous studies and found that FGA is superior to GA for the problem of finding the optimum value of a predetermined function, but this function is not included in the multi-objective problem. In this study, the testing and comparison of FGA and GA were conducted for the problem of scheduling lectures at STMIK XYZ. Based on the results obtained, FGA can produce a schedule without any hard constraint violations. FGA can be used to solve multi-objective problems. FGA has a smaller number of generations than GA. However, overall GA is superior in producing schedules without any problems.

A SHIFT REGISTER-BASED SYSTOLIC ARRAY FOR THE UNBOUNDED KNAPSACK PROBLEM

1995 ◽  
Vol 05 (02) ◽  
pp. 251-262 ◽  
Author(s):  
R. ANDONOV ◽  
P. QUINTON ◽  
S. RAJOPADHYE ◽  
D. WILDE
Keyword(s):  
Knapsack Problem ◽  
Systolic Array ◽  
Shift Register ◽  
Hard Problem ◽  
Np Hard ◽  
Parallel Implementations ◽  
Np Hard Problem ◽  
Low Efficiency

We present a shift register-based systolic array for a class of recurrences, with dynamic dependencies called knapsack problem recurrences. All previous arrays or parallel implementations led to either low efficiency or to complicated control. To the best of our knowledge, the proposed design is the first realistic pure systolic and optimal array for this pseudo-polynomial, NP-hard problem. The key feature of the array is that it requires almost no control circuitry.

scholarly journals Genetic Algorithm Based Resource Minimization in Network Code Based Peer-to-Peer Network

2020 ◽  
pp. 2150092
Author(s):  
M. Anandaraj ◽  
K. Selvaraj ◽  
P. Ganeshkumar ◽  
K. Rajkumar ◽  
K. Sriram
Keyword(s):  
Genetic Algorithm ◽  
Minimization Problem ◽  
Dynamic Change ◽  
Network Code ◽  
System Throughput ◽  
Hard Problem ◽  
Np Hard ◽  
Interesting Study ◽  
Np Hard Problem ◽  
Resource Minimization

Block scheduling is difficult to implement in P2P network since there is no central coordinator. This problem can be solved by employing network coding technique which allows intermediate nodes to perform the coding operation instead of store and forward the received data. There is a general assumption in this area of research so far that a target download rate is always attainable at every peer as long as coding operation is performed at all the nodes in the network. An interesting study is made that a maximum download rate can be attained by performing the coding operation at relatively small portion of the network. The problem of finding the minimal set of node to perform the coding operation and links to carry the coded data is called as a network code minimization problem (NCMP). It is proved to be an NP hard problem. It can be solved using genetic algorithm (GA) because GA can be used to solve the diverse NP hard problem. A new NCMP model which considers both minimize the resources needed to perform coding operation and dynamic change in network topology due to disconnection is proposed. Based on this new NCMP model, an effective and novel GA is proposed by implementing problem specific GA operators into the evolutionary process. There is an attempt to implement the different compositions and several options of GA elements which worked well in many other problems and pick the one that works best for this resource minimization problem. Our simulation results prove that the proposed system outperforms the random selection and coding at all possible node mechanisms in terms of both download time and system throughput.

scholarly journals A New Manner of Crossing in the Genetic Algorithm for Resolving Job Shop Problem (JSP)

2020 ◽  
Vol 8 ◽  
pp. 39-43
Author(s):  
Said Bourazza
Keyword(s):  
Genetic Algorithm ◽  
Job Shop ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Respective Probability

The minimization of the makespan of the job shop problem with J jobs and M machines is NP-hard problem. To resolve it we apply a genetic algorithm [1,2]. We use a real coding for the representation of chromosomes. The originality of our variant lies by the choice of two effective crossover operators and one for mutation, As well as their respective probability, determined by numeric simulations on several examples known in the literature. We compare our results on ''OR library'' benchmarks [3] with Adamas and al. [4], Ombuki and al [5] and Yamada and al [6] results.

scholarly journals Bounds of Fractional Metric Dimension and Applications with Grid-Related Networks

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1383
Author(s):  
Ali H. Alkhaldi ◽  
Muhammad Kamran Aslam ◽  
Muhammad Javaid ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Metric Dimension ◽  
Hard Problem ◽  
Np Hard ◽  
Weighted Version ◽  
Sharp Bounds ◽  
Np Hard Problem ◽  
Metric Dimensions

Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.

scholarly journals Offline Algorithms in Low-Frequency Trading

Queue ◽  
2020 ◽  
Vol 18 (6) ◽  
pp. 37-51
Author(s):  
Terence Kelly
Keyword(s):  
Real Time ◽  
Real World ◽  
High Frequency ◽  
Low Frequency ◽  
Combinatorial Auctions ◽  
Hard Problem ◽  
Np Hard ◽  
High Stakes ◽  
Drill Bits ◽  
Np Hard Problem

Expectations run high for software that makes real-world decisions, particularly when money hangs in the balance. This third episode of the Drill Bits column shows how well-designed software can effectively create wealth by optimizing gains from trade in combinatorial auctions. We'll unveil a deep connection between auctions and a classic textbook problem, we'll see that clearing an auction resembles a high-stakes mutant Tetris, we'll learn to stop worrying and love an NP-hard problem that's far from intractable in practice, and we'll contrast the deliberative business of combinatorial auctions with the near-real-time hustle of high-frequency trading. The example software that accompanies this installment of Drill Bits implements two algorithms that clear combinatorial auctions.

scholarly journals A Recursive Formula for the Reliability of a r-Uniform Complete Hypergraph and Its Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Ke Zhang ◽  
Haixing Zhao ◽  
Zhonglin Ye ◽  
Lixin Dong
Keyword(s):  
Recurrence Relations ◽  
Recursive Formula ◽  
Finite Graph ◽  
Hard Problem ◽  
Np Hard ◽  
Spanning Subgraph ◽  
Reliability Polynomial ◽  
Np Hard Problem

The reliability polynomial R(S,p) of a finite graph or hypergraph S=(V,E) gives the probability that the operational edges or hyperedges of S induce a connected spanning subgraph or subhypergraph, respectively, assuming that all (hyper)edges of S fail independently with an identical probability q=1-p. In this paper, we investigate the probability that the hyperedges of a hypergraph with randomly failing hyperedges induce a connected spanning subhypergraph. The computation of the reliability for (hyper)graphs is an NP-hard problem. We provide recurrence relations for the reliability of r-uniform complete hypergraphs with hyperedge failure. Consequently, we determine and calculate the number of connected spanning subhypergraphs with given size in the r-uniform complete hypergraphs.

scholarly journals Metric dimension of metric transform and wreath product

2019 ◽  
Vol 11 (2) ◽  
pp. 418-421
Author(s):  
B.S. Ponomarchuk
Keyword(s):  
Wreath Product ◽  
Metric Space ◽  
Metric Spaces ◽  
Metric Dimension ◽  
Hard Problem ◽  
Np Hard ◽  
Resolving Set ◽  
Np Hard Problem ◽  
Metric Transform ◽  
Empty Subset

Let $(X,d)$ be a metric space. A non-empty subset $A$ of the set $X$ is called resolving set of the metric space $(X,d)$ if for two arbitrary not equal points $u,v$ from $X$ there exists an element $a$ from $A$, such that $d(u,a) \neq d(v,a)$. The smallest of cardinalities of resolving subsets of the set $X$ is called the metric dimension $md(X)$ of the metric space $(X,d)$. In general, finding the metric dimension is an NP-hard problem. In this paper, metric dimension for metric transform and wreath product of metric spaces are provided. It is shown that the metric dimension of an arbitrary metric space is equal to the metric dimension of its metric transform.

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

scholarly journals Randomized heuristic for the maximum clique problem

2020 ◽  
Author(s):  
Shalin Shah
Keyword(s):  
Approximation Algorithm ◽  
Randomized Algorithm ◽  
Maximum Clique ◽  
Constant Factor ◽  
Maximum Clique Problem ◽  
Hard Problem ◽  
Np Hard ◽  
Np Hard Problem ◽  
Java Code ◽  
Clique Problem

<p>A clique in a graph is a set of vertices that are all directly connected</p><p>to each other i.e. a complete sub-graph. A clique of the largest size is</p><p>called a maximum clique. Finding the maximum clique in a graph is an</p><p>NP-hard problem and it cannot be solved by an approximation algorithm</p><p>that returns a solution within a constant factor of the optimum. In this</p><p>work, we present a simple and very fast randomized algorithm for the</p><p>maximum clique problem. We also provide Java code of the algorithm</p><p>in our git repository. Results show that the algorithm is able to find</p><p>reasonably good solutions to some randomly chosen DIMACS benchmark</p><p>graphs. Rather than aiming for optimality, we aim to find good solutions</p><p>very fast.</p>

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