Unique optimal solution instance and computational complexity of backbone in the graph bi-partitioning problem

2007 ◽  
Vol 52 (20) ◽  
pp. 2871-2875 ◽  
Author(s):  
He Jiang ◽  
XianChao Zhang ◽  
GuoLiang Chen
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.


2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.


2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xinhe Zhang ◽  
Yuehua Zhang ◽  
Chang Liu ◽  
Hanzhong Jia

In this paper, the authors propose three low-complexity detection schemes for spatial modulation (SM) systems based on the modified beam search (MBS) detection. The MBS detector, which splits the search tree into some subtrees, can reduce the computational complexity by decreasing the nodes retained in each layer. However, the MBS detector does not take into account the effect of subtree search order on computational complexity, and it does not consider the effect of layers search order on the bit-error-rate (BER) performance. The ost-MBS detector starts the search from the subtree where the optimal solution is most likely to be located, which can reduce total searches of nodes in the subsequent subtrees. Thus, it can decrease the computational complexity. When the number of the retained nodes is fixed, which nodes are retained is very important. That is, the different search orders of layers have a direct influence on BER. Based on this, we propose the oy-MBS detector. The ost-oy-MBS detector combines the detection order of ost-MBS and oy-MBS together. The algorithm analysis and experimental results show that the proposed detectors outstrip MBS with respect to the BER performance and the computational complexity.


2014 ◽  
Vol 591 ◽  
pp. 172-175
Author(s):  
M. Chandrasekaran ◽  
P. Sriramya ◽  
B. Parvathavarthini ◽  
M. Saravanamanikandan

In modern years, there has been growing importance in the design, analysis and to resolve extremely complex problems. Because of the complexity of problem variants and the difficult nature of the problems they deal with, it is arguably impracticable in the majority time to build appropriate guarantees about the number of fitness evaluations needed for an algorithm to and an optimal solution. In such situations, heuristic algorithms can solve approximate solutions; however suitable time and space complication take part an important role. In present, all recognized algorithms for NP-complete problems are requiring time that's exponential within the problem size. The acknowledged NP-hardness results imply that for several combinatorial optimization problems there are no efficient algorithms that realize a best resolution, or maybe a close to best resolution, on each instance. The study Computational Complexity Analysis of Selective Breeding algorithm involves both an algorithmic issue and a theoretical challenge and the excellence of a heuristic.


2009 ◽  
Vol 13 (1) ◽  
pp. 46-80 ◽  
Author(s):  
Jacek Krawczyk ◽  
Kunhong Kim

Herbert A. Simon, 1978 Economics Nobel Prize laureate, talked about satisficing (his neologism) rather than optimizing as being what economists really need. Indeed, optimization might be an unsuitable solution procedure (in that it suggests a unique “optimal” solution) for problems where many solutions could be satisfactory. We think that looking for an applicable monetary policy is a problem of this kind because there is no unique way in which a central bank can achieve a desired inflation (unemployment, etc.) path. We think that it is viability theory, which is a relatively young area of mathematics, that rigorously captures the essence of satisficing. We aim to use viability analysis to analyze a simple macro policy model and show how some robust adjustment rules can be endogenously obtained.


Author(s):  
Thomas Bläsius ◽  
Philipp Fischbeck ◽  
Tobias Friedrich ◽  
Maximilian Katzmann

AbstractThe computational complexity of the VertexCover problem has been studied extensively. Most notably, it is NP-complete to find an optimal solution and typically NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on many real-world networks the run time to solve VertexCover is way smaller than even the best known FPT-approaches can explain. We link these observations to two properties that are observed in many real-world networks, namely a heterogeneous degree distribution and high clustering. To formalize these properties and explain the observed behavior, we analyze how a branch-and-reduce algorithm performs on hyperbolic random graphs, which have become increasingly popular for modeling real-world networks. In fact, we are able to show that the VertexCover problem on hyperbolic random graphs can be solved in polynomial time, with high probability. The proof relies on interesting structural properties of hyperbolic random graphs. Since these predictions of the model are interesting in their own right, we conducted experiments on real-world networks showing that these properties are also observed in practice.


2020 ◽  
Vol 16 (3) ◽  
pp. 224-231
Author(s):  
Saruti Gupta ◽  
Ashish Goel

Partial transmit sequence (PTS) is a well-known PAPR reduction scheme for the OFDM system. One of the major challenge of this scheme is to find an optimal phase vector using exhaustive search over all the allowed phase factor combinations. This leads to increased search complexity which grows exponentially as the number of sub-blocks is increased. In this paper, chicken swarm optimization (CSO) based PTS system is designed that aims to find an optimal solution in less number of average iterations and therefore results in reduced computational complexity of the system. We have proposed two categories of the algorithm: (i) CSO-PTS system without threshold limit on PAPR (ii) CSO-PTS system with threshold limit on PAPR. Both the schemes offer effective trade-offs between the computationalcomplexity and the PAPR reduction capability of the system. Simulation results confirm that our proposed schemes perform well in terms of low computational complexity, lesser number of average iterations and improved PAPR reduction capability of the OFDM signal without any loss in BER performance of the system.


Sensors ◽  
2021 ◽  
Vol 21 (24) ◽  
pp. 8449
Author(s):  
Zofia Długosz ◽  
Michał Rajewski ◽  
Rafał Długosz ◽  
Tomasz Talaśka

In this work, we propose a novel metaheuristic algorithm that evolved from a conventional particle swarm optimization (PSO) algorithm for application in miniaturized devices and systems that require low energy consumption. The modifications allowed us to substantially reduce the computational complexity of the PSO algorithm, translating to reduced energy consumption in hardware implementation. This is a paramount feature in the devices used, for example, in wireless sensor networks (WSNs) or wireless body area sensors (WBANs), in which particular devices have limited access to a power source. Various swarm algorithms are widely used in solving problems that require searching for an optimal solution, with simultaneous occurrence of a different number of sub-optimal solutions. This makes the hardware implementation worthy of consideration. However, hardware implementation of the conventional PSO algorithm is challenging task. One of the issues is an efficient implementation of the randomization function. In this work, we propose novel methods to work around this problem. In the proposed approach, we replaced the block responsible for generating random values using deterministic methods, which differentiate the trajectories of particular particles in the swarm. Comprehensive investigations in the software model of the modified algorithm have shown that its performance is comparable with or even surpasses the conventional PSO algorithm in a multitude of scenarios. The proposed algorithm was tested with numerous fitness functions to verify its flexibility and adaptiveness to different problems. The paper also presents the hardware implementation of the selected blocks that modify the algorithm. In particular, we focused on reducing the hardware complexity, achieving high-speed operation, while reducing energy consumption.


2021 ◽  
Vol 35 (6) ◽  
pp. 802-813
Author(s):  
Megan Cook ◽  
Frédéric Bouchette ◽  
Bijan Mohammadi ◽  
Léa Sprunck ◽  
Nicolas Fraysse

AbstractOptimization theory is applied to a coastal engineering problem that is the design of a port. This approach was applied to the redesign of La Turballe Port in order to increase the exploitable surface area and simultaneously reduce the occurrence of long waves within the port. Having defined the cost function as a weighted function of wave amplitude and with the chosen parameterization of the port, results show that an extended jetty and a widened mole yield a unique optimal solution. This work demonstrates that numerical optimization may be quick and efficient in the identification of port solutions consistent with classic engineering even in the context of complex problems.


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