arXiv subjects

Jun He

Publications and source records attributed to Jun He.

At least 325 records · Page 18Linked to original sources

arXiv2014

A Polynomial Time Approximation Scheme for a Single Machine Scheduling Problem Using a Hybrid Evolutionary Algorithm

Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while some others playing the role of random search, have become rather popular for tackling various NP-hard optimization problems. While empirical studies demonstrate that hybrid evolutionary algorithms are frequently successful at finding solutions having fitness sufficiently close to the optimal, many fewer articles address the computational complexity in a mathematically rigorous fashion. This paper is devoted to a mathematically motivated design and analysis of a parameterized family of evolutionary algorithms which provides a polynomial time approximation scheme for one of the well-known NP-hard combinatorial optimization problems, namely the "single machine scheduling problem without precedence constraints". The authors hope that the techniques and ideas developed in this article may be applied in many other situations.

cs.NE↗

arXiv2014

Mixed Strategy May Outperform Pure Strategy: An Initial Study

In pure strategy meta-heuristics, only one search strategy is applied for all time. In mixed strategy meta-heuristics, each time one search strategy is chosen from a strategy pool with a probability and then is applied. An example is classical genetic algorithms, where either a mutation or crossover operator is chosen with a probability each time. The aim of this paper is to compare the performance between mixed strategy and pure strategy meta-heuristic algorithms. First an experimental study is implemented and results demonstrate that mixed strategy evolutionary algorithms may outperform pure strategy evolutionary algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then Complementary Strategy Theorem is rigorously proven for applying mixed strategy at the population level. The theorem asserts that given two meta-heuristic algorithms where one uses pure strategy 1 and another uses pure strategy 2, the condition of pure strategy 2 being complementary to pure strategy 1 is sufficient and necessary if there exists a mixed strategy meta-heuristics derived from these two pure strategies and its expected number of generations to find an optimal solution is no more than that of using pure strategy 1 for any initial population, and less than that of using pure strategy 1 for some initial population.

cs.NE↗

arXiv2014

Combining Drift Analysis and Generalized Schema Theory to Design Efficient Hybrid and/or Mixed Strategy EAs

Hybrid and mixed strategy EAs have become rather popular for tackling various complex and NP-hard optimization problems. While empirical evidence suggests that such algorithms are successful in practice, rather little theoretical support for their success is available, not mentioning a solid mathematical foundation that would provide guidance towards an efficient design of this type of EAs. In the current paper we develop a rigorous mathematical framework that suggests such designs based on generalized schema theory, fitness levels and drift analysis. An example-application for tackling one of the classical NP-hard problems, the "single-machine scheduling problem" is presented.

cs.NE↗

arXiv2014

Pure Strategy or Mixed Strategy?

Mixed strategy EAs aim to integrate several mutation operators into a single algorithm. However few theoretical analysis has been made to answer the question whether and when the performance of mixed strategy EAs is better than that of pure strategy EAs. In theory, the performance of EAs can be measured by asymptotic convergence rate and asymptotic hitting time. In this paper, it is proven that given a mixed strategy (1+1) EAs consisting of several mutation operators, its performance (asymptotic convergence rate and asymptotic hitting time)is not worse than that of the worst pure strategy (1+1) EA using one mutation operator; if these mutation operators are mutually complementary, then it is possible to design a mixed strategy (1+1) EA whose performance is better than that of any pure strategy (1+1) EA using one mutation operator.

cs.NE↗

arXiv2014

A Theoretical Assessment of Solution Quality in Evolutionary Algorithms for the Knapsack Problem

Evolutionary algorithms are well suited for solving the knapsack problem. Some empirical studies claim that evolutionary algorithms can produce good solutions to the 0-1 knapsack problem. Nonetheless, few rigorous investigations address the quality of solutions that evolutionary algorithms may produce for the knapsack problem. The current paper focuses on a theoretical investigation of three types of (N+1) evolutionary algorithms that exploit bitwise mutation, truncation selection, plus different repair methods for the 0-1 knapsack problem. It assesses the solution quality in terms of the approximation ratio. Our work indicates that the solution produced by pure strategy and mixed strategy evolutionary algorithms is arbitrarily bad. Nevertheless, the evolutionary algorithm using helper objectives may produce 1/2-approximation solutions to the 0-1 knapsack problem.

cs.NE↗

arXiv2014

A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm.

cs.NE↗

arXiv2014

A Collaborative Framework for In-network Video Caching in Mobile Networks

Due to explosive growth of online video content in mobile wireless networks, in-network caching is becoming increasingly important to improve the end-user experience and reduce the Internet access cost for mobile network operators. However, caching is a difficult problem due to the very large number of online videos and video requests,limited capacity of caching nodes, and limited bandwidth of in-network links. Existing solutions that rely on static configurations and average request arrival rates are insufficient to handle dynamic request patterns effectively. In this paper, we propose a dynamic collaborative video caching framework to be deployed in mobile networks. We decompose the caching problem into a content placement subproblem and a source-selection subproblem. We then develop SRS (System capacity Reservation Strategy) to solve the content placement subproblem, and LinkShare, an adaptive traffic-aware algorithm to solve the source selection subproblem. Our framework supports congestion avoidance and allows merging multiple requests for the same video into one request. We carry extensive simulations to validate the proposed schemes. Simulation results show that our SRS algorithm achieves performance within 1-3% of the optimal values and LinkShare significantly outperforms existing solutions.

cs.NI↗

arXiv2013

A Unified Markov Chain Approach to Analysing Randomised Search Heuristics

The convergence, convergence rate and expected hitting time play fundamental roles in the analysis of randomised search heuristics. This paper presents a unified Markov chain approach to studying them. Using the approach, the sufficient and necessary conditions of convergence in distribution are established. Then the average convergence rate is introduced to randomised search heuristics and its lower and upper bounds are derived. Finally, novel average drift analysis and backward drift analysis are proposed for bounding the expected hitting time. A computational study is also conducted to investigate the convergence, convergence rate and expected hitting time. The theoretical study belongs to a prior and general study while the computational study belongs to a posterior and case study.

math.OC↗

arXiv2013

Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments

In the current work we introduce a novel estimation of distribution algorithm to tackle a hard combinatorial optimization problem, namely the single-machine scheduling problem, with uncertain delivery times. The majority of the existing research coping with optimization problems in uncertain environment aims at finding a single sufficiently robust solution so that random noise and unpredictable circumstances would have the least possible detrimental effect on the quality of the solution. The measures of robustness are usually based on various kinds of empirically designed averaging techniques. In contrast to the previous work, our algorithm aims at finding a collection of robust schedules that allow for a more informative decision making. The notion of robustness is measured quantitatively in terms of the classical mathematical notion of a norm on a vector space. We provide a theoretical insight into the relationship between the properties of the probability distribution over the uncertain delivery times and the robustness quality of the schedules produced by the algorithm after a polynomial runtime in terms of approximation ratios.

cs.DS↗

arXiv2013

XYZ States

In the past decade, many new charmonium (or charmonium-like) and bottomonium (or bottomonium-like) states were observed experimentally. I will review these XYZ states which do not fit into the quark model spectrum easily.

hep-ph↗

arXiv2013

$Z_c(4025)$ as the hadronic molecule with hidden charm

We have studied the loosely bound $D^*\bar{D}^*$ system. Our results indicate that the recently observed charged charmonium-like structure $Z_c(4025)$ can be an ideal $D^*\bar{D}^*$ molecular state. We have also investigated its pionic, dipionic, and radiative decays. We stress that both the scalar isovector molecular partner $Z_{c0}$ and three isoscalar partners ${\tilde Z}_{c0,c1,c2}$ should also exist if $Z_c(4025)$ is a $D^*\bar{D}^*$ molecular state {in the framework of the one-pion-exchange model}. $Z_{c0}$ can be searched for in the channel $e^+e^-\to Y \to Z_{c0}(4025)\left(ππ\right)_{P-wave}$ where $Y$ can be Y(4260) or any other excited $1^{--}$ charmonium or charmonium-like states such as Y(4360), Y(4660) etc. The isoscalar $D^*\bar{D}^*$ molecular states ${\tilde Z}_{c0,c2}$ with $0^+(0^{++})$ and $0^+(2^{++})$ can be searched for in the three pion decay channel $e^+e^-\to Y \to {\tilde Z}_{c0,c2} \left(3π\right)^{I=0}_{P-wave}$. The isoscalar molecular state ${\tilde Z}_{c1}$ with $0^-(1^{+-})$ can be searched for in the channel ${\tilde Z}_{c1}η$. Experimental discovery of these partner states will firmly establish the molecular picture.

hep-ph↗

arXiv2013

Understanding Y(4274) and X(4320) in the $J/ψϕ$ invariant mass spectrum

In this work we study the structures near 4.3 GeV in the $J/ψϕ$ invariant mass spectra in B meson decay process $B^+\to J/ψϕK^+$ and two photon fusion process $γγ\to J/ψϕ$. The Y(4274) as a $D_sD_{s0}$ $(2317)$ molecular is studied in the Bethe-Salpeter equation approach with quasipotential approximation. The absence of Y(4274) in $γγ\to J/ψϕ$ channel can be well explained by the decay widths of Y(4274) decaying to $γγ$ and $J/ψϕ$. The distribution of mass difference released by CMS collaboration is reproduced by two resonances near 4.3 GeV, Y(4274) and X(4320). The different production mechanism suggests X(4320) observed in the B decay should be the missing $3^3P_1$ charmonium state $χ''_{c1}$ and different from X(4350) observed in two photon fusion which can be assigned as $χ''_{c2}$.

hep-ph↗

arXiv2013

The $γp \to n a^+_2(1320) \to n ρ^0 π^+$ reactions within an effective Lagrangian approach

We investigate the $a_2(1320)$ meson photon production in the $γp \to n a^+_2(1320)$ and $γp \to n ρ^0 π^+$ reactions within the effective Lagrangian method. For $γp \to n a^+_2(1320)$ reaction, by considering the contributions only from the $t-$channel $π^+$ exchange, we get a fairly good description of the current experimental total cross section data. We also studied the $γp \to n ρ^0 π^+$ reaction, which mainly contribute to the $γp \to n π^+ π^+ π^-$ reaction. The latter reaction has measured by the CLAS Collaboration. The total cross sections, invariant mass distribution, and the Dalitz Plot of $γp \to n ρ^0 π^+$ reaction are shown, which can be tested by future experiments.

hep-ph↗

arXiv2013

Iterative Grassmannian Optimization for Robust Image Alignment

Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found application in many areas of computer vision. In image and video processing and face recognition, the opportunity to process massive image databases is emerging as people upload photo and video data online in unprecedented volumes. However, data quality and consistency is not controlled in any way, and the massiveness of the data poses a serious computational challenge. In this paper we present t-GRASTA, or "Transformed GRASTA (Grassmannian Robust Adaptive Subspace Tracking Algorithm)". t-GRASTA iteratively performs incremental gradient descent constrained to the Grassmann manifold of subspaces in order to simultaneously estimate a decomposition of a collection of images into a low-rank subspace, a sparse part of occlusions and foreground objects, and a transformation such as rotation or translation of the image. We show that t-GRASTA is 4 $\times$ faster than state-of-the-art algorithms, has half the memory requirement, and can achieve alignment for face images as well as jittered camera surveillance images.

cs.CV↗

arXiv2013

A Further Generalization of the Finite-Population Geiringer-like Theorem for POMDPs to Allow Recombination Over Arbitrary Set Covers

A popular current research trend deals with expanding the Monte-Carlo tree search sampling methodologies to the environments with uncertainty and incomplete information. Recently a finite population version of Geiringer theorem with nonhomologous recombination has been adopted to the setting of Monte-Carlo tree search to cope with randomness and incomplete information by exploiting the entrinsic similarities within the state space of the problem. The only limitation of the new theorem is that the similarity relation was assumed to be an equivalence relation on the set of states. In the current paper we lift this "curtain of limitation" by allowing the similarity relation to be modeled in terms of an arbitrary set cover of the set of state-action pairs.

cs.AI↗

arXiv2013

Geiringer Theorems: From Population Genetics to Computational Intelligence, Memory Evolutive Systems and Hebbian Learning

The classical Geiringer theorem addresses the limiting frequency of occurrence of various alleles after repeated application of crossover. It has been adopted to the setting of evolutionary algorithms and, a lot more recently, reinforcement learning and Monte-Carlo tree search methodology to cope with a rather challenging question of action evaluation at the chance nodes. The theorem motivates novel dynamic parallel algorithms that are explicitly described in the current paper for the first time. The algorithms involve independent agents traversing a dynamically constructed directed graph that possibly has loops. A rather elegant and profound category-theoretic model of cognition in biological neural networks developed by a well-known French mathematician, professor Andree Ehresmann jointly with a neurosurgeon, Jan Paul Vanbremeersch over the last thirty years provides a hint at the connection between such algorithms and Hebbian learning.

cs.NE↗

arXiv2013

Novel Analysis of Population Scalability in Evolutionary Algorithms

Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of an EA may be evaluated by different measures, such as the average convergence rate to the optimal set per generation or the expected number of generations to encounter an optimal solution for the first time. Population scalability is the performance ratio between a benchmark EA and another EA using identical genetic operators but a larger population size. Although intuitively the performance of an EA may improve if its population size increases, currently there exist only a few case studies for simple fitness functions. This paper aims at providing a general study for discrete optimisation. A novel approach is introduced to analyse population scalability using the fundamental matrix. The following two contributions summarize the major results of the current article. (1) We demonstrate rigorously that for elitist EAs with identical global mutation, using a lager population size always increases the average rate of convergence to the optimal set; and yet, sometimes, the expected number of generations needed to find an optimal solution (measured by either the maximal value or the average value) may increase, rather than decrease. (2) We establish sufficient and/or necessary conditions for the superlinear scalability, that is, when the average convergence rate of a $(μ+μ)$ EA (where $μ\ge2$) is bigger than $μ$ times that of a $(1+1)$ EA.

cs.NE↗

arXiv2012

Does the enhancement observed in $γγ\to D\bar{D}$ contain two $P$-wave higher charmonia?

Solved is a new puzzle raised by the observation of an enhancement structure Z(3930) in $γγ\to D\bar{D}$. If categorizing Z(3930) as $χ_{c2}(2P)$ suggested by Belle and BaBar, we must explain why $χ_{c0}(2P)$ dominantly decaying into $D\bar{D}$ is missing in the $D\bar{D}$ invariant mass spectrum. In this work, we propose that the Z(3930) enhancement structure may contain two $P$-wave higher charmonia {$χ_{c0}(2P)$} and $χ_{c2}(2P)$. We show that this assumption is supported by our analysis of the $D\bar{D}$ invariant mass spectrum and $\cosθ^\ast$ distribution of $γγ\to D\bar{D}$. This observation would not only provide valuable information of two P-wave higher charmonia $χ_{c0}(2P)$ and $χ_{c2}(2P)$, but also serve as the crucial test of our novel proposal to the observed enhancement structure Z(3930), especially at the forthcoming BelleII and the approved SuperB.

hep-ph↗