752 publications from this institution
This chapter introduces the foundations for computational linear algebra, starting with vectors and dot product. Then the matrix inverse and systems of linear equations are introduced. The eigenvalues and eigenvectors of a symmetric matrix are calculated, and their relationship to the definiteness of the corresponding matrix is also explained. Iterative methods for solving linear systems are also given with a worked example.
Finding an appropriate set of features from data of high dimensionality for building an accurate classification model is a well-known NP-hard computational problem. Unfortunately in data mining, some big data are not only big in volume but they are described by a large number of features. Many feature subset selection algorithms have been proposed in the past, they are nevertheless far from perfect. Since using brute-force in exhaustively trying every possible combination of features takes seemingly forever, stochastic optimization may be a solution. In this paper, we propose a new feature selection algorithm for finding an optimal feature set by using metaheuristic, called Swarm Search. The advantage of Swarm Search is its flexibility in integrating any classifier as its fitness function, and installing in any metaheuristic algorithm for facilitating heuristic search. Simulation experiments are carried out by testing the Swarm Search over a high-dimensional dataset, with different classification algorithms and various metaheuristic algorithms. Swarm search is observed to achieve satisfactory results.
No abstract is provided for this article.
This chapter focuses on the fundamental idea of the finite volume method and the property of finite volumes. Basic finite-volume schemes for one-dimensional heat conduction equation and two-dimensional Laplace equation are introduced. Criteria for numerical stability are derived.
Based on Universal Mobile Telecommunications System (UMTS) wideband code division multiple access (WCDMA) technology, the mobile user objective system (MUOS) provides a wide range of wireless telecommunications services to the war fighter over geosynchronous satellites. As MUOS is a multiple beam system, it is of paramount importance for the user entry (UE) to select the best beam, which in turn requires accurate transmit power from the satellite. To minimize the satellite path gain uncertainty from the base station to the UE, the enhanced gain variation reduction (EGVR) algorithm is proposed. Implemented on the basis of the measurements of the received signal code power (RSCP) of the pilot channel from the UE and the measurements of the received signal code power at the terrestrial base station, the EGVR process generates the transmission power estimate and integrates it into the overall gain adjust system to keep the transmission power levels as desired. The features of the algorithm include the weighted gain adjusts generated from the estimation error, appropriate timers to control the measurement flow, and differential measurements to eliminate the common errors between satellite beams. The preliminary study shows that the EGVR can reduce the power uncertainty from 2.4 dB to 0.4 dB, in addition to reducing any differential errors encountered. With the blending of the telemetry feedback into the algorithm, it can make the transmit power uncertainty even smaller.
The pressure vessel design problem is a well-known design benchmark for validating bio-inspired optimization algorithms. However, its global optimality is not clear and there has been no mathematical proof put forward. In this paper, a detailed mathematical analysis of this problem is provided that proves that 6059.714335048436 is the global minimum. The Lagrange multiplier method is also used as an alternative proof and this method is extended to find the global optimum of a cantilever beam design problem.
No abstract is provided for this article.
No abstract is provided for this article.
The increasing popularity of metaheuristic algorithms has attracted a great deal of attention in algorithm analysis and performance evaluations. No-free-lunch theorems are of both theoretical and practical importance, while many important studies on convergence analysis of various metaheuristic algorithms have proven to be fruitful. This paper discusses the recent results on no-free-lunch theorems and algorithm convergence, as well as their important implications for algorithm development in practice. Free lunches may exist for certain types of problem. In addition, we will highlight some open problems for further research.
Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.
Nowadays, many stochastic metaheuristics have been developed to solve various optimisation problems. The primary characteristics of these heuristics often involve the use of randomness in their search process. Essentially, randomness is useful when determining the next point in the search space and therefore has a crucial impact when exploring new solutions. In this paper, an extensive comparison is made between various probability distributions that can be used for randomising the swarm intelligence algorithms, e.g., uniform, Gaussian, Lévy flights, chaotic maps, and the random sampling in turbulent fractal cloud. These randomisation methods were incorporated into the bat algorithm that is one of the newest member of this domain. In line with this, various variants of bat algorithms randomised with different randomisation methods have been developed and extensive experiments were conducted on a well–known set of 24 BBOB benchmark functions. In addition, the results of randomised bat algorithms were compared with the results of the other well–known algorithms, including the firefly algorithm, differential evolution and artificial bee colony algorithms. The results of these experiments show that the efficiencies of the distributions used during the tests depend on the problem to be solved as well as on the algorithm used.
This paper studies a non-convex power minimization problem for reconfigurable-intelligent-surfaces-aided communication systems whose constraints are multivariate functions of two independent optimization variables, i.e., active and passive beamforming vectors. A widely adopted alternative optimization (AO) approach approximates the originally non-convex problem by two convex sub-optimization problems where each sub-optimization problem deals with one variable considering the other variable as a constant. The solution for the original problem is obtained by iteratively solving these sub-optimization problems. Although the AO approach converts the original NP-hard optimization problem to two convex sub-problems, the solutions attained by this method may not be the global optimal solution due to the approximation process as well as the inherent non-convexity of the original problem. To overcome the issue, this paper adopts a nature-inspired optimization approach and introduces a novel Firefly algorithm (FA) to simultaneously solve for two independent optimization variables of the originally non-convex optimization problem. Computational complexity analyses are provided for the proposed FA and the AO approaches. Simulation results reveal that the proposed FA approach prevails its AO counterpart in obtaining a better solution for the understudied optimization problem with the same order of computational complexity.
Many metaheuristic algorithms are nature-inspired, and most are population-based. Particle swarm optimization is a good example as an efficient metaheuristic algorithm. Inspired by PSO, many new algorithms have been developed in recent years. For example, firefly algorithm was inspired by the flashing behaviour of fireflies. In this chapter, the authors analyze the standard firefly algorithm and study the chaos-enhanced firefly algorithm with automatic parameter tuning. They first compare the performance of these algorithms and then use them to solve a benchmark design problem in engineering. Results obtained by other methods are compared and analyzed. The authors also discuss some important topics for further research.
A mathematical model for poro-visco-plastic compaction and pressure solution in porous sediments has been formulated using the Voigt-type rheological constitutive relation as derived from experimental data. The governing equations reduce to a nonlinear hyperbolic heat conduction equation in the case of slow deformation where permeability is relatively high and the pore fluid pressure is nearly hydrostatic, while travelling wave exists in the opposite limit where over-pressuring occurs and the pore fluid pressure is almost quasi-lithostatic. Full numerical simulation using a finite element method agree well with the approximate analytical solutions.
The testability of equipment has become the key factor affecting equipment availability, and detracts from readiness and mission success. To overcome the current problems associated with the analysis of equipment testability, such as non-comprehensive failure mode coverage, low fault detection rate, and low fault location accuracy, this paper presents a system testability modeling and analysis method based on a summary of the results of device level failure mode effect and criticality analysis (FMECA), which is developed according to the failure data of components and a hardware impact analysis. In particular, we present a mathematical multi-signal model, quantitative methods and mathematical models of system testability, and the implementation processes of system testability modeling. The proposed method allows the failure modes of a module to be obtained accurately and comprehensively. By functioning at the device level, the method provides good fault location accuracy, and improves the authenticity of system testability analysis results. Finally, the testability of an actual electronic system is conducted using CARMES, which is a widely used reliability engineering software. The results verify the effectiveness and authenticity of the presented method, which can also provide a reference for the testability modeling and analysis of follow-up system design.
