752 publications from this institution
The theoretical analyses of any algorithm and its iteration behavior require rigorous mathematics. This chapter introduces some foundations for algorithm analysis, including norms, eigenvalues, convergence, computational complexity, and convexity.
Statistics is the mathematics of data collection and interpretation, and the analysis and characterization of numerical data by inference from sampling. Statistical methods involve reduction of data, estimates and significance tests, relationship between two or more variables by analysis of variance and the test of hypotheses. This chapter introduces all the fundamentals of statistical methods.
There are many different nature-inspired algorithms in the literature, and almost all such algorithms have algorithm-dependent parameters that need to be tuned. The proper setting and parameter tuning should be carried out to maximize the performance of the algorithm under consideration. This work is the extension of the recent work on parameter tuning by Joy et al. (2024) presented at the International Conference on Computational Science (ICCS 2024), and the Firefly Algorithm (FA) is tuned using three different methods: the Monte Carlo method, the Quasi-Monte Carlo method and the Latin Hypercube Sampling. The FA with the tuned parameters is then used to solve a set of six different optimization problems, and the possible effect of parameter setting on the quality of the optimal solutions is analyzed. Rigorous statistical hypothesis tests have been carried out, including Student’s t-tests, F-tests, non-parametric Friedman tests and ANOVA. Results show that the performance of the FA is not influenced by the tuning methods used. In addition, the tuned parameter values are largely independent of the tuning methods used. This indicates that the FA can be flexible and equally effective in solving optimization problems, and any of the three tuning methods can be used to tune its parameters effectively.
Since the development of cuckoo search (CS) by Yang and Deb in 2009, CS has been applied in a diverse range of applications. This paper first outlines the key features of the algorithm and its variants, and then briefly summarizes the state-of-the-art developments in many applications. The opportunities for further research are also identified.
and science.In numerous fields, including mechanical engineering, civil engineering, electrical engineering, structural and aerospace engineering, automotive industry, oil industry, chemical engineering, ocean science and climate research to name just a few, simulation plays a critical role not only for verification purposes, but, more importantly in the design process itself.The complexity of structures and systems makes it analytically intractable, and it is thus extremely time-consuming and challenging to carry out any realistic design tasks, and in many cases, it is almost impossible to achieve any sensible design solutions under stringent constraints.These challenging tasks can be to optimally adjust the geometry and/or material parameters so that the system meets given performance requirements, or to calibrate the model parameters to make it fit given measurements, or to generate the optimal paths/routes for scheduling and planning tasks.In most cases, the interactions can be highly complex and multifold, and it is not easy or possible to isolate the processes of interest in the simplest, solvable form.For example, in the design of an electronic device, it is not just the isolated device to be designed that needs to be considered but also its -sometimes complex -interactions with the environment that affect the device's performance.On the other hand, using accurate, realistic simulations allows the engineers to avoid costly prototyping and to realize the design closure with numerical models rather than through physical system measurements and prototype re-building.Furthermore, accurate simulations make it possible to analyze phenomena that could not be captured using simplistic theoretical models or too expensive or too time-consuming to be investigated through physical measurements.While high-fidelity numerical models can be very accurate, they tend to be computationally expensive.Simulation times of several hours, days, or weeks are not uncommon.In many cases, it may be a highly challenging task to just set up the model that takes into account all main, relevant system components and their interactions.One of the consequences is that a direct use of high-fidelity simulations in the optimization process may be prohibitive.The presence of massive computing resources is not always translated into computational speedup in practice, which is due to a growing demand for simulation
Modern metaheuristic algorithms are in general suited for global optimization. This paper combines the recently developed eagle strategy algorithm with differential evolution. The new algorithm, denoted as the ES–DE, is implemented by interfacing SAP2000 structural analysis code and MATLAB mathematical software. The performance of the ES–DE is evaluated by solving four benchmark problems where the objective is to minimize the weight of steel frames. The optimized designs obtained by the proposed algorithm are better than those found by the standard differential evolution algorithm and also very competitive with literature. The overall convergence behavior is significantly enhanced by the hybrid optimization strategy.
No abstract is provided for this article.
It is a great pleasure to welcome you to the 27th International Conference on CADCAM, Robotics and Factories of the Future, sponsored by the International Society for Productivity Enhancement, Middlesex University, Festo Limited GB, National Instruments UK & Ireland, the Sector Skills Council for Science, Engineering and Manufacturing Technologies and our proceedings publisher Institute of Physics Publications.
Fourier series and fast Fourier transforms have important applications in signal and image processing. This chapter first introduces Fourier series and then Fourier transforms.
No abstract is provided for this article.
Test functions are important to validate and compare the performance of optimization algorithms. There have been many test or benchmark functions reported in the literature; however, there is no standard list or set of benchmark functions. Ideally, test functions should have diverse properties so that can be truly useful to test new algorithms in an unbiased way. For this purpose, we have reviewed and compiled a rich set of 175 benchmark functions for unconstrained optimization problems with diverse properties in terms of modality, separability, and valley landscape. This is by far the most complete set of functions so far in the literature, and tt can be expected this complete set of functions can be used for validation of new optimization in the future.
Particle swarm optimization (PSO) was developed by Kennedy and Eberhart in 1995 based on the swarm behavior, such as fish and bird schooling in nature, which has generated much interest in the ever-expanding area of swarm intelligence. There are over two dozen PSO variants, and hybridization with other algorithms has also been investigated. This chapter reviews the basic ideas of particle swarm optimization, some common variants, and convergence properties.
No abstract is provided for this article.
In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure $p_e$ and porosity $\phi$, that is $p_e=p_e(\phi)$. The compaction law is essentially a poroelastic one. However, viscous compaction due to pressure solution becomes important at larger depths and causes this relationship to become more akin to a viscous rheology. A generalised viscoelastic compaction model of Maxwell type is formulated, and different styles of nonlinear behaviour are asymptotically analysed and compared in this paper.
Most global optimization problems are nonlinear and thus difficult to solve, and they become even more challenging when uncertainties are present in objective functions and constraints. This paper provides a new two-stage hybrid search method, called Eagle Strategy, for stochastic optimization. This strategy intends to combine the random search using L\'evy walk with the firefly algorithm in an iterative manner. Numerical studies and results suggest that the proposed Eagle Strategy is very efficient for stochastic optimization. Finally practical implications and potential topics for further research will be discussed.
