752 publications from this institution
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Random walks and other stochastic components are an intrinsic part of nature-inspired metaheursitic algorithms. They are often used as random numbers and randomization techniques in metaheuristic algorithms, and the efficiency of a metaheuristic algorithm may implicitly depend on the appropriate use of such randomization. In this chapter, we first introduce the fundamental ideas of random variables and theory of random walks and Lévy flights. Then, we discuss the relationship between optimization, random walks and Markov chains, followed by the analysis of step sizes and efficiency of an algorithm using the framework of Markov chain theory.
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Real-world optimization problems often have multiple and potentially conflicting objectives. The algorithms that work for single objective optimization require some modifications before they can be used to solve multi-objective optimization problems. In addition, new concepts such as Pareto optimality need to be introduced. This chapter introduces the commonly used methods to deal with multi-objective optimization.
This chapter introduces the basic methods for data fitting, focusing on the regression-based curve-fitting, methods of least squares, and various regularization methods. Information criteria are also introduced.
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For any metaheuristic algorithm, it is important to balance exploration and exploitation because the interaction of these two key components can significantly affect the efficiency. However, how to achieve a fine balance is still an open problem. We attempt to explore this challenging issue by using eagle strategy in combination with the recently developed flower algorithm. Our results on test benchmarks suggest that more effort should focus on explorative search for multimodal problems.
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Mathematical models of compaction in sedimentary basins typically assume a relationship between effective pressure p e and porosity ϕ, which is of a non‐linear type; that is, p e = p e (ϕ). However, at depths greater than a kilometer, pressure solution becomes important and this relationship approaches a viscous one. We derive a mathematical model for viscous compaction in sedimentary basins and show how the model suggests different styles of behavior in the limits of slow and fast compaction.
Optimization is often subject to complex constraints. Constraint-handling techniques form an important area of problem solving in optimization. There many constraint-handling methods that allow the algorithms to solve unconstrained optimization problems to solve constrained optimization problems efficiently. This chapter provides a basic overview of the common techniques used with nature-inspired algorithms.
Modern metaheuristic algorithms such as particle swarm optimization and cuckoo search start to demonstrate their power in dealing with tough optimization problems and even NP-hard problems. This book reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms for global optimization, including ant and bee algorithms, bat algorithm, cuckoo search, differential evolution, firefly algorithm, genetic algorithms, harmony search, particle swarm optimization, simulated annealing and support vector machines. In this revised edition, we also include how to deal with nonlinear constraints. Worked examples with implementation have been used to show how each algorithm works. This book is thus an ideal textbook for an undergraduate and/or graduate course as well as for self study. As some of the algorithms such as the cuckoo search and firefly algorithms are at the forefront of current research, this book can also serve as a reference for researchers.
We present a model for the study of the effect of rheological hysteresis on compaction in sedimentary basins, when surface loading and unloading occurs. When compaction is slow (sedimentation rate is large and/or permeability is small), the hysteresis has little effect on the basal compaction layer, but in the more realistic case where compaction is fast (i.e., sedimentation is slow and/or permeability is large), surface unloading leads to downward propagation of a decompaction front, across which the vertical porosity gradient jumps, while subsequent surface reloading leads to downward propagation of a discontinuity in porosity, despite the fact that the porosity is governed by a diffusive equation of Richards type.
All nature-inspired algorithms have algorithm-dependent parameters. Tuning such parameters can be a challenging task. This chapter introduces the objective of parameter tuning and highlights the challenges in this area.
